ch1: [ { q: “Which of the following is the best example of a categorical variable?”, options: [ “The time required to finish a marathon”, “The exact height of an adult in centimetres”, “The country in which a person was born”, “The total balance in a personal savings account”, “The road distance between two capital cities” ], answer: 2, explanation: “A categorical variable takes a fixed number of distinct categories (like countries), whereas the other options are continuous variables, which can take any value within a range.” }, { q: “A researcher wants to study the opinions of all residents in a large town. Since they can’t ask everyone, they select a smaller group of 200 residents to survey. What does this group of 200 represent?”, options: [ “A population”, “A census”, “The outliers”, “A continuous variable”, “A sample” ], answer: 4, explanation: “The sample is a subset of the population from whom data is actually collected. The population is the wider group the researcher is interested in (all residents).” }, { q: “Why might a researcher add ‘jitter’ to a strip chart?”, options: [ “To correct accidental transcription and data-entry errors”, “To reveal overlapping data points that share identical values”, “To improve visual appeal through varied colour schemes”, “To rescale the vertical axis to compress extreme ranges”, “To filter out unusual observations from the active dataset” ], answer: 1, explanation: “Jitter adds a small amount of random displacement to overlapping points, allowing the viewer to distinguish individual data points that would otherwise be hidden on top of one another.” }, { q: “Which of the following best describes a continuous variable?”, options: [ “A variable restricted to whole-number counts (e.g., 1, 2, 3)”, “A variable defined by a fixed list of qualitative labels”, “A variable representing mutually exclusive unordered categories”, “A variable splitting observations into binary groups (e.g., Yes/No)”, “A variable taking any numerical value along an unbroken scale” ], answer: 4, explanation: “Continuous variables (such as height or time) can take infinitely many values within a range, whereas categorical variables have distinct categories.” }, { q: “What is an outlier?”, options: [ “An observation that sits unusually far from the main data cluster”, “The single most frequently occurring measurement in a distribution”, “A data point located at the exact arithmetic centre of a sample”, “A respondent who failed to complete an assigned survey questionnaire”, “The underlying characteristic currently being quantified in a study” ], answer: 0, explanation: “An outlier is an observation that stands out because it’s unusual or distant from the main cluster of data.” }, { q: “If a researcher finds a data point for an adult’s height recorded as ‘16 cm’, what is the best initial step in data cleaning?”, options: [ “Delete the suspicious observation immediately from the working dataset”, “Assume the participant was a child and retain the score unaltered”, “Replace the recorded value with the overall sample average”, “Check whether the score represents a transcription or data-entry typo”, “Proceed with the planned statistical analyses without adjusting the value” ], answer: 3, explanation: “While 16 cm is impossible for an adult, automatically deleting or changing it is risky. The best first step is to check for a typo or transcription error, to see if the data can be corrected.” }, { q: “What is listwise deletion, in the context of missing data?”, options: [ “Removing an entire variable column across all participants”, “Excluding a participant entirely if they lack data on any variable”, “Imputing missing values using the mean of observed responses”, “Omitting a missing score only during that specific computation”, “Collecting replacement observations to fill incomplete records” ], answer: 1, explanation: “Listwise deletion involves removing a participant completely from the analysis if they have even one missing data point. This can reduce sample size and potentially introduce bias.” }, { q: “If you stand outside a basketball club to sample people for a study on average human height, what is the likely result?”, options: [ “The sample will represent the broader general population accurately”, “The sample will produce categorical rather than continuous data”, “The sample will be systematically skewed toward shorter individuals”, “The sample will be systematically biased toward taller individuals”, “The sample will fail to yield any usable numerical observations” ], answer: 3, explanation: “Basketball players tend to be taller than the average person. Sampling only from this specific location introduces bias, because the sample does not accurately reflect the wider population.” }, { q: “Height can change slightly during the day for a single individual. What is this type of variation called?”, options: [ “Within-person variation”, “Between-person variation”, “Categorical variation”, “Measurement sampling variation”, “Population distribution variation” ], answer: 0, explanation: “Within-person variation refers to changes happening to the same person (like shrinking slightly during the day), whereas between-person variation refers to differences between different people.” }, { q: “What happens visually when you zoom in on a strip chart by changing the axis scale (e.g., starting at 150 cm rather than 0 cm)?”, options: [ “The individual data points collapse together”, “The data points disappear completely from view”, “The data points spread apart, making differences clearer”, “The continuous measurements become categorical bins”, “The outlying scores are automatically trimmed away” ], answer: 2, explanation: “Adjusting the scale to remove empty space allows the data points to fill more of the chart, making it easier to distinguish separate points and see the spread, though it is important to read the axis labels to understand the true context.” } ], ch2: [ { q: “Which of the following best describes the median of a data set?”, options: [ “The value occurring with the greatest overall frequency”, “The difference between the highest and lowest scores”, “The sum of all values divided by the total count”, “The middle value when observations are sorted in order”, “The mean distance of all observations from the center” ], answer: 3, explanation: “The median is the middle value. If you line up all the data points from smallest to largest, the median is the value exactly in the middle.” }, { q: “Which of the following best describes the process of finding the mean of a data set of people’s heights?”, options: [ “Redistributing the total height equally across all individuals”, “Identifying the height score that occurs most frequently”, “Recording the measurement corresponding to the tallest person”, “Calculating the middle boundary of the observed numerical range”, “Subtracting the minimum recorded height from the maximum height” ], answer: 0, explanation: “The mean involves taking the total height of everyone in the group and redistributing it, so everyone has exactly the same height.” }, { q: “If you were to draw lines representing the deviations of every person’s height from the mean height, which of the following would be true about those lines?”, options: [ “All deviation lines would have identical lengths regardless of position”, “Lines above the mean would be systematically longer than lines below it”, “Lines below the mean would be systematically longer than lines above it”, “The total length above the mean would equal the total length below it”, “No lines would exist because all observations match the mean exactly” ], answer: 3, explanation: “The mean acts as a balance point. The sum of the deviations for values above the mean exactly cancels out the sum of the deviations for values below the mean.” }, { q: “In a perfectly symmetrical data set (one with no skew), how do the mean and median typically relate to each other?”, options: [ “The mean is noticeably higher than the median”, “The median is noticeably higher than the mean”, “The mean is always exactly double the median”, “The mean and median cannot be meaningfully compared”, “The mean and median are approximately the same” ], answer: 4, explanation: “In a symmetrical distribution, the data is balanced evenly on both sides. Therefore, the ‘middle’ value (median) and the ‘balance point’ (mean) will be in roughly the same place.” }, { q: “What is likely to happen to the mean and median in a skewed distribution in which there are a few very tall people but mostly shorter people?”, options: [ “The mean will remain exactly identical to the median”, “The median will be pulled farther toward the tall end than the mean”, “The mean will be pulled farther toward the tall end than the median”, “Both the mean and median will drop substantially toward zero”, “The presence of positive skew will have no effect on either average” ], answer: 2, explanation: “The mean takes into account the value of every data point. Therefore, extreme values will pull the mean towards them, while the median is less affected.” }, { q: “Which descriptive statistic focuses only on the most extreme values (the highest and the lowest) to describe spread?”, options: [ “Standard Deviation”, “Variance”, “Range”, “Arithmetic Mean”, “Sample Median” ], answer: 2, explanation: “The range is the difference between the maximum and minimum values in the data set. It ignores how the rest of the data is distributed between these two points.” }, { q: “How is variance defined in this chapter?”, options: [ “The average distance between the sample median and mean”, “The difference between the maximum and minimum observed values”, “The square root of the estimated standard deviation”, “The total sum of all individual scores divided by two”, “The mean squared deviation of observations from the mean” ], answer: 4, explanation: “To find the variance, you calculate the deviation of each person from the mean, square those deviations, and then find the mean of those squared values.” }, { q: “Why is the standard deviation often preferred over the variance for describing spread?”, options: [ “It is expressed in the original units rather than squared units”, “It is computationally much simpler to evaluate by hand”, “It is mathematically guaranteed to always yield a smaller number”, “It calculates dispersion without referencing the sample mean”, “It remains completely unaffected by the presence of extreme outliers” ], answer: 0, explanation: “Variance is measured in squared units. The standard deviation is the square root of the variance, bringing the measure back to the original units (like centimetres).” }, { q: “In the book’s visual explanation, if the variance is represented by the area of a square, what represents the standard deviation?”, options: [ “The perimeter around the exterior of the square”, “The length of one individual side of the square”, “The straight diagonal distance crossing the square”, “The total count of squares drawn in the diagram”, “The coordinate locating the center of the square” ], answer: 1, explanation: “Variance is a value in squared units (an area). Since the standard deviation is the square root of the variance, it corresponds geometrically to the length of one side of that variance square.” }, { q: “Two data sets have the same mean height of 170 cm. Data Set A has a standard deviation of 2 cm. Data Set B has a standard deviation of 10 cm. What does this tell you?”, options: [ “Individuals in Data Set A are generally taller than those in Data Set B”, “The heights in Data Set B are more spread out than in Data Set A”, “Individuals in Data Set B are generally taller than those in Data Set A”, “The heights in Data Set A are more spread out than in Data Set B”, “Data Set B necessarily contains more participants than Data Set A” ], answer: 1, explanation: “A larger standard deviation indicates that the data points are, on average, further away from the mean. Therefore, Data Set B is more varied (spread out).” } ], ch3: [ { q: “What is the general shape of a normal distribution curve?”, options: [ “It is positively skewed with an extended right tail”, “It has two distinct peaks, making it bimodal”, “It is a uniform straight horizontal line”, “It is perfectly symmetrical with a bell shape”, “It has sharply truncated tails on both sides” ], answer: 3, explanation: “The normal distribution is often called a ‘bell curve’ because it is symmetrical, with a peak in the middle and identical tails tapering off on either side.” }, { q: “In a normal distribution, what is true about the mean, median, and mode?”, options: [ “The mean is always noticeably larger than the median”, “The mode is always noticeably smaller than the mean”, “The median is zero, but the mean is always one hundred”, “They are all distinct values spread across the distribution”, “They are all equal to each other at the central peak” ], answer: 4, explanation: “Because the normal distribution is perfectly symmetrical, the balance point (mean), middle value (median), and peak (mode) all fall at the exact same location in the centre.” }, { q: “What does the ‘peak’ or ‘bulge’ of a normal distribution curve represent?”, options: [ “The mode (the most common value)”, “The standard deviation of the scores”, “The overall range of the observations”, “The point containing extreme outliers”, “The least frequently occurring score” ], answer: 0, explanation: “The highest point of the curve shows where the data points are most densely concentrated, corresponding to the mode.” }, { q: “How can you obtain any normal distribution curve from the standard normal distribution?”, options: [ “By inserting additional raw data points into the sample”, “By modifying the underlying probability equation to be bimodal”, “By sliding it (adjusting mean) and scaling it (adjusting SD)”, “By rotating the probability density curve ninety degrees”, “By trimming away the extreme upper and lower tails entirely” ], answer: 2, explanation: “All normal curves share