Question 1

Why is it inappropriate to use multiple $t$ tests instead of a one-way between-groups ANOVA when comparing three or more groups?

Accepted Answer

Because multiple $t$ tests increase the probability of a Type I error and inflate alpha.

Question 2

Which of the following is an assumption of all ANOVAs?

Accepted Answer

Samples must be randomly selected, normally distributed, and homoscedastic.

Question 3

What does the $F$ statistic in a one-way between-groups ANOVA represent?

Accepted Answer

The ratio of between-groups variability to within-groups variability.

Question 4

Given the following sums of squares: $SS_{between} = 461.643$, $SS_{within} = 167.419$, and $SS_{total} = 629.074$, what is the effect size $R^2$ for this ANOVA?

Accepted Answer

$R^2 = \frac{461.643}{629.074}$

Question 5

A researcher conducts a one-way between-groups ANOVA with three groups and obtains $F = 8.27$. The critical value at $\alpha = 0.05$ is $3.86$. What should the researcher conclude?

Accepted Answer

Reject the null hypothesis; there is a significant difference between group means.

Question 6

Which post hoc test is commonly used after a significant ANOVA to determine which group means differ?

Accepted Answer

Tukey HSD test

Question 7

What is the formula for the degrees of freedom for the between-groups variance in a one-way ANOVA with $k$ groups?

Accepted Answer

$df_{between} = k - 1$

Question 8

In the context of ANOVA, what does homoscedasticity mean?

Accepted Answer

All groups have equal variances.

Question 9

If you have four groups with 20 participants each, what is the total degrees of freedom for the within-groups variance?

Accepted Answer

$df_{within} = 80 - 4 = 76$

Question 10

Which of the following best describes a one-way between-groups ANOVA?

Accepted Answer

A hypothesis test with one nominal variable with more than two levels and a scale dependent variable.

Question 11

What is the main advantage of using ANOVA over multiple $t$ tests when comparing more than two groups?

Accepted Answer

ANOVA controls the overall Type I error rate.

Question 12

Which formula correctly calculates the mean square between groups ($MS_{between}$) in ANOVA?

Accepted Answer

$MS_{between} = \frac{SS_{between}}{df_{between}}$

Question 13

A researcher finds a significant $F$ statistic in a one-way ANOVA. What is the next appropriate step?

Accepted Answer

Conduct post hoc tests to determine which groups differ.

Question 14

Which of the following is the correct formula for the Tukey HSD test statistic?

Accepted Answer

$HSD = \frac{M_1 - M_2}{s_M}$

Question 15

If the calculated $F$ statistic is less than the critical value from the $F$ table, what is the correct decision?

Accepted Answer

Fail to reject the null hypothesis.

Question 16

Which of the following is NOT a type of variance estimated in ANOVA?

Accepted Answer

Paired variance

Question 17

What is the main purpose of the source table in ANOVA?

Accepted Answer

To summarize the sources of numerical variability and calculations.

Question 18

Which of the following best describes the logic behind the $F$ statistic in ANOVA?

Accepted Answer

It quantifies the overlap between group means and variances.

One-Way Between-Groups ANOVA: Principles, Calculations, and Interpretation

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