Question 1

Which of the following best describes the main purpose of a one-way ANOVA?

Accepted Answer

To compare the means of three or more groups to determine if at least one group mean is significantly different from the others.

Question 2

In the context of ANOVA, what does the 'factor' refer to?

Accepted Answer

The independent variable that defines the groups being compared.

Question 3

Given the formula $$F = \frac{	ext{Between-group variance}}{	ext{Within-group variance}}$$, what does a large F ratio indicate?

Accepted Answer

The between-group variance is much larger than the within-group variance, suggesting at least one group mean differs significantly.

Question 4

Which of the following is an assumption of one-way ANOVA?

Accepted Answer

The variances across groups are approximately equal (homogeneity of variance).

Question 5

A researcher wants to compare the average happiness scores among three groups: no puppies, 10 minutes with puppies, and 30 minutes with puppies. What is the null hypothesis for this ANOVA?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \$$mu_3$$

Question 6

Which formula correctly represents the calculation of the total sum of squares in ANOVA?

Accepted Answer

$$SS_{Total} = \sum (x_i - \overline{x})^2$

Question 7

In the Pew generational study, 'generation' is used as the independent variable (factor). Which of the following are the levels of this factor?

Accepted Answer

Gen Z, Millennials, Gen X, Boomers and older

Question 8

Why is it problematic to use multiple t-tests instead of an ANOVA when comparing more than two groups?

Accepted Answer

It increases the risk of Type I error (family-wise error rate).

Question 9

What is the formula for eta squared ($$\$$eta^2$$), the effect size in one-way ANOVA?

Accepted Answer

$$\$$eta^2$$ = \frac{SS_{Between}}{SS_{Total}}$$

Question 10

If an ANOVA yields $$\$$eta^2$$ = 0.08$$, how would you interpret the effect size according to Table 9.1?

Accepted Answer

Medium

Question 11

After finding a significant F ratio in a one-way ANOVA, what is the next appropriate step?

Accepted Answer

Conduct post hoc tests (e.g., Tukey's) to determine which group means differ.

Question 12

Which of the following best describes 'within-group variance' in the context of ANOVA?

Accepted Answer

Variance due to natural variability among individuals within each group.

Question 13

Given the formulas $$SS_{Between} = \sum n_j (\overline{x}_j - \overline{x})^2$ and SS$$_{Within} = \sum (x_i - \overline{x}_$$j)^2$$, what does $$n_j$$ represent?

Accepted Answer

The number of participants in group $$j.$$

Question 14

A study finds $$F(3, 36) = 4.25, p = 0.01, \$$eta^2$$ = 0.15. $$How should the effect size be interpreted?

Accepted Answer

Large effect

Question 15

Which post hoc test is commonly used after a significant one-way ANOVA to compare all possible group pairings?

Accepted Answer

Tukey's HSD test

Question 16

In the context of the Pew generational study, which of the following would be an example of within-group variance?

Accepted Answer

Differences in climate change attitudes among Millennials.

Question 17

Which of the following is NOT an assumption of one-way ANOVA?

Accepted Answer

The dependent variable must be categorical.

Question 18

If you run three t-tests at $$\alpha = 0.05$$ each, what is the approximate family-wise error rate?

Accepted Answer

0.14

Question 19

Which of the following best explains why ANOVA is preferred over multiple t-tests for comparing more than two groups?

Accepted Answer

ANOVA controls the overall Type I error rate across all comparisons.

Analysis of Variance (ANOVA): Comparing More Than Two Groups

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