the same fundamental shape. You can create any specific normal curve by shifting (sliding) and scaling (stretching/squashing).” }, { q: “What are the mean and standard deviation of the standard normal distribution?”, options: [ “Mean = 100, Standard Deviation = 10”, “Mean = 1, Standard Deviation = 0”, “Mean = 0, Standard Deviation = 1”, “Mean = 50, Standard Deviation = 5”, “Mean = 10, Standard Deviation = 2” ], answer: 2, explanation: “The standard normal distribution is the simplest normal curve, defined as having a mean of 0 and a standard deviation of 1.” }, { q: “Approximately what percentage of data points lie within one standard deviation of the mean in a normal distribution?”, options: [“50%”, “68%”, “95%”, “99%”, “100%”], answer: 1, explanation: “In any normal distribution, roughly 68% of the data falls in the range between one standard deviation below the mean and one standard deviation above it.” }, { q: “Approximately what percentage of data points lie within two standard deviations of the mean in a normal distribution?”, options: [“50%”, “68%”, “100%”, “95%”, “99%”], answer: 3, explanation: “Extending the range to two standard deviations on either side of the mean captures approximately 95% of all data points.” }, { q: “What is a z score?”, options: [ “The total count of observations contained in a sample”, “A numerical measure of the skewness in a distribution”, “The percentage of measurement error in an estimate”, “The magnitude of the population standard deviation”, “The number of standard deviations a value is from the mean” ], answer: 4, explanation: “A z score standardises a value by expressing it in terms of how many standard deviations it is away from the mean.” }, { q: “What are quantiles?”, options: [ “Boundaries that split data into equal-sized groups”, “The total number of respondents completing a survey”, “The extreme scores located at the tails of a curve”, “Alternative terms denoting the sample mean and mode”, “Systematic errors introduced during data collection” ], answer: 0, explanation: “Quantiles are cut-points that divide the range of a probability distribution into continuous intervals with equal probabilities.” }, { q: “In a box plot (or box and whisker plot), what does the box itself typically represent?”, options: [ “The full range spanned from lowest to highest score”, “The middle 50% of data (the interquartile range)”, “The individual data points flagged as extreme outliers”, “The interval defining the sample mean and standard error”, “The total proportion of participants in each condition” ], answer: 1, explanation: “The central box spans from the lower quartile (25th percentile) to the upper quartile (75th percentile), covering the middle 50% of the data.” } ],

ch4: [ { q: “What is the primary goal of inferential statistics?”, options: [ “To describe sample characteristics using numerical summaries and charts”, “To eliminate random measurement error and outliers from the dataset”, “To calculate the exact arithmetic parameters of the collected scores”, “To infer broader population characteristics using data from a sample”, “To guarantee that sample observations are distributed with zero bias” ], answer: 3, explanation: “Inferential statistics involves taking data from a sample and generalising properties about the larger population of interest.” }, { q: “In the context of hypothesis testing, what is a null hypothesis?”, options: [ “A baseline claim positing no true effect, difference, or relationship”, “A directional claim that the researcher expects to substantiate”, “A mathematical model proven definitively false prior to testing”, “A statement that the selected sample size is statistically inadequate”, “An assumption that missing values occurred entirely at random” ], answer: 0, explanation: “The null hypothesis represents the baseline assumption of no effect or no difference, which the researcher attempts to reject.” }, { q: “What does a p value represent?”, options: [ “The probability that the stated null hypothesis is factually true in reality”, “The probability that the proposed alternative hypothesis reflects the true population state”, “The probability that sample discrepancies resulted entirely from researcher data-entry errors”, “The probability of data as extreme as observed, assuming the null holds”, “The probability that calculated inferential test metrics are free of sampling noise” ], answer: 3, explanation: “The p value quantifies how surprising the data would be under the assumption that the null hypothesis is correct.” }, { q: “If a researcher sets a significance level (alpha level) of 5%, what are they deciding?”, options: [ “To target an overall statistical power threshold of exactly ninety-five percent”, “To tolerate an upper limit of five percent for making a false-negative decision”, “To reject the null hypothesis whenever the calculated p value is below 0.05”, “To recruit at least five percent of the target population into the sample”, “To ensure that sample estimates deviate by no more than five percent” ], answer: 2, explanation: “The significance level is the decision threshold: if the calculated p value falls below this level, the null hypothesis is rejected.” }, { q: “What is a Type 1 error?”, options: [ “Failing to reject the null hypothesis when it is actually false”, “Rejecting the null hypothesis when it is actually true”, “Underestimating the true standard deviation of the population”, “Selecting an unrepresentative sample from the target population”, “Miscalculating the degrees of freedom in an inferential test” ], answer: 1, explanation: “A Type 1 error occurs when you conclude there is an effect when in reality there is not (a false positive).” }, { q: “What is a Type 2 error?”, options: [ “Rejecting the null hypothesis when it is actually true”, “Underestimating the true standard deviation of the population”, “Selecting an unrepresentative sample from the target population”, “Miscalculating the degrees of freedom in an inferential test”, “Failing to reject the null hypothesis when it is actually false” ], answer: 4, explanation: “A Type 2 error happens when an effect exists in the population, but the analysis fails to detect it (a miss).” }, { q: “What is meant by statistical power?”, options: [ “The probability of falsely rejecting a true null hypothesis (Type 1 error)”, “The probability of correctly rejecting a false null hypothesis”, “The overall number of independent observations recruited into the study”, “The numerical strength of the linear association between two variables”, “The prior probability that the null hypothesis is true before testing” ], answer: 1, explanation: “Power is the probability of correctly detecting a genuine effect (avoiding a Type 2 error).” }, { q: “What is the difference between a one-tailed and a two-tailed test?”, options: [ “A one-tailed test tests one sample; a two-tailed test tests two samples”, “A one-tailed test uses alpha of 1%; a two-tailed test uses alpha of 2%”, “A one-tailed test evaluates categorical data; a two-tailed test evaluates continuous data”, “A one-tailed test is mathematically more robust than any two-tailed test”, “A one-tailed test specifies direction; a two-tailed test tests either direction” ], answer: 4, explanation: “A two-tailed test checks for effects in either direction, whereas a one-tailed test focuses only on one pre-specified direction.” }, { q: “If you obtain a p value of .20 (20%), what should you conclude about the null hypothesis (assuming a standard 5% significance level)?”, options: [ “Reject the null hypothesis because the evidence is strong”, “Accept the null hypothesis as proven definitively true”, “Fail to reject the null hypothesis due to insufficient evidence”, “Accept the alternative hypothesis because p exceeds alpha”, “Reset the significance threshold to twenty percent post-hoc” ], answer: 2, explanation: “Because 0.20 > 0.05, there is insufficient evidence to reject the null hypothesis. We state ‘fail to reject’ rather than ‘accept’.” }, { q: “Why is it problematic to interpret ‘statistically significant’ as meaning ‘important’ or ‘large’?”, options: [ “Significance reflects unlikelihood under chance, not the magnitude of practical effect”, “Significance is computed from median ranks rather than parametric mean differences”, “Significance testing cannot be mathematically trusted in large observational samples”, “Significance thresholds are routinely fixed too permissively in standard practice”, “Significance implies the observed relationship occurred purely as a random accident” ], answer: 0, explanation: “Significance confirms the existence of an effect beyond chance, but does not measure its real-world magnitude or practical importance.” } ], ch5: [ { q: “What is the key difference between a population distribution and a sampling distribution of the mean?”, options: [ “The population distribution depicts individual scores; the sampling distribution depicts sample means”, “The population distribution is strictly normal; the sampling distribution is perpetually skewed”, “The population distribution reflects sample size 50; the sampling distribution uses size 1”, “The population distribution is theoretical; the sampling distribution is impossible to compute”, “The population distribution evaluates variance; the sampling distribution evaluates ranges” ], answer: 0, explanation: “The population distribution describes individual measurements, while the sampling distribution describes how the means of many samples distribute.” }, { q: “According to the Central Limit Theorem, what happens to the shape of the sampling distribution of the mean as the sample size gets larger?”, options: [ “It becomes increasingly irregular and skewed toward extreme outliers”, “It flattens out into an unbroken uniform line across all values”, “It splits into distinct bimodal clusters reflecting subgroups”, “It becomes approximately normally distributed, even if the population is not”, “It mirrors the exact skew and modality of the underlying raw population” ], answer: 3, explanation: “With sufficiently large samples, the averages of those samples will form a normal curve regardless of the original population distribution shape.” }, { q: “What statistic describes the standard deviation of the sampling distribution of the mean?”, options: [ “The Sample Variance”, “The Interquartile Range”, “The Standard Error”, “The Standardised Score”, “The Population Median” ], answer: 2, explanation: “The standard error of the mean is the standard deviation of the sample means.” }, { q: “How does the standard error compare to the standard deviation of the population?”, options: [ “It is always strictly larger than the population standard deviation”, “It is always strictly identical to the population standard deviation”, “It is exactly double the magnitude of the population standard deviation”, “It varies independently with no mathematical relationship to population spread”, “It is smaller than the population standard deviation (when sample size exceeds 1)” ], answer: 4, explanation: “Sample means vary less than individual scores because extreme values cancel out when averaged. Therefore, standard error is smaller than standard deviation.” }, { q: “What happens to the standard error as you increase the sample size (e.g., from 20 people to 50 people)?”, options: [ “The standard error increases noticeably”, “The standard error decreases noticeably”, “The standard error remains exactly identical”, “The standard error drops below zero”, “The standard error becomes infinitely large” ], answer: 1, explanation: “Larger samples produce more precise estimates of the population mean, narrowing the sampling distribution and reducing standard error.” }, { q: “Which of the following is the best definition of a confidence interval?”, options: [ “An interval of parameter values consistent with the sample data at the chosen level”, “A subjective metric scoring the personal certainty of the principal research team”, “A guaranteed boundary that definitively encloses the true population mean every time”, “The estimated timeframe required to achieve statistical confidence in experimental trials”, “The absolute numerical difference between the observed sample mean and population mean” ], answer: 0, explanation: “A confidence interval contains the range of population parameter values that would not be rejected if tested against the sample data.” }, { q: “Why is it incorrect to say ‘There’s a 95% probability that the true population mean lies inside my confidence interval’?”, options: [ “Because empirical confidence levels are mathematically fixed at 99% rather than 95%”, “Because confidence interval procedures apply exclusively to medians, never to means”, “Because observational sample sizes in social sciences are never large enough to ensure certainty”, “Because frequentist probability models cannot prove or test any real-world claims”, “Because the population mean is a fixed constant; it is either inside the interval or not” ], answer: 4, explanation: “In frequentist statistics, the population mean is fixed. The 95% refers to the procedure’s long-run success rate across repeated sampling.” }, { q: “If you keep the sample size the same, but increase the confidence level from 95% to 99%, what happens to the width of the confidence interval?”, options: [ “The confidence interval becomes narrower”, “The confidence interval remains unchanged”, “The confidence interval becomes wider”, “The confidence interval collapses to zero”, “The confidence interval becomes asymmetrical” ], answer: 2, explanation: “To increase confidence and reduce the risk of excluding the true mean, the interval must widen to cover more values.” }, { q: “Why are larger samples generally preferred for hypothesis testing?”, options: [ “They inflate the standard error, making statistical formulas simpler to calculate by hand”, “They guarantee that the underlying population distribution is perfectly symmetrical and normal”, “They eliminate the practical