Question 1

In the context of ANOVA, what does a significant F-test (e.g., $$F = 9.231$$, $$p \u003c .001) $$indicate about the group means?

Accepted Answer

At least one group mean is different from the others.

Question 2

After finding a significant ANOVA result, why is it important to conduct post-hoc tests such as Tukey, Scheffe, or Bonferroni?

Accepted Answer

To determine which specific group means differ from each other.

Question 3

If you conduct three pairwise t-tests after a significant ANOVA with $$\alpha = .05$$, what is the actual familywise error rate?

Accepted Answer

$$\alpha = 1 - .95^3$ = .143$$

Question 4

Which of the following is NOT an assumption of the standard ANOVA F-test?

Accepted Answer

The dependent variable is measured on an ordinal scale.

Question 5

Given the regression model summary with $$R^2 = .917$, what does this value represent?

Accepted Answer

91.7% of the variance in the dependent variable is explained by the predictors.

Question 6

A 95% confidence interval for a mean is calculated as $$\bar{x} \pm 1.96 	imes SE. If$$ $$\bar{x} = 4.738$$ and $$SE = 0.0376$$, what is the lower bound of the interval?

Accepted Answer

$$4.738 - 0.0737 = 4.6643 ($$rounded), but the correct calculation is $$4.738 - 0.0737 = 4.6643$$; however, the value from the notes is $$4.5937.$$

Question 7

Which nonparametric test is appropriate for comparing the distributions of a continuous variable across three independent groups?

Accepted Answer

Kruskal-Wallis test

Question 8

In multiple regression, which of the following is a key assumption for obtaining unbiased estimates of regression coefficients?

Accepted Answer

All relevant predictors are included in the model.

Question 9

What is the main advantage of using nonparametric tests like the Kruskal-Wallis or Wilcoxon tests?

Accepted Answer

They do not require assumptions about the distribution of the data.

Question 10

If the 95% confidence interval for the difference between two means is $$0.59487 \leq 0.72046 \leq 0.84605$$, what does this imply?

Accepted Answer

Zero is not included in the interval, so the difference is statistically significant.

Question 11

Which effect size measure is commonly used to describe the magnitude of difference between two means?

Accepted Answer

Cohen’s d

Question 12

In the context of the Kruskal-Wallis test, what does a significant result (e.g., $$p = .002) $$indicate?

Accepted Answer

At least one group distribution differs from the others.

Question 13

Which of the following statements about the Wilcoxon signed-rank test is TRUE?

Accepted Answer

It is used for two dependent samples.

Question 14

Why is it important to control for Type I error when conducting multiple comparisons after ANOVA?

Accepted Answer

To avoid inflating the probability of making a false positive conclusion.

Question 15

Given the regression coefficients table, which predictor has the largest standardized effect on perceived learning?

Accepted Answer

Student Motivation

Question 16

Which of the following best describes the relationship shown in the scatterplot of regression standardized predicted value vs. perceived learning?

Accepted Answer

A strong positive linear relationship

Question 17

If the adjusted $$R^2 in a $$regression model is much lower than the $$R^2$$, what might this indicate?

Accepted Answer

The model may be overfitting the data.

Question 18

Which of the following is a correct interpretation of a 95% confidence interval for a mean?

Accepted Answer

We are 95% confident that the population mean lies within the interval.

Question 19

Which of the following is NOT a reason to use nonparametric tests?

Accepted Answer

The data are perfectly normally distributed.

Advanced Topics in ANOVA, Regression, and Nonparametric Statistics: A Study Guide

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