Q: The F statistic in ANOVA is calculated as:

$$ F = \frac{\text{Between-group variance}}{\text{Within-group variance}} $$

Q: Which of the following is the correct formula for the effect size $$\$$eta^2$$ (eta squared) in ANOVA?

$$ \$$eta^2$$ = \frac{SS_{\text{between}}}{SS_{\text{total}}} $$

Question 1

Which of the following best describes the primary purpose of an Analysis of Variance (ANOVA)?

Accepted Answer

To determine whether the means of three or more groups are significantly different from each other.

Question 2

In a one-way ANOVA, what is the independent variable and what is the dependent variable?

Accepted Answer

The independent variable is categorical and the dependent variable is always quantitative.

Question 3

Which of the following is NOT an assumption of ANOVA?

Accepted Answer

The data are paired.

Question 4

Suppose you conduct a one-way ANOVA and obtain a significant F statistic. What is the next step you should take?

Accepted Answer

Conduct post-hoc pairwise comparisons to determine which group means differ.

Question 5

The F statistic in ANOVA is calculated as:

Accepted Answer

$$ F = \frac{	ext{Between-group variance}}{	ext{Within-group variance}} $$

Question 6

A researcher wants to know if anxiety levels differ among patients with inflammatory bowel disease (IBD), irritable bowel syndrome (IBS), and healthy controls. Which statistical test is most appropriate?

Accepted Answer

One-way ANOVA

Question 7

Which of the following statements about the interpretation of a significant ANOVA result is correct?

Accepted Answer

At least one group mean is significantly different from the others.

Question 8

If the sample variances are not equal (i.e., the homogeneity of variance assumption is violated), which of the following is a potential consequence for ANOVA results?

Accepted Answer

The Type I error rate may increase, leading to incorrect conclusions.

Question 9

In the context of ANOVA, what does a large F statistic indicate?

Accepted Answer

There is more variability between group means than within groups, suggesting significant differences.

Question 10

Which of the following is the correct formula for the effect size $$\$$eta^2$$ (eta squared) in ANOVA?

Accepted Answer

$$ \$$eta^2$$ = \frac{SS_{	ext{between}}}{SS_{	ext{total}}} $$

Question 11

A study finds a significant ANOVA result for mean anxiety scores among three groups. The post-hoc test shows that group A differs from group B, but not from group C. What does this imply?

Accepted Answer

Only group A and group B have significantly different means; group A and group C do not differ significantly.

Question 12

Which of the following is a real-world example where a one-way ANOVA would be appropriate?

Accepted Answer

Comparing average cholesterol levels among people following three different diets.

Question 13

In SPSS, which table provides the F statistic and significance value for an ANOVA?

Accepted Answer

The ANOVA table

Question 14

If the p-value for the F statistic in an ANOVA is less than 0.05, what should you conclude?

Accepted Answer

There is a statistically significant difference among the group means.

Question 15

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

Accepted Answer

The variability of scores within each group, reflecting individual differences not explained by group membership.

Question 16

A researcher finds $$ \$$eta^2$$ = 0.15  in an $$ANOVA study. According to the guidelines, how should this effect size be interpreted?

Accepted Answer

Medium effect

Question 17

Which of the following is a key difference between a t-test and a one-way ANOVA?

Accepted Answer

A t-test compares two means, while ANOVA can compare three or more means.

Question 18

Which of the following would violate the independence assumption in ANOVA?

Accepted Answer

Measuring anxiety in the same group of patients before and after treatment.

Question 19

In an ANOVA, what does the 'between-group variance' represent?

Accepted Answer

The variability of group means around the overall mean.

Question 20

A health researcher uses ANOVA to compare mean anxiety scores among three patient groups. The F statistic is not significant. What is the most appropriate interpretation?

Accepted Answer

There is no evidence that the mean anxiety scores differ among the groups.

Analysis of Variance (ANOVA) in Applied Statistics for Health Sciences

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