need for exploratory data inspection and data cleaning”, “They reduce standard error, making genuine differences easier to detect (higher power)”, “They provide mathematical proof that the stated null hypothesis is definitively true” ], answer: 3, explanation: “A smaller standard error narrows the sampling distribution, making it easier to detect genuine differences and reject the null hypothesis.” }, { q: “If a 95% confidence interval for the difference between two means includes the number 0 (e.g., [-2.5, +4.5]), what can you conclude?”, options: [ “The mean difference is statistically significant at the standard 5% alpha level”, “The difference between the two means is not statistically significant at the 5% level”, “The true difference in the underlying population is definitively proven to be zero”, “An arithmetic mistake was inevitably made during the computation of standard errors”, “The sample recruited for the study was excessively large for parametric testing” ], answer: 1, explanation: “If zero is inside the confidence interval, a difference of zero cannot be rejected; thus, the result is not statistically significant at the 5% level.” } ], ch6: [ { q: “When do we need to use the t distribution instead of the normal distribution when testing hypotheses about a mean?”, options: [ “When the outcome variable is measured on a nominal or ordinal categorical scale”, “When sample sizes become excessively large for standard normal z-approximations”, “When population variance is unknown and must be estimated from sample standard deviation”, “When the null hypothesis specifically tests a population mean of exactly zero”, “When sample observations violate unimodal symmetry with severe negative skew” ], answer: 2, explanation: “Estimating the population standard deviation from the sample introduces extra uncertainty, which the t distribution accounts for.” }, { q: “How does the shape of a t distribution curve compare to a standard normal distribution curve?”, options: [ “The t distribution has a markedly taller peak and noticeably thinner tails”, “The t distribution curve is identical to the standard normal curve across all sample sizes”, “The t distribution has heavier, fatter tails, reflecting added parameter uncertainty”, “The t distribution is systematically asymmetric with an extended right-side tail”, “The t distribution forms an unbroken horizontal density across finite intervals” ], answer: 2, explanation: “Because the standard deviation is estimated, there is a higher probability of extreme values, giving the t distribution heavier tails.” }, { q: “What does the term degrees of freedom generally relate to in the context of a t test?”, options: [ “The total number of independent predictor variables entered in the model”, “The freedom of the investigator to choose directional hypothesis thresholds”, “The financial resources allocated to support data collection procedures”, “The sample size (how many values can vary once parameters are fixed)”, “The count of distinct sub-populations sampled within the wider study” ], answer: 3, explanation: “Degrees of freedom are tied to sample size, representing the number of observations free to vary once parameters like the mean are calculated.” }, { q: “When would you use an independent-samples t test?”, options: [ “When comparing means between two entirely separate, unrelated groups of participants”, “When benchmarking a single observed group average against an established standard”, “When assessing the same participants repeatedly across two distinct testing times”, “When simultaneously evaluating mean differences across three or more treatment arms”, “When analysing associations between two cross-tabulated categorical variables” ], answer: 0, explanation: “An independent-samples t test compares means between two unrelated, distinct groups of participants.” }, { q: “When would you use a paired-samples t test?”, options: [ “When comparing mean scores across two distinct, independently sampled groups”, “When testing whether an observed empirical distribution conforms to normality”, “When evaluating simultaneously across three or more repeated assessment points”, “When quantifying the strength of linear association between continuous variables”, “When comparing two linked measurements collected from the same individual participants” ], answer: 4, explanation: “A paired-samples t test is used when measurements are linked, such as repeated measures on the same individuals.” }, { q: “Why is a paired-samples t test often more ‘powerful’ (more likely to detect an effect if there is one) than an independent-samples t test?”, options: [ “It naturally doubles the total count of distinct individuals recruited into the study”, “It sets a more permissive significance threshold during critical value evaluation”, “It guarantees that sample differences conform to an exact normal distribution”, “It isolates and eliminates extraneous between-person variability from the error term”, “It streamlines the mathematical calculation by bypassing standard error estimation” ], answer: 3, explanation: “Comparing participants to themselves controls for between-person variability, reducing error noise and making effects easier to detect.” }, { q: “What is Cohen’s d?”, options: [ “A formal hypothesis test evaluating whether sample observations follow a normal curve”, “An effect size quantifying the difference between two means in standard deviation units”, “The exact mathematical probability that the observed null hypothesis is factually true”, “An alternative technical designation for the standard error of the mean difference”, “The number of independent observations free to vary in a one-sample test statistic” ], answer: 1, explanation: “Cohen’s d quantifies effect size by standardising the difference between group means in standard deviation units.” }, { q: “Why can’t we simply assume causation (e.g., that living in the East causes you to be taller) when we find a significant difference in a t test?”, options: [ “Confounding variables (e.g., socioeconomic factors) may explain the observed group difference”, “Parametric t tests lack sufficient mathematical precision to identify true differences”, “Sample sizes in regional observational comparisons are invariably too restricted in scope”, “Height is technically an ordered categorical metric rather than a continuous variable”, “Causation can never be established unless data are gathered via a full national census” ], answer: 0, explanation: “Observational associations can be driven by confounding variables. Controlled experiments are needed to establish causation.” }, { q: “What does it mean if a t test assumes homogeneity of variance?”, options: [ “It assumes that all individual participants possess identical raw score values”, “It assumes that sample sizes across both groups are mathematically identical”, “It assumes that the underlying population means of both comparison groups are zero”, “It assumes that both comparison groups contain no outlying or extreme values”, “It assumes that the score variability in both comparison groups is roughly equal” ], answer: 4, explanation: “Homogeneity of variance assumes that both groups have approximately equal score variability.” }, { q: “What happens to the critical value of t (the value needed to reach significance) as the sample size gets larger?”, options: [ “The critical value increases, making statistical significance harder to achieve”, “The critical value decreases, making statistical significance easier to achieve”, “The critical value remains completely constant regardless of sample size”, “The critical value drops immediately to an absolute magnitude of zero”, “The critical value transitions to a negative sign under two-tailed conditions” ], answer: 1, explanation: “As sample size and degrees of freedom grow, the t distribution converges toward the normal curve, slimming the tails and lowering the critical value.” } ],

ch7: [ { q: “What does an F test in statistics do?”, options: [ “Compares sample means across two independent groups”, “Assesses whether continuous observations follow a normal curve”, “Computes the standard error of a grand sample mean”, “Compares two sample variances by evaluating their numerical ratio”, “Determines the sample median across ranked ordinal scores” ], answer: 3, explanation: “The F test compares two variances by evaluating their ratio to test whether populations share the same variance.” }, { q: “Why is Analysis of Variance (ANOVA) generally preferred over running multiple t tests, when comparing more than two groups?”, options: [ “Running multiple t tests inflates the familywise Type 1 error rate”, “ANOVA eliminates the mathematical requirement of score homogeneity”, “Two-sample t tests can only be computed on categorical variables”, “ANOVA is computationally much simpler to evaluate by hand”, “ANOVA guarantees that at least one comparison reaches significance” ], answer: 0, explanation: “Multiple separate tests inflate the overall risk of a Type 1 error. ANOVA evaluates all groups simultaneously while controlling this error rate.” }, { q: “In a ‘1-way ANOVA’ what does the term ‘1-way’ refer to?”, options: [ “There is only one individual participant observed in the study”, “There is only one continuous outcome variable measured in the design”, “The inferential hypothesis is strictly one-tailed in its formulation”, “There is only one mathematically valid sequence for data estimation”, “There is only one categorical predictor (factor) grouping the observations” ], answer: 4, explanation: “A 1-way ANOVA contains a single factor (independent grouping variable), regardless of how many categories it contains.” }, { q: “What does a statistically significant result from a 1-way ANOVA tell you?”, options: [ “All group means across the conditions are identical in the population”, “At least one group mean differs from the others, but not which one”, “Every single group mean differs significantly from every other group mean”, “The variances of the groups differ significantly from one another”, “The recruited sample size was statistically insufficient for testing” ], answer: 1, explanation: “The omnibus F test indicates that not all group means are equal, but post-hoc comparisons are required to determine which specific groups differ.” }, { q: “What is a main effect in a 2-way ANOVA?”, options: [ “The combined synergistic impact of both factors acting together”, “The empirical outcome of the very first pairwise test executed”, “The effect of one factor averaged across all levels of the other”, “The influence of whichever independent variable exhibits larger variance”, “The statistical residual variance remaining unexplained by the model” ], answer: 2, explanation: “A main effect represents the overall influence of one factor collapsed across all levels of the second factor.” }, { q: “What is an interaction effect in a 2-way ANOVA?”, options: [ “When both experimental factors demonstrate statistically significant main effects across group conditions”, “When individual participants communicate and collaborate with one another during testing sessions”, “When the two independent grouping variables show severe collinearity with each other”, “When group differences remain completely identical across every level of the second factor”, “When the effect of one factor changes depending on the level of the other” ], answer: 4, explanation: “An interaction means the effect of one predictor changes depending on the condition or level of the other predictor.” }, { q: “In an interaction plot, what visual feature suggests that an interaction is present?”, options: [ “The plotted condition lines are flat and horizontal”, “The plotted condition lines are noticeably non-parallel”, “The plotted condition lines run exactly parallel across levels”, “The plotted condition lines share the exact same display colour”, “The plotted confidence intervals are exceptionally small in height” ], answer: 1, explanation: “Non-parallel lines (diverging, converging, or crossing) indicate that the relationship between one variable and the outcome changes across levels of the other.” }, { q: “What is eta squared used for in ANOVA?”, options: [ “To test whether sample residuals follow an unbroken normal distribution”, “To compute the exact p value corresponding to the observed F ratio”, “To quantify effect size as the proportion of variance explained”, “To determine the minimum sample size required for statistical power”, “To apply a Bonferroni adjustment for planned multiple pairwise contrasts” ], answer: 2, explanation: “Eta squared measures effect size by expressing the proportion of total outcome variance accounted for by a factor or model.” }, { q: “What is the key advantage of a repeated-measures ANOVA compared to an independent-measures ANOVA?”, options: [ “It eliminates the necessity for making distributional assumptions”, “It is the only ANOVA model capable of analyzing nominal outcomes”, “It guarantees that all pairwise post-hoc tests achieve significance”, “It removes participant-level variance from the error term, increasing power”, “It circumvents the requirement for an untreated baseline control group” ], answer: 3, explanation: “Repeated testing partitions out individual differences from the error term, increasing sensitivity to changes across conditions.” }, { q: “If you see two error bars (confidence intervals) on a graph that do not overlap at all, what is a reasonable quick conclusion?”, options: [ “The difference between the two groups is likely statistically significant”, “The difference between the two groups is likely not statistically significant”, “The underlying measurements definitely violate parametric normality”, “Additional sample data must be gathered before calculating group averages”, “The two observed group means are mathematically identical in magnitude” ], answer: 0, explanation: “Non-overlapping 95% confidence intervals strongly suggest that the difference between group means