Quantitative Methods Final Exam Recap

A comprehensive set of practice questions and answers based on the Quantitative Methods Final Exam Recap Guide, covering introductory statistics, various t-tests and ANOVAs, non-parametric alternatives, correlation, regression, moderation, and mediation.

What is the difference between descriptive and inferential statistics?

Descriptive statistics summarize, organize, and simplify data (e.g., mean, mode, standard deviation), while inferential statistics use sample data to make conclusions about a wider population (e.g., t-tests, ANOVA).

Define the four scales of measurement: nominal, ordinal, interval, and ratio.

Nominal involves categories with names; Ordinal involves ordered categories; Interval has equal intervals without a true zero; Ratio has equal intervals with a true zero.

What is a confounding variable?

A variable related to both the independent variable (IV) and dependent variable (DV) that can distort interpretation of the results.

Contrast Type I and Type II errors.

Type I error is a false positive (rejecting $H_0$ when it is true), whereas Type II error is a false negative (failing to reject $H_0$ when it is false).

How does the Bonferroni correction address family-wise error?

It reduces the risk by dividing the alpha level ($0.05$) by the number of statistical comparisons conducted.

When should the median be used instead of the mean as a measure of central tendency?

The median is more appropriate when the distribution is skewed or contains extreme outliers, as the mean is sensitive to extreme values.

Which normality tests are used based on sample size ($n$)?

Shapiro-Wilk is commonly used when $n < 50$, while Kolmogorov-Smirnov is used when $n > 50$.

What is the difference between chi-square goodness-of-fit and chi-square test of independence?

Goodness-of-fit tests one nominal variable against expected frequencies; the test of independence tests whether two nominal variables are associated with each other.

What is the primary assumption for expected frequencies in a chi-square test?

Expected frequency must be at least $1$ in every cell, and no more than $20\%$ of cells should have an expected frequency below $5$.

What is the purpose of Levene's test in an independent-samples t-test?

It checks the homogeneity of variance; if $p > .05$, equal variances are assumed, but if $p < .05$, a corrected row of data must be used.

Identify the non-parametric equivalents for the independent-samples t-test and paired-samples t-test.

The Mann-Whitney U test is the non-parametric equivalent for the independent-samples t-test, and the Wilcoxon signed-rank test is the equivalent for the paired-samples t-test.

How is the F-ratio defined in ANOVA?

The F-ratio is the explained variance (variance between group means) divided by the unexplained variance (variance within groups).

When should Greenhouse-Geisser corrections be applied in a within-subjects ANOVA?

They are used when the assumption of sphericity is violated.

Define 'main effect' and 'interaction effect' in a two-way ANOVA.

A main effect is the independent influence of one IV on the DV regardless of the other IV; an interaction effect occurs when the effect of one IV depends on the level of another IV.

What are the non-parametric alternatives to one-way between-subjects and within-subjects ANOVA?

Kruskal-Wallis H test is the alternative for between-subjects ANOVA, and the Friedman test is the alternative for within-subjects ANOVA.

Differentiate between Pearson and Spearman correlation.

Pearson is used for two continuous, normally distributed variables with a linear relationship; Spearman is non-parametric and used for ordinal data, non-normal data, or monotonic relationships.

In regression, what does the R-square ($R^2$) value represent?

It shows how much variance in the outcome variable is explained by the predictor or the entire model (e.g., $R^2 = .79$ means $79\%$ variance explained).

What is multicollinearity and why is it a problem in multiple regression?

It occurs when predictors are highly correlated with each other, making it difficult to interpret the unique contribution of each individual predictor.

What is the core focus of Moderation analysis?

It explains when, for whom, or under what conditions a relationship changes by examining the interaction effect ($X \times W$) between an IV ($X$) and a moderator ($W$).

What is the primary difference between Mediation and Moderation?

Mediation asks 'how' or 'why' an effect happens (the mechanism), while moderation asks 'when' or 'for whom' the effect changes.

How is a significant indirect effect determined in mediation analysis?

The indirect effect ($a \times b$) is significant if the bootstrapped confidence interval (often using $5000$ samples) does not include $0$.

Distinguish between partial and full mediation.

Partial mediation occurs when the indirect effect is significant and the direct effect remains significant; full mediation occurs when the indirect effect is significant but the direct effect is no longer significant.