Question 1

Why is it inappropriate to use multiple t-tests instead of ANOVA when comparing the means of three or more groups?

Accepted Answer

Because multiple t-tests increase the family-wise error rate, inflating the probability of making a Type I error.

Question 2

Which formula correctly calculates the family-wise error rate for $$c$$ comparisons, each at significance level $$\alpha$$?

Accepted Answer

$$\alpha_{c} = 1 - (1 - \$$alpha)^{c}$$

Question 3

In a one-way independent ANOVA, what does the F-ratio represent?

Accepted Answer

The ratio of the experimental variance (signal) to the random variance (noise).

Question 4

Given $$SS_{model} = 34.11$$, $$df_{model} = 2$$, $$SS_{error} = 19.33$$, and $$df_{error} = 6$$, what is the F-ratio?

Accepted Answer

$$F = \frac{34.11/2}{19.33/6} = \frac{17.055}{3.222} = 5.30$$

Question 5

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

Accepted Answer

Ordinal measurement of the dependent variable

Question 6

What does Levene’s test assess in the context of ANOVA?

Accepted Answer

Whether the variances of the groups are equal (homogeneity of variance)

Question 7

If Levene’s test is significant, which post-hoc test is most appropriate for comparing group means in ANOVA?

Accepted Answer

Games-Howell

Question 8

In a repeated measures ANOVA, what additional assumption must be checked compared to an independent ANOVA?

Accepted Answer

Sphericity

Question 9

Which test is used to check the assumption of sphericity in repeated measures ANOVA?

Accepted Answer

Mauchly’s test

Question 10

If Mauchly’s test is significant and $$\epsilon \u003c 0.75$$, which correction should be applied to the degrees of freedom in repeated measures ANOVA?

Accepted Answer

Greenhouse-Geisser correction

Question 11

A researcher wants to compare the effect of three types of therapy on depression scores. The data are interval, normally distributed, and group variances are equal. Which statistical test should be used?

Accepted Answer

One-way independent ANOVA

Question 12

What is the main advantage of a repeated measures design over an independent groups design?

Accepted Answer

It controls for individual differences by testing the same participants in all conditions.

Question 13

Which of the following best describes a factorial ANOVA?

Accepted Answer

An ANOVA with more than one independent variable, each with multiple levels.

Question 14

If the F-ratio in an ANOVA is much less than 1, what does this suggest about the effect of the independent variable?

Accepted Answer

The random variance is greater than the experimental variance, so the effect is likely not significant.

Question 15

A psychologist runs a one-way ANOVA and finds $$F(2, 6) = 10.59, p = .011. $$What does this result indicate?

Accepted Answer

There is a significant difference between at least two group means.

Question 16

Which of the following is a reason to use post-hoc tests after finding a significant ANOVA result?

Accepted Answer

To determine which specific group means differ from each other.

Question 17

What is the purpose of the Bonferroni correction in multiple comparisons?

Accepted Answer

To control the family-wise error rate by adjusting the significance threshold.

Question 18

In a repeated measures ANOVA, the assumption of sphericity is violated. The Greenhouse-Geisser correction is applied, and the main effect is significant. What does this mean?

Accepted Answer

The effect is significant, but the degrees of freedom have been adjusted to account for the violation.

Question 19

Which of the following is an example of a planned comparison in ANOVA?

Accepted Answer

Comparing group A to group B because you hypothesized this difference before collecting data.

Analysis of Variance (ANOVA): Concepts, Assumptions, and Applications

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