is statistically significant.” } ], ch8: [ { q: “What does ‘simple’ refer to in ‘simple linear regression’?”, options: [ “The model is restricted to a small number of observed participants”, “The mathematical computations can be carried out entirely by hand”, “The fitted trajectory assumes a monotonic curvilinear relationship”, “The model involves only one predictor variable and one outcome variable”, “The underlying statistical concepts can be mastered within a single lesson” ], answer: 3, explanation: “‘Simple’ signifies that the model includes only one predictor and one continuous outcome variable.” }, { q: “What is a residual in linear regression?”, options: [ “The vertical distance between an observed data point and the fitted line”, “The exact recorded score on the independent predictor variable”, “The coordinate location where the fitted trajectory intersects the vertical axis”, “The rate of directional change expressed by the slope coefficient”, “An observation flagged as an extreme outlier and removed from analysis” ], answer: 0, explanation: “A residual is the vertical difference between an observed data value and the corresponding value predicted by the fitted line.” }, { q: “What method is most commonly used to determine the regression line?”, options: [ “Connecting the first and last coordinates with a straight line”, “Identifying the single line yielding the steepest possible empirical slope”, “Ordinary Least Squares (OLS), which minimises squared vertical residuals”, “Connecting consecutive data points into a multi-segmented geometric curve”, “Selecting a line constrained to pass only through the exact sample median” ], answer: 2, explanation: “Ordinary Least Squares finds the line that minimises the sum of the squared vertical residuals.” }, { q: “In a regression model, what does the intercept represent?”, options: [ “The steepness and directional sign of the fitted linear slope”, “The overall proportion of variance in the outcome accounted for”, “The location along the abscissa where the regression slope becomes vertical”, “The arithmetic mean of all observed scores across the predictor variable”, “The predicted value of the outcome variable when the predictor equals zero” ], answer: 4, explanation: “The intercept represents the expected value of the outcome variable when the predictor equals zero.” }, { q: “What is the problem of overfitting?”, options: [ “The sample size recruited is excessively large for parametric estimation”, “The model fits sample-specific noise rather than just the general trend”, “The calculated regression slope fails to achieve sufficient statistical steepness”, “The estimated intercept coordinate falls below zero on the outcome axis”, “The independent predictor variable is formatted as nominal categories” ], answer: 1, explanation: “Overfitting occurs when an overly complex model conforms to idiosyncratic sample noise, reducing its predictive accuracy on new data.” }, { q: “What does it mean if a data point has high leverage?”, options: [ “It displays an exceptionally high score on the dependent outcome variable”, “It falls within a close Euclidean distance of the mean of the predictor”, “It represents an obvious clerical error requiring deletion during cleaning”, “It exhibits an extreme or outlying value on the independent predictor variable”, “It lies directly along the regression trajectory with a vertical residual of zero” ], answer: 3, explanation: “A point with high leverage sits far from the mean of the predictor, giving it greater potential influence on the slope of the line.” }, { q: “Which of the following is true about confidence bands versus prediction bands around a regression line?”, options: [ “The confidence band is strictly wider than the corresponding prediction band”, “The two bands maintain an identical mathematical width across all values”, “The prediction band shrinks to an interval of zero as sample size grows”, “The confidence band identifies the boundaries enclosing all future individual observations”, “The prediction band is wider because it incorporates individual score variability” ], answer: 4, explanation: “Prediction bands account for line estimation uncertainty plus individual score variance, making them strictly wider than confidence bands.” }, { q: “What does the R-squared statistic tell you?”, options: [ “The steepness and directional rate of change in the regression line”, “The proportion of variance in the outcome explained by the model”, “The value of the outcome variable when the predictor is fixed at zero”, “The exact mathematical probability that the observed null hypothesis is true”, “The total count of observations identified as statistical outliers” ], answer: 1, explanation: “R-squared indicates goodness of fit by measuring the proportion of variance in the outcome explained by the regression line.” }, { q: “Why might a researcher look at adjusted R-squared instead of standard R-squared?”, options: [ “To penalise added predictors and correct for small-sample inflation”, “To make the observed correlation appear artificially stronger in reports”, “To rescale the regression coefficients into metric units of measurement”, “To accommodate non-linear polynomial relationships rather than straight trajectories”, “To prevent the explained variance estimate from taking negative values” ], answer: 0, explanation: “Adjusted R-squared penalises for small samples and added predictors to prevent artificial inflation of explained variance.” }, { q: “If the slope (regression coefficient) of a regression line is zero, what does this indicate?”, options: [ “As the predictor increases, the outcome variable increases at an accelerating rate”, “As the predictor increases, the outcome variable decreases at an accelerating rate”, “The predictor provides no linear information for forecasting the outcome”, “The intercept of the fitted regression line must also be mathematically zero”, “The observed data points fall in a perfect deterministic linear correlation” ], answer: 2, explanation: “A slope of zero yields a horizontal line, meaning that values of the predictor do not assist in predicting the outcome.” } ], ch9: [ { q: “In a path diagram, how is a correlational relationship (where neither variable is designated as the predictor or outcome) typically represented?”, options: [ “A single directional arrow pointing from left to right”, “A single directional arrow pointing from right to left”, “A dashed non-directional path without terminal arrowheads”, “A double-headed arrow connecting the two related variables”, “A prominent rectangular border encompassing both measures” ], answer: 3, explanation: “Correlations are symmetric and non-directional, indicated in path diagrams by a double-headed arrow.” }, { q: “If you standardise two variables (convert them to z scores) and calculate the regression line, what does the slope of that line represent?”, options: [ “Pearson’s correlation coefficient (r)”, “The pooled variance of the variables”, “The standard deviation of residuals”, “The vertical intercept of the line”, “The total sample size of the study” ], answer: 0, explanation: “When variables are standardised to mean = 0 and SD = 1, the regression slope is identical to Pearson’s r.” }, { q: “What does a correlation coefficient (r) of 0 indicate?”, options: [ “A deterministic positive linear association between variables”, “A deterministic negative linear association between variables”, “The individual observations form a perfectly circular boundary”, “A pronounced non-linear relationship must be present in the data”, “The absence of a linear relationship between the two variables” ], answer: 4, explanation: “An r of 0 indicates the absence of a linear relationship between the two variables.” }, { q: “Which of the following values represents the strongest correlation?”, options: [ “+0.10”, “-0.80”, “+0.50”, ” 0.00”, “-0.10” ], answer: 1, explanation: “Correlation strength depends on absolute magnitude regardless of sign; |-0.80| is larger than |0.50|.” }, { q: “What is regression to the mean?”, options: [ “The systematic bias where longitudinal measurements drift toward maximum scores”, “A computational algorithm used for calculating the arithmetic average of a sample”, “Extreme values on one measure tend to pair with less extreme values on another”, “The theoretical premise that population variance contracts across generations”, “A sampling distortion introduced when empirical studies use restricted sample sizes” ], answer: 2, explanation: “When variables correlate imperfectly, extreme scores on one measure tend to be paired with less extreme scores on the other.” }, { q: “Does regression to the mean happen only over time (e.g., from past to future)?”, options: [ “No, it operates symmetrically in both temporal directions”, “Yes, it occurs only when predicting future scores from past baseline records”, “No, it manifests exclusively when the underlying linear correlation is negative”, “Yes, it applies solely to physical anthropometric measures such as adult height”, “No, it emerges exclusively when statistical analyses rely on very small samples” ], answer: 0, explanation: “Regression to the mean is a mathematical property of imperfect correlation that applies symmetrically in both temporal directions.” }, { q: “In the book’s geometric visualisation using vectors (arrows), what is the angle between two variables that have zero correlation?”, options: [ “0 degrees (pointing in parallel directions)”, “45 degrees (pointing in acute directions)”, “180 degrees (pointing in opposite directions)”, “360 degrees (completing a full planar circle)”, “90 degrees (perpendicular, orthogonal vectors)” ], answer: 4, explanation: “In geometric vector representation, uncorrelated variables are orthogonal (perpendicular, at 90 degrees).” }, { q: “What is a spurious correlation?”, options: [ “A deterministic association where the bivariate correlation reaches exactly one”, “An apparent correlation produced by a confounding third factor or chance alone”, “A correlation coefficient calculated manually without the use of computer software”, “A specialised correlation between an ordinal category and a continuous measurement”, “A non-significant correlation observed within an underpowered clinical experiment” ], answer: 1, explanation: “A spurious correlation is an apparent association produced by a common confounding factor rather than direct causation.” }, { q: “What does a partial correlation allow you to do?”, options: [ “Compute the association between two variables using half of the available records”, “Quantify the strength of association between two variables that are non-linear”, “Estimate the unknown population mean while tolerating substantial missing data”, “Measure the relationship between two variables while adjusting for a third”, “Artificially increase statistical power by multiplying observed sample sizes” ], answer: 3, explanation: “Partial correlation isolates the unique relationship between two variables after statistically adjusting for the variance of a third.” }, { q: “Why is the crud factor a reason to be sceptical of tiny but significant correlations in huge datasets?”, options: [ “It indicates that collected datasets contain pervasive data-entry transcription errors”, “It implies that the underlying computational software contains algorithmic bugs”, “In nature, nearly all variables share trivial non-causal correlations with each other”, “It confirms that measured variables were coded as discrete categories rather than intervals”, “It provides empirical proof that researchers selectively fabricated observed findings” ], answer: 2, explanation: “In very large datasets, trivial background associations reach statistical significance without reflecting substantive real-world relationships.” } ],

ch10: [ { q: “What is the key difference between simple linear regression and multiple linear regression?”, options: [ “Simple regression uses categorical data; multiple regression uses continuous variables”, “Simple regression models one outcome; multiple regression models multiple outcomes simultaneously”, “Simple regression has one predictor variable; multiple regression has two or more predictors”, “Simple regression is computed manually; multiple regression requires automated computing”, “Simple regression generates curvilinear trajectories; multiple regression fits planar trajectories” ], answer: 2, explanation: “Multiple regression extends simple linear regression by using two or more predictors to model a single outcome.” }, { q: “What is collinearity (or multicollinearity) in the context of multiple regression?”, options: [ “When the continuous dependent outcome variable correlates perfectly with one predictor”, “When individual empirical observations fall along an exact straight trajectory in space”, “When the recruited sample size is statistically inadequate for estimating multiple slopes”, “When regression residuals exhibit non-normal distributions with severe skewness”, “When two or more independent predictor variables correlate strongly with each other” ], answer: 4, explanation: “Collinearity occurs when predictor variables correlate strongly with each other, obscuring their individual contributions.” }, { q: “What is the difference between a partial correlation and a semi-partial correlation?”, options: [ “Partial removes covariate variance from both variables; semi-partial removes it only from the predictor”, “Partial removes covariate variance from only the predictor; semi-partial removes it from both variables”, “Partial correlation evaluates categorical predictors; semi-partial correlation evaluates continuous metrics”, “Partial correlation is mathematically constrained to yield smaller numerical values than semi-partial”, “Partial correlation requires bivariate normal data; semi-partial correlation is strictly non-parametric” ], answer: 0, explanation: “Partial correlation removes the third variable from both variables; semi-partial correlation removes it only from the predictor.” }, { q: “Which regression method involves entering predictors into the model in a specific, theory-driven order (e.g., in blocks)?”, options: [ “Stepwise regression”, “Simultaneous entry regression”, “All-subsets regression”, “Hierarchical regression”, “Binary logistic regression” ], answer: 3, explanation: “Hierarchical regression allows the researcher to control the entry sequence of predictors based on theoretical rationale.” }, { q: “Why is stepwise regression often criticised?”, options: [ “It relies heavily on prior substantive theory rather than empirical data distributions”, “It capitalises on sample noise, causing overfitting and poor replication in new data”, “It is computationally too complex to implement within standard modern statistical software”, “It is mathematically incapable of managing models that contain more than two predictors”, “It systematically suppresses test statistics so models fail to achieve significance” ], answer: 1, explanation: “Stepwise selection relies on sample-specific noise, producing models that often capitalise on chance and fail to replicate.” }, { q: “What is a suppressor variable?”, options: [ “A nuisance variable whose inclusion artificially deflates the effective sample size”, “An extraneous factor that introduces complete collinearity and causes estimation failure”, “A predictor that enhances prediction by correlating with error variance in another predictor”, “A measured variable that shares a deterministic bivariate correlation of one with the outcome”, “A screening filter applied during preliminary data preparation to remove extreme outliers” ], answer: 2, explanation: “A suppressor variable suppresses irrelevant noise in another predictor, enhancing that predictor’s relationship with the outcome.” }, { q: “When would someone use logistic regression?”, options: [ “When the dependent outcome variable is categorical (e.g., binary Yes/No decisions)”, “When the independent predictor variables are measured on continuous scales”, “When the dependent outcome variable is strictly continuous (e.g., adult height)”, “When total sample sizes fall below the threshold required for linear estimation”, “When testing whether sample means differ between two matched experimental groups” ], answer: 0, explanation: “Logistic regression is used when the dependent variable is categorical or binary rather than continuous.” }, { q: “In logistic regression, what does the odds ratio tell you?”, options: [ “The raw unconditional probability of the target outcome event occurring in the population”, “The standardized difference between the means of two independent comparison groups”, “The total number of observations correctly classified into binary categorical groups”, “The standard deviation of estimated logit residuals around the fitted sigmoid line”, “The multiplicative change in the odds of the outcome for a one-unit predictor increase” ], answer: 4, explanation: “An odds ratio indicates the multiplicative change in the odds of the outcome for each one-unit increase in the predictor.” }, { q: “What is the purpose of Analysis of Covariance (ANCOVA)?”, options: [ “To test whether variances differ between groups while bypassing assumptions about means”, “To cluster participants into discrete groups based on shared multivariate covariance profiles”, “To impute missing values across several continuous metrics using iterative regressions”, “To compare group means while statistically controlling for a continuous covariate”, “To compute the median difference between repeated measurements across several treatment arms” ], answer: 3, explanation: “ANCOVA compares group means while statistically removing variance attributable to a continuous covariate.” }, { q: “What does the deviance statistic measure in the context of logistic regression?”, options: [ “The dispersion and standard deviation among continuous independent predictors”, “How poorly the fitted model fits the observed data (a measure of badness of fit)”, “The proportion of participants who dropped out before final assessment intervals”, “The numerical discrepancy between the sample median and the sample trimmed mean”, “The magnitude of bivariate collinearity between two competing predictor variables” ], answer: 1, explanation: “Deviance reflects badness of fit; lower deviance values indicate closer agreement between model predictions and observations.” } ], ch11: [ { q: “What does a contingency table (or cross-tabulation) display?”, options: [ “The complete record of raw participant responses organized in a single column”, “The bivariate trajectory of two continuous variables displayed as a scatterplot”, “The parametric summary metrics (mean and standard deviation) across subgroups”, “The monotonic rankings of all study participants ordered from highest to lowest”, “The frequency of observations across combinations of two categorical variables” ], answer: 4, explanation: “A contingency table tabulates frequencies across combinations of categories for two nominal variables.” }, { q: “In a chi-squared test for independence, what do the expected frequencies represent?”, options: [ “The actual observed cell counts recorded during the active data collection process”, “The cell counts expected if the two categorical variables were completely independent”, “The number of survey respondents who withdrew or failed to supply complete records”, “The cell frequencies projected by fitting an ordinary bivariate least-squares line”, “The arithmetic average computed across all observed rows and columns in the table” ], answer: 1, explanation: “Expected frequencies represent counts anticipated under the null hypothesis of complete independence between the variables.” }, { q: “Which statistical test is suitable for analysing a small contingency table, where the sample size is too small for a chi-squared test?”, options: [ “Independent-samples t test”, “One-way analysis of variance (ANOVA)”, “Fisher’s exact test”, “Simple linear regression”, “Exploratory factor analysis” ], answer: 2, explanation: “Fisher’s exact test calculates exact hypergeometric probabilities without relying on large-sample approximations.” }, { q: “When would someone use McNemar’s test?”, options: [ “When comparing mean values between two independent groups on a continuous metric”, “When testing for associations across three independent groups on nominal variables”, “When computing the bivariate linear correlation between adult height and body weight”, “When evaluating paired or repeated categorical responses from the same individuals”, “When extracting latent dimensions from large batteries of questionnaire responses” ], answer: 3, explanation: “McNemar’s test assesses changes in paired or repeated categorical responses from the same individuals.” }, { q: “What is the difference between the chi-squared test for independence and the chi-squared goodness-of-fit test?”, options: [ “Independence evaluates two variables; goodness-of-fit tests one against a distribution”, “Independence evaluates continuous variables; goodness-of-fit tests nominal variables”, “Independence assumes normal distributions; goodness-of-fit is strictly distribution-free”, “Independence assesses score equality; goodness-of-fit compares sample variances”, “Independence is directional; goodness-of-fit is non-directional and two-tailed” ], answer: 0, explanation: “Independence tests for associations between two variables; goodness-of-fit tests a single distribution against an expected distribution.” }, { q: “Why is percentage agreement often a poor measure of inter-rater reliability?”, options: [ “It is computationally too burdensome to compute reliably across large samples”, “It is mathematically impossible for agreement percentages to attain one hundred percent”, “It fails to adjust for the baseline agreement that would occur purely by chance”, “It requires underlying data to be measured on continuous scales rather than categories”, “It can only be mathematically computed when evaluating panels of more than five raters” ], answer: 2, explanation: “Percentage agreement fails to adjust for the baseline agreement that would occur by random chance alone.” }, { q: “What does Cohen’s kappa measure?”, options: [ “The linear correlation coefficient between two continuous experimental metrics”, “The total count of missing or unclassifiable observations across survey items”, “The absolute discrepancy between the observed sample mean and sample median”, “The agreement between two raters, corrected for the proportion expected by chance”, “The statistical power of a contingency test given fixed degrees of freedom” ], answer: 3, explanation: “Cohen’s kappa measures inter-rater concordance while correcting for chance agreement.” }, { q: “Which of these is a reason why Comparative Judgement may be useful?”, options: [ “Evaluating pairs completely eliminates subjective cognitive and personal bias”, “Pairwise comparisons require substantially longer completion times per participant”, “Absolute marking schemes require specialized algorithmic statistical software”, “Relative ranking procedures eliminate the need for qualitative assessment rubrics”, “Humans compare pairs more reliably than assigning isolated absolute numeric scores” ], answer: 4, explanation: “Making pairwise relative comparisons is cognitively easier and more reliable than assigning isolated absolute numerical ratings.” }, { q: “What does the chi-squared statistic measure?”, options: [ “The normalized sum of squared discrepancies between observed and expected frequencies”, “The total sample size of participants completing all assigned testing protocols”, “The estimated standard error of the sampling distribution of proportions”, “The squared bivariate correlation between two independent continuous metrics”, “The total degrees of freedom remaining after estimating row and column marginals” ], answer: 0, explanation: “The chi-squared statistic aggregates normalised squared differences between observed and expected frequencies.” }, { q: “If a chi-squared test returns a significant result (e.g. p < .05), what conclusion can you draw?”, options: [ “The two categorical variables are entirely independent of each other in the population”, “There is a significant association between variables (they are not independent)”, “The observed cell counts match the expected frequencies with negligible deviation”, “The sample size recruited was statistically insufficient to support inferential claims”, “A Type 2 decision error was definitively committed during the statistical testing” ], answer: 1, explanation: “A significant result indicates that the variables are associated, rejecting the null hypothesis of independence.” } ], ch12: [ { q: “What is the difference between parametric and non-parametric tests?”, options: [ “Parametric tests require large samples; non-parametric tests are designed for small samples”, “Parametric tests assume a specific distribution (e.g. normal); non-parametric make minimal assumptions”, “Parametric tests must be calculated manually; non-parametric tests require automated software”, “Parametric tests evaluate nominal metrics; non-parametric tests evaluate continuous measures”, “Parametric tests always achieve significance; non-parametric tests fail to reject the null” ], answer: 1, explanation: “Parametric tests assume specific population distributions; non-parametric methods are distribution-free, typically relying on ranks.” }, { q: “What is the purpose of Levene’s test when comparing groups?”, options: [ “To test whether sample data deviate significantly from a theoretical normal curve”, “To evaluate whether the population means of the groups are significantly different”, “To screen for bivariate outliers along the regression trajectory across conditions”, “To test whether the variances of the comparison groups are significantly different”, “To calculate the rank-order correlation coefficient between continuous predictors” ], answer: 3, explanation: “Levene’s test checks whether group variances are equal (homogeneity of variance).” }, { q: “Which statistical test is used to check if a dataset deviates significantly from a normal distribution?”, options: [ “The two-sample Student’s t test”, “The Mann-Whitney U test”, “The non-parametric Sign test”, “The two-sample Fisher’s F test”, “The Shapiro-Wilk test” ], answer: 4, explanation: “The Shapiro-Wilk test evaluates the null hypothesis that sample observations follow a normal distribution.” }, { q: “What is a Q-Q plot used for?”, options: [ “To assess normality visually by plotting sample quantiles against theoretical normal quantiles”, “To compare interquartile ranges and median values across multiple independent treatments”, “To evaluate whether bivariate continuous measures conform to a monotonic linear trajectory”, “To compute standard errors and parametric confidence intervals across successive iterations”, “To identify multivariate leverage points along an ordinary least-squares regression line” ], answer: 0, explanation: “A Q-Q plot contrasts sample quantiles with theoretical normal quantiles; points falling along a diagonal line indicate normality.” }, { q: “How does the Sign test analyse data to test a hypothesis about the median?”, options: [ “It computes the arithmetic mean and calculates standardized deviations from the center”, “It ranks all raw observation scores from smallest to largest before computing group sums”, “It counts observations above and below the hypothesized median, ignoring difference magnitudes”, “It estimates the population variance using iterative maximum likelihood approximations”, “It evaluates the ratio of between-group deviations against within-group residual spread” ], answer: 2, explanation: “The Sign test evaluates only the direction (sign) of differences from the median, ignoring magnitudes.” }, { q: “Why is the Wilcoxon signed-rank test generally preferred over the Sign test?”, options: [ “Because it is computationally simpler to evaluate by hand without specialized software”, “Because it evaluates differences using parametric means rather than median thresholds”, “Because it completely eliminates the mathematical requirement for independent sampling”, “Because it relies on the strict assumption that differences follow an exact normal curve”, “Because it incorporates the rank and magnitude of differences, providing greater power” ], answer: 4, explanation: “The Wilcoxon signed-rank test incorporates both the direction and the relative magnitude of differences, giving it greater power.” }, { q: “Which non-parametric test is the counterpart of the independent-samples t test (comparing two separate groups)?”, options: [ “The Wilcoxon signed-rank test”, “The Mann-Whitney U test”, “The Kruskal-Wallis test”, “The Friedman rank-sum test”, “The Shapiro-Wilk test” ], answer: 1, explanation: “The Mann-Whitney U test compares ranks between two independent groups.” }, { q: “Which non-parametric test is the counterpart of the one-way ANOVA (comparing more than two groups)?”, options: [ “The Wilcoxon signed-rank test”, “The Mann-Whitney U test”, “The Kruskal-Wallis test”, “The Friedman rank-sum test”, “The Shapiro-Wilk test” ], answer: 2, explanation: “The Kruskal-Wallis test extends rank comparisons to three or more independent groups.” }, { q: “When might you use Spearman’s rho instead of Pearson’s r to calculate correlation?”, options: [ “When data contain outliers or skewness, as rho relies on ranks rather than raw values”, “When the underlying bivariate distribution is verified to be perfectly bivariate normal”, “When total sample sizes recruited in the observational investigation exceed one thousand”, “When the association is strictly linear and completely free of extreme outlying values”, “When both variables are recorded exclusively as unordered nominal categories” ], answer: 0, explanation: “Spearman’s rho converts raw values to ranks, making it robust against outliers and non-normality.” }, { q: “What is bootstrapping, in the context of statistics?”, options: [ “An algorithmic routine for linking and formatting relational database tables”, “A screening procedure for identifying and trimming extreme bivariate outliers”, “A parametric hypothesis test evaluating whether sample variances are equal”, “A method for estimating sampling distributions by repeatedly resampling with replacement”, “A manual formula for calculating unbiased standard errors in small pilot studies” ], answer: 3, explanation: “Bootstrapping constructs empirical sampling distributions by repeatedly resampling from the original data with replacement.” } ],

ch13: [ { q: “What is the main difference between cluster analysis and factor analysis?”, options: [ “Cluster analysis evaluates categorical metrics; factor analysis evaluates continuous scores”, “Cluster analysis groups variables together; factor analysis groups individual participants”, “Cluster analysis is an inferential test; factor analysis is purely exploratory and descriptive”, “Cluster analysis groups similar participants; factor analysis groups correlated variables”, “Cluster analysis requires normal distributions; factor analysis makes no assumptions” ], answer: 3, explanation: “Cluster analysis identifies groupings of similar participants; factor analysis uncovers groupings among variables.” }, { q: “What is a Likert-type scale?”, options: [ “An ordered rating scale measuring graded levels of agreement or disagreement”, “A physical instrument designed for recording continuous biometric variations”, “An algorithmic distance metric used to compute multidimensional proximity”, “A graphical scatterplot illustrating standardized component loading values”, “A forced-choice binary format restricted strictly to dichotomous categories” ], answer: 0, explanation: “Likert-type scales offer ordered response options denoting levels of agreement or disagreement.” }, { q: “In hierarchical cluster analysis, what is a dendrogram?”, options: [ “A correlation matrix summarizing bivariate associations across all surveyed indicators”, “A scree diagram plotting successive eigenvalues against component sequence numbers”, “A tabulated roster identifying participants flagged as multivariate leverage outliers”, “A profile plot contrasting sub-cluster means across continuous baseline covariates”, “A branching tree diagram visualising successive mergers of participants into clusters” ], answer: 4, explanation: “A dendrogram is a tree diagram depicting successive cluster mergers across distance thresholds.” }, { q: “What is the defining feature of k-means clustering, compared to hierarchical clustering?”, options: [ “It generates an unbroken hierarchical tree diagram displaying cluster distances”, “The researcher must pre-specify the target number of clusters (k) in advance”, “It is mathematically restricted to analyzing datasets containing only two variables”, “It is unable to process large computational datasets exceeding fifty observations”, “It partitions measured questionnaire items rather than individual participants” ], answer: 1, explanation: “In k-means clustering, the researcher specifies the target number of clusters k before running the algorithm.” }, { q: “What does Cronbach’s alpha measure?”, options: [ “The bivariate Pearson correlation between two matched individual participants”, “The total number of underlying latent constructs present within a survey battery”, “The internal consistency reliability across a set of associated scale items”, “The inferential significance of separation observed between derived clusters”, “The numerical discrepancy between the observed sample mean and sample median” ], answer: 2, explanation: “Cronbach’s alpha estimates how consistently a set of survey items measures a single underlying construct.” }, { q: “What is the primary goal of principal component analysis?”, options: [ “To test whether the multidimensional centroids of comparison groups differ significantly”, “To determine the exact probability that an individual participant belongs to a cluster”, “To randomly assign participants to experimental treatment conditions without selection bias”, “To identify and delete multivariate leverage points from the active covariance matrix”, “To reduce many variables into fewer composite components that retain maximum variance” ], answer: 4, explanation: “PCA reduces many correlated variables into fewer uncorrelated components that retain maximum variance.” }, { q: “In a scree plot, what does the ‘elbow’ indicate?”, options: [ “The point where extracting further components yields diminishing returns in variance”, “The boundary coordinate where empirical observations become contaminated with noise”, “The highest mathematical eigenvalue extracted across the entire correlation matrix”, “The total sample size of participants required to achieve stable factor loadings”, “The magnitude of bivariate association between the first and last measured variables” ], answer: 0, explanation: “The elbow marks the point where subsequent components explain diminishing, trivial amounts of variance.” }, { q: “What is a factor loading?”, options: [ “The total count of measured indicator items assigned to a single latent factor”, “The overall processing time required to compute the iterative extraction algorithm”, “The correlation between a specific observed variable and an extracted latent factor”, “The unique residual error variance left unexplained by the extracted factor model”, “The theoretical conceptual label assigned to a component by the principal researcher” ], answer: 2, explanation: “A factor loading is the correlation between an observed variable and an extracted latent factor.” }, { q: “What is communality in the context of factor analysis?”, options: [ “The total number of respondents completing all items in the questionnaire battery”, “The proportion of an item’s variance accounted for across all extracted factors”, “The shared bivariate covariance between two specific manifest indicators exclusively”, “The demographic setting and population context where empirical testing occurred”, “The orthogonal correlation between the first extracted component and the second” ], answer: 1, explanation: “Communality is the proportion of an item’s total variance accounted for across all extracted factors.” }, { q: “Why is rotation used in factor analysis?”, options: [ “To alter underlying eigenvalue weights until components achieve statistical significance”, “To artificially maximize the overall proportion of variance explained by the model”, “To transform extracted factor dimensions back into raw manifest indicator variables”, “To achieve simple structure and make the pattern of factor loadings interpretable”, “To suppress and conceal extreme multivariate outliers within the residual matrix” ], answer: 3, explanation: “Rotation reorients factor axes toward simple structure, making loading patterns easier to interpret.” } ], ch14: [ { q: “When is multilevel modelling (also known as hierarchical linear modelling) required?”, options: [ “When sample observations follow a perfectly symmetrical normal distribution”, “When total sample sizes fall below ten independent observations per condition”, “When observations are nested or clustered, violating assumption of independence”, “When the empirical design includes only a single independent predictor variable”, “When the primary goal of the investigation is calculating an arithmetic mean” ], answer: 2, explanation: “Multilevel modelling is required when observations are clustered into hierarchies, violating independence assumptions.” }, { q: “What is the ecological fallacy?”, options: [ “The assumption that increasing sample sizes invariably eliminates measurement error”, “The erroneous choice of computing a Student’s t test instead of a one-way ANOVA”, “A data collection flaw arising from unmeasured environmental nuisance variables”, “The flawed assumption that relationships observed at group level apply to individuals”, “The mistaken premise that all clusters in a population contain identical sample sizes” ], answer: 3, explanation: “The ecological fallacy occurs when relationships observed across aggregate groups are assumed to apply to individuals.” }, { q: “What does an intraclass correlation coefficient of 0 indicate?”, options: [ “Clustering explains none of the variance; all variation exists at individual level”, “Clustering is complete; every individual within a cluster exhibits identical scores”, “The continuous outcome variable displays zero variability across the entire dataset”, “The effective sample size recruited within higher-level clusters is statistically zero”, “The bivariate linear association between two distinct manifest indicators is zero” ], answer: 0, explanation: “An ICC of 0 indicates that clustering accounts for none of the variance; single-level regression is sufficient.” }, { q: “Conversely, what would an intraclass correlation coefficient of 1 indicate?”, options: [ “No clustering exists, meaning single-level regression models are completely adequate”, “The independent predictor variables exhibit severe collinearity with each other”, “The iterative numerical estimation algorithm failed to achieve statistical convergence”, “Substantial additional sample data must be recruited before evaluating cluster effects”, “All variance is between clusters; individuals within each cluster are identical” ], answer: 4, explanation: “An ICC of 1 indicates that individuals within each cluster are identical, with all variation occurring between clusters.” }, { q: “In a random-intercepts model, what is allowed to vary between groups?”, options: [ “Only the slope of the regression line, while the baseline intercept remains fixed”, “The intercept of the regression line, while the slope remains fixed for all groups”, “Both the baseline intercept and the predictor slope simultaneously across all groups”, “Neither the intercept nor the predictor slope, constraining all trajectories to match”, “The total count of individual participants sampled within each higher-level cluster” ], answer: 1, explanation: “Random-intercept models permit each group to have its own baseline intercept while keeping predictor slopes constant.” }, { q: “What distinguishes a random-slopes model from a random-intercepts model?”, options: [ “It permits the predictor-outcome relationship (slope) to vary across clusters”, “It assumes that higher-level clusters share perfectly identical baseline values”, “It mathematically forces the baseline regression intercept to equal zero in all units”, “It is restricted strictly to modeling binary categorical outcomes rather than scales”, “It reduces model complexity by estimating fewer random parameter coefficients” ], answer: 0, explanation: “Random-slopes models allow the effect of the predictor on the outcome to vary from group to group.” }, { q: “How can repeated-measures data be viewed as a multilevel structure?”, options: [ “By defining time points as Level 2 units and individual participants as Level 1 units”, “By averaging repeated observations per participant into a single composite score”, “By assuming every sequential measurement represents a fully independent observation”, “By treating participants as Level 2 clusters with repeated occasions nested within them”, “By applying repeated-measures ANOVA, as multilevel modeling cannot handle time series” ], answer: 3, explanation: “Repeated measurements (Level 1) can be conceptualised as nested inside individual participants (Level 2).” }, { q: “What is the difference between nested and crossed data?”, options: [ “Nested structures apply exclusively to human participants; crossed structures apply to non-human items”, “In nested data, units belong to one group; in crossed data, units belong to multiple groups”, “Nested structures evaluate paired continuous comparisons; crossed structures evaluate rank correlations”, “Nested structures require strictly balanced cluster sample sizes; crossed designs accommodate unequal sizes”, “Nested and crossed hierarchies represent interchangeable terms describing identical clustered arrangements” ], answer: 1, explanation: “In nested hierarchies, units belong to a single cluster; in crossed structures, classification groups overlap.” }, { q: “How might we determine if adding a new random effect makes the model significantly better?”, options: [ “By verifying whether total recruitment sample size increases after model re-specification”, “By visually confirming that plotted regression trajectories look more aesthetic and smooth”, “By evaluating whether the estimated grand mean of the outcome variable shifts noticeably”, “By checking whether the calculated p value of the omnibus test is exactly equal to .05”, “By comparing model deviance values using a likelihood-ratio chi-squared test” ], answer: 4, explanation: “Models are compared using likelihood-ratio tests evaluating the drop in deviance against a chi-squared distribution.” }, { q: “What is a null 2-level model?”, options: [ “A model specified with an effective sample size of zero participants across all groups”, “A model that assumes higher-level clusters share perfectly identical baseline parameters”, “A model predicting outcome variance from cluster structure only, with no fixed predictors”, “A model that retains infinite degrees of freedom during numerical estimation of parameters”, “A computational model that fails to achieve iterative convergence during execution” ], answer: 2, explanation: “The null model includes only random intercepts without fixed covariates, providing the baseline partition of variance.” } ], ch15: [ { q: “In a path diagram, what distinguishes an exogenous variable from an endogenous variable?”, options: [ “Exogenous variables receive single-headed arrows; endogenous variables receive no directed arrows”, “Exogenous variables are always latent constructs; endogenous variables are always manifest indicators”, “Exogenous variables designate disturbance terms; endogenous variables represent empirical scores”, “Exogenous variables have outgoing paths only; endogenous variables receive incoming directed paths”, “Exogenous variables represent categorical factors; endogenous variables are continuous metrics” ], answer: 3, explanation: “Exogenous variables receive no directional arrows within the model; endogenous variables receive structural paths.” }, { q: “How are latent variables typically represented in a structural equation modelling path diagram?”, options: [ “As solid rectangles or squares”, “As geometric ovals or circles”, “As equilateral triangles”, “As dashed non-directional paths”, “As bold, underlined typographic text” ], answer: 1, explanation: “Unobserved latent constructs are depicted as circles or ovals; observed manifest variables are shown as rectangles.” }, { q: “What is the function of a measurement model in the context of structural equation modelling?”, options: [ “To define how unobserved latent variables are measured by observed indicators”, “To specify direct and indirect structural regressions connecting latent constructs”, “To estimate the required statistical sample size prior to structural equation testing”, “To compute the omnibus chi-squared p value for the entire causal network simultaneously”, “To screen for and trim multidimensional leverage outliers from the sample dataset” ], answer: 0, explanation: “The measurement model specifies how latent variables are measured by observed indicators.” }, { q: “What does it mean if a model is ‘just identified’ (or ‘saturated’)?”, options: [ “It possesses more observed covariances than parameters, allowing formal empirical testing”, “It cannot be mathematically solved by estimation algorithms due to insufficient information”, “It represents the poorest possible empirical representation of the underlying data structure”, “It specifies structural relationships among variables while eliminating all measurement error”, “It has zero degrees of freedom and fits the data perfectly, testing no substantive theory” ], answer: 4, explanation: “A saturated model has zero degrees of freedom and fits the data perfectly by definition, testing no scientific theory.” }, { q: “Which variable type acts as a common cause that affects two other variables, potentially creating a spurious correlation between them?”, options: [ “A collider variable”, “A mediating variable”, “A confounding variable”, “An endogenous outcome”, “A manifest indicator” ], answer: 2, explanation: “A confounder simultaneously affects two variables of interest, generating a non-causal association between them.” }, { q: “What is the defining characteristic of a collider variable?”, options: [ “It is mutually caused by two other variables of interest in the causal graph”, “It transmits the causal influence of the predictor forward to the outcome variable”, “It simultaneously influences both the independent predictor and the dependent outcome”, “It represents unmodelled measurement error associated with a manifest indicator”, “It must be recorded as an unordered nominal category rather than a continuous metric” ], answer: 0, explanation: “A collider is a variable where causal paths from two other variables meet (collide).” }, { q: “Why is it generally a mistake to statistically control for (condition on) a collider?”, options: [ “It completely eliminates all meaningful substantive variation from the measured outcome”, “It artificially reduces the recruited statistical sample size to zero during model estimation”, “It mathematically transforms the collider variable into an unobserved confounding factor”, “It inflates the standard errors of remaining predictor variables beyond acceptable bounds”, “It induces collider stratification bias, creating a spurious correlation between its causes” ], answer: 4, explanation: “Conditioning on a shared effect induces collider bias, artificially creating an association between its causes.” }, { q: “In mediation analysis, what does the indirect effect represent?”, options: [ “The direct influence of the predictor on the outcome that completely bypasses the mediator”, “The portion of the predictor’s effect that is transmitted through the intervening mediator”, “The total bivariate Pearson correlation between the predictor variable and the outcome”, “The unique disturbance and residual variance left unexplained by structural paths”, “The reciprocal reverse influence exerted by the dependent outcome back onto the predictor” ], answer: 1, explanation: “The indirect effect represents the pathway through which the predictor affects the outcome via the mediator.” }, { q: “If a variable is a mediator, what happens to the relationship between the predictor and outcome when you control for that mediator?”, options: [ “The observed relationship becomes noticeably stronger and more positive”, “The observed relationship remains entirely unchanged in magnitude and sign”, “The observed relationship is attenuated or disappears entirely”, “The observed relationship inverts to create a collider stratification bias”, “The residual error variance of the predictor variable contracts to zero” ], answer: 2, explanation: “Controlling for the mediating variable blocks that transmission pathway, diminishing the remaining direct relationship.” }, { q: “What is the meaning of the total effect in a simple mediation model?”, options: [ “The mathematical product obtained by multiplying the direct and indirect pathway coefficients”, “The numerical difference obtained by subtracting the indirect effect from the direct effect”, “The absolute numerical value of the variance accounted for within the intervening mediator”, “The arithmetic sum of the direct pathway effect and the indirect mediated effect”, “The bivariate Pearson correlation observed between the mediator and the unobserved confounder” ], answer: 3, explanation: “The total effect equals the sum of the direct effect and the indirect (mediated) effect.” } ],

ch16: [ { q: “What is the primary purpose of a meta-analysis?”, options: [ “To qualitatively narrate historical literature trends without computing numerical metrics”, “To re-analyse digital file metadata and computational scripts from a single laboratory”, “To gather new primary experimental measurements from freshly recruited clinical participants”, “To aggregate findings across related studies to calculate a pooled summary effect size”, “To formulate novel scientific hypotheses prior to beginning preliminary exploratory studies” ], answer: 3, explanation: “Meta-analysis quantitatively aggregates findings across studies to calculate a weighted summary effect size.” }, { q: “In a meta-analysis, studies are typically ‘weighted’ before being combined. What determines the weight of a study?”, options: [ “Its statistical precision (typically derived from its standard error and sample size)”, “The calendar year of publication, giving greater influence to contemporary findings”, “The academic journal impact factor and prestige of the publishing institution”, “The alphabetical order of the lead author’s surname in the reference list”, “Whether the reported empirical outcome supported or contradicted the null hypothesis” ], answer: 0, explanation: “Larger studies with smaller standard errors are more precise and receive greater weight in the pooled estimate.” }, { q: “In a forest plot, what does the diamond shape at the bottom typically represent?”, options: [ “The single study that contributed the largest total sample size to the pooled dataset”, “The presence and estimated severity of publication bias detected across the literature”, “The total count of published and unpublished studies included in the final synthesis”, “The individual outlying studies flagged for sensitivity trimming during re-analysis”, “The summary pooled effect size and its corresponding inferential confidence interval” ], answer: 4, explanation: “The diamond represents the overall summary effect size at its centre and the confidence interval across its horizontal width.” }, { q: “What is the key assumption of a fixed-effects model in meta-analysis?”, options: [ “That the true population effect sizes vary systematically across diverse study populations”, “That all included studies share a single identical underlying true population effect”, “That the sample sizes of all included studies are mathematically constrained to be equal”, “That empirical measurements within each included study contain zero random sampling error”, “That the identified studies evaluate completely unrelated constructs and methodologies” ], answer: 1, explanation: “Fixed-effects models assume that all studies share a single underlying true population effect.” }, { q: “Conversely, what does a random-effects model assume?”, options: [ “That all evaluated studies share one identical true effect in the underlying population”, “That empirical study outcomes are generated purely at random with no systematic signal”, “That observed study effects are sampled from a distribution of true population effects”, “That the standard error of the pooled effect estimate is mathematically fixed at zero”, “That calculating a pooled summary effect size is impossible due to methodological heterogeneity” ], answer: 2, explanation: “Random-effects models assume true effect sizes vary across studies due to differences in populations and methods.” }, { q: “What does the I2 statistic measure?”, options: [ “The total number of independent empirical studies retained in the final meta-analysis”, “The bivariate linear correlation between published effect sizes and study sample sizes”, “The statistical power of the pooled meta-analytic model to reject a false null hypothesis”, “The probability that the observed distribution of study findings reflects publication bias”, “The percentage of variation in observed effects due to true heterogeneity rather than sampling error” ], answer: 4, explanation: “I2 reflects the proportion of observed effect variation attributable to real between-study heterogeneity.” }, { q: “What is the file-drawer problem?”, options: [ “The tendency for non-significant findings to remain unpublished, biasing the literature”, “The physical loss of raw research datasets due to inadequate digital backup practices”, “The indexing misclassification of published journal articles into incorrect research disciplines”, “The practical difficulty of screening and retrieving excessive volumes of relevant studies”, “The computational failure of statistical software packages during complex meta-regressions” ], answer: 0, explanation: “Non-publication of non-significant results biases the published literature toward inflated effect sizes.” }, { q: “What visual tool is commonly used to check for publication bias?”, options: [ “A bivariate scatterplot matrix contrasting all continuous study covariates simultaneously”, “A branching hierarchical dendrogram displaying Euclidean distances between studies”, “A funnel plot displaying study effect sizes against their respective standard errors”, “A clustered bar chart contrasting mean outcome values across different treatment conditions”, “A standardized box-and-whisker plot highlighting extreme effect size distribution outliers” ], answer: 2, explanation: “A funnel plot plots effect size against precision; asymmetry suggests publication bias.” }, { q: “What is the difference between a confidence interval and a prediction interval in a random-effects meta-analysis?”, options: [ “The confidence interval applies to fixed-effects models; the prediction interval applies to random-effects”, “The confidence interval reflects the summary mean; the prediction interval projects a future study’s effect”, “The confidence interval evaluates 99% probability; the prediction interval evaluates 95% probability”, “The confidence interval is strictly wider than the prediction interval across all meta-analytic models”, “The two intervals represent mathematically identical bounds expressing the exact same dispersion parameter” ], answer: 1, explanation: “The confidence interval describes precision around the mean effect; the prediction interval projects the dispersion of a future study.” }, { q: “In a p curve analysis, what does a ‘pile-up’ of p values just below .05 suggest?”, options: [ “That the stated null hypothesis is definitively true across all evaluated investigations”, “That the underlying phenomenon possesses an exceptionally large and robust population effect”, “That the evaluated primary studies suffered systematically from severely underpowered sample sizes”, “That the published literature may have been distorted by p-hacking or selective reporting”, “That publication bias is absent and all conducted studies are represented in the literature” ], answer: 3, explanation: “A concentration of findings just below .05 is an empirical diagnostic of p-hacking or publication filtering.” } ], ch17: [ { q: “What is the main difference between the frequentist and Bayesian views of probability?”, options: [ “Frequentists view probability as subjective belief; Bayesians define it as objective frequency”, “Frequentists incorporate informative priors; Bayesians rely exclusively on empirical likelihoods”, “Frequentists evaluate distributions using medians; Bayesians evaluate models using trimmed means”, “Frequentists define probability as long-run frequency; Bayesians view it as degree of belief”, “There is no conceptual difference; both frameworks calculate posterior probabilities identically” ], answer: 3, explanation: “Frequentists view probability as long-run frequency over repeated trials; Bayesians view it as a degree of certainty updated by evidence.” }, { q: “How does a Bayesian credible interval differ from a frequentist confidence interval?”, options: [ “A credible interval allows direct probability statements about the parameter; a confidence interval does not”, “A credible interval is mathematically guaranteed to be strictly wider than any confidence interval”, “A credible interval treats parameters as fixed constants; a confidence interval treats parameters as random”, “A confidence interval allows direct probability statements about the parameter; a credible interval does not”, “A credible interval can only be estimated manually, whereas confidence intervals require algorithms” ], answer: 0, explanation: “A Bayesian credible interval permits direct probability statements about parameter location given the data and prior.” }, { q: “What is the concept of inverse probability?”, options: [ “The mathematical probability that an observed experimental outcome failed to occur”, “The probability of committing a false-positive decision error during hypothesis testing”, “The inversion between the probability of data given a hypothesis, and hypothesis given data”, “The reciprocal quotient obtained by dividing one by the frequentist p value”, “The prior baseline probability assigned to an alternative directional scientific model” ], answer: 2, explanation: “Inverse probability concerns inverting conditional likelihoods: P(Data | Hypothesis) versus P(Hypothesis | Data).” }, { q: “What is a prior distribution?”, options: [ “The empirical frequency distribution of the data collected in the current investigation”, “The final updated parameter distribution computed at the conclusion of the Bayesian analysis”, “A theoretical probability density function that is mathematically constrained to be normal”, “The theoretical sampling distribution of sample means generated across infinite replications”, “A probability distribution representing parameter knowledge or beliefs before observing new data” ], answer: 4, explanation: “The prior represents beliefs or existing knowledge about a parameter before collecting new data.” }, { q: “What is a posterior distribution?”, options: [ “The initial baseline belief about parameter values prior to gathering experimental observations”, “The updated belief about a parameter after combining the prior distribution with observed data”, “The empirical distribution of vertical residuals remaining unexplained by the fitted model”, “The theoretical sampling distribution expected under the assumption of a true null hypothesis”, “A uniform probability distribution that completely ignores the observed empirical dataset” ], answer: 1, explanation: “The posterior distribution is the updated state of knowledge obtained by combining the prior with the observed data via Bayes’ rule.” }, { q: “When would a researcher use an uninformative (or flat) prior?”, options: [ “When they hold strong empirical certainty regarding parameter values prior to beginning testing”, “When they wish to force the posterior distribution to achieve conventional statistical significance”, “When they want the data to drive the posterior with minimal influence from prior beliefs”, “When recruited sample sizes are exceptionally small and require artificial stabilization”, “When carrying out traditional null-hypothesis significance testing within frequentist bounds” ], answer: 2, explanation: “An uninformative prior spreads probability evenly across parameters so that sample data dominates the posterior.” }, { q: “What is a Bayes factor?”, options: [ “The posterior probability that the stated null hypothesis is definitively true in reality”, “The standard deviation and dispersion parameter of the derived posterior distribution”, “A familywise correction factor applied to control the Type 1 error rate in multiple contrasts”, “The estimated residual disturbance term left unexplained by structural model pathways”, “A metric quantifying the relative evidence in the data for one hypothesis versus another” ], answer: 4, explanation: “A Bayes factor quantifies the relative predictive performance of two competing scientific hypotheses.” }, { q: “If you obtain a Bayes factor of 0.20 in favour of the alternative hypothesis, what does this tell you?”, options: [ “The alternative hypothesis is five times more supported by the data than the null”, “The observed empirical result is statistically significant at the conventional alpha level”, “A computational error was committed because Bayes factors cannot fall below one”, “The observed data provide evidence against the alternative hypothesis (supporting the null)”, “The posterior probability that the null hypothesis is factually true is exactly twenty percent” ], answer: 3, explanation: “A Bayes factor of 0.20 in favour of H1 represents 1 / 0.20 = 5 in favour of H0, supporting the null.” }, { q: “Which of these is a notable advantage of Bayesian hypothesis testing over frequentist hypothesis testing?”, options: [ “It calculates exact p values with greater numerical precision in small observational datasets”, “It can quantify positive evidence supporting the null, rather than only failing to reject it”, “It completely eliminates the mathematical requirement for digital computing software during estimation”, “It guarantees that empirical analyses will produce statistically significant parameter estimates”, “It allows researchers to draw valid inferential conclusions without collecting empirical data” ], answer: 1, explanation: “Bayesian testing can provide positive evidence supporting the null, whereas frequentist tests can only fail to reject it.” }, { q: “If the Bayes factor for the alternative hypothesis is 4, what is the Bayes factor for the null hypothesis?”, options: [ “0.25 (the reciprocal value: 1 / 4)”, “4.00 (the identical value: 4 / 1)”, “-4.00 (the negative inverse value)”, “0.00 (representing zero support)”, “40.0 (the scaled tenfold value)” ], answer: 0, explanation: “Competing Bayes factors are reciprocal values: 1 / 4 = 0.25.” } ], ch18: [ { q: “Which of the following is an example of data cleaning?”, options: [ “Computing summary metrics such as the sample mean and standard deviation”, “Executing a two-sample Student’s t test to contrast two experimental groups”, “Generating a publication-ready histogram illustrating the final observed scores”, “Investigating an impossible score (e.g. 3-metre height) for potential entry error”, “Drafting the qualitative interpretation section of a formal research report” ], answer: 3, explanation: “Data cleaning involves identifying and resolving errors, missing values, and outliers before conducting statistical analysis.” }, { q: “Why is standard deviation usually preferred over variance for describing the spread of data in a research report?”, options: [ “Because variance is mathematically capable of taking negative numerical values”, “Because standard deviation is in original measurement units rather than squared units”, “Because sample variance can only be computed on unordered categorical metrics”, “Because the standard deviation is mathematically constrained to be smaller than the mean”, “Because modern statistical software packages cannot compute sample variance directly” ], answer: 1, explanation: “Taking the square root converts the squared units of variance back into the native units of the raw variable.” }, { q: “What does it mean if a distribution of data is skewed?”, options: [ “The observations are distributed in perfect mirror symmetry around the central mean”, “The sample mean, median, and mode are all located at the exact same numeric coordinate”, “The recruited sample size is statistically inadequate for conducting inferential testing”, “The calculated standard deviation across all observed scores is equal to zero”, “The distribution has an extended tail on one side, making it asymmetrical around the center” ], answer: 4, explanation: “Skew describes asymmetry where a prolonged tail on one side pulls the mean away from the median.” }, { q: “In hypothesis testing, what is a p value?”, options: [ “The probability of data as extreme as observed, assuming the null hypothesis holds true”, “The probability that the proposed alternative scientific hypothesis is factually true”, “The probability that the principal investigator committed a clerical error during analysis”, “The exact arithmetic parameter value of the underlying target population mean”, “The proportion of recruited participants who completed all assigned testing protocols” ], answer: 0, explanation: “The p value measures the likelihood of observing sample data at least as extreme as the current data assuming the null hypothesis holds true.” }, { q: “What is the standard error of the mean?”, options: [ “The standard deviation of raw observation scores in the target population”, “The average measurement error introduced by clerical data-entry mistakes”, “The standard deviation of the theoretical sampling distribution of the mean”, “The absolute discrepancy between the maximum and minimum observed sample values”, “The total proportion of missing records across the collected experimental dataset” ], answer: 2, explanation: “Standard error quantifies the dispersion of sample means across repeated theoretical sampling from the population.” }, { q: “Which of these statistical tests would be most appropriate to compare the mean test scores of three different groups of students (e.g., Class A, Class B, and Class C)?”, options: [ “An independent-samples Student’s t test”, “A paired-samples repeated t test”, “A chi-squared test of contingency independence”, “A one-way Analysis of Variance (ANOVA)”, “A bivariate Pearson correlation coefficient” ], answer: 3, explanation: “A one-way ANOVA evaluates equality of means across three or more groups while controlling the type 1 error rate.” }, { q: “In a linear regression model, what does the coefficient of determination (R-squared) tell you?”, options: [ “The steepness and directional sign of the fitted linear regression slope”, “The exact omnibus p value evaluating the statistical significance of the model”, “The total count of observations flagged as bivariate outliers along the line”, “The standardized Pearson correlation coefficient between independent predictors”, “The proportion of variance in the outcome variable accounted for by the predictor(s)” ], answer: 4, explanation: “The coefficient of determination (R2) reflects the proportion of outcome variance explained by the predictor set.” }, { q: “What is the purpose of partial correlation?”, options: [ “To compute the correlation between two variables using half of the available records”, “To quantify the non-linear monotonic association between two categorical variables”, “To measure the relationship between two variables while controlling for a third”, “To estimate unknown population parameters while tolerating substantial missing data”, “To test whether the bivariate correlation coefficient differs from zero” ], answer: 2, explanation: “Partial correlation measures the unique association between two variables while holding third-variable influences constant.” }, { q: “What is multilevel modelling used for?”, options: [ “To analyse hierarchical or clustered data that violate the assumption of independence”, “To construct multi-panel data visualisations employing varied colour palettes”, “To conduct inferential regression analyses on models containing only one variable”, “To carry out systematic meta-analyses restricted exclusively to unpublished studies”, “To compute non-parametric median scores across small independent pilot samples” ], answer: 0, explanation: “Multilevel models account for correlated residuals and non-independence arising from hierarchical nesting structures.” }, { q: “What is a Bayes factor used for?”, options: [ “To calculate the dispersion and standard deviation of an empirical sample distribution”, “To quantify the relative strength of empirical evidence for two competing hypotheses”, “To determine the minimum sample size required to attain desired statistical power”, “To detect and resolve accidental clerical data-entry errors in raw spreadsheets”, “To plot the shape and skewness of an unobserved continuous probability density function” ], answer: 1, explanation: “The Bayes factor provides a continuous weight of relative empirical evidence in favour of one competing model over another.” } ]