Question 1

Why is it not advisable to use multiple independent t-tests to compare the means of four or more groups?

Accepted Answer

Because using multiple t-tests increases the probability of making at least one Type I error.

Question 2

Suppose a researcher compares the means of 5 groups using all possible pairwise t-tests at $$\alpha = 0.05. $$What is the probability of making at least one Type I error across all tests?

Accepted Answer

$$1 - (1 - 0.05$$)^{10}$$ = 0.4013$$

Question 3

Which of the following best describes the null hypothesis in a one-way ANOVA?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \cdots = \mu_k$$

Question 4

What does the F statistic in ANOVA represent?

Accepted Answer

The ratio of between-group mean square to within-group mean square.

Question 5

Given the following ANOVA summary: $$SS_{Between} = 300$$, $$df_{Between} = 3$$, $$SS_{Within} = 600$$, $$df_{Within} = 16. $$What is the value of the F statistic?

Accepted Answer

$$F = \frac{100}{37.5} = 2.67$$

Question 6

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

Accepted Answer

The response variable is categorical.

Question 7

A clinical trial compares the effect of four cholesterol-lowering drugs on LDL reduction. The ANOVA F test is significant. What is the next appropriate step?

Accepted Answer

Conduct post-hoc tests to determine which pairs of drugs differ.

Question 8

Which post-hoc method controls the family-wise error rate and is less conservative than Bonferroni?

Accepted Answer

Tukey's HSD

Question 9

How is the critical value for Tukey's HSD calculated for equal group sizes?

Accepted Answer

$$HSD = q_\alpha \sqrt{\frac{MS_{Error}}{n}}$$

Question 10

In the context of ANOVA, what does 'between-group variability' measure?

Accepted Answer

Variability due to differences among group means.

Question 11

A researcher finds $$p = 0.013$$ for the F test in an ANOVA comparing three fertilizers. What does this imply at $$\alpha = 0.05$$?

Accepted Answer

There is sufficient evidence to conclude that at least one fertilizer mean differs from the others.

Question 12

Which of the following best describes the family-wise error rate?

Accepted Answer

The probability of making at least one Type I error across a set of comparisons.

Question 13

If the F statistic is close to 1 in a one-way ANOVA, what does this suggest?

Accepted Answer

The variability between group means is similar to the variability within groups.

Question 14

Which of the following is a valid reason for using ANOVA instead of multiple t-tests?

Accepted Answer

ANOVA controls the overall Type I error rate when comparing multiple groups.

Question 15

Which of the following is NOT a common post-hoc method after a significant ANOVA?

Accepted Answer

Linear regression

Question 16

A plant growth experiment yields the following ANOVA results: $$F = 9.0625$$, $$p = 0.0004. $$What is the correct interpretation?

Accepted Answer

There is strong evidence that at least one fertilizer mean is different from the others.

Question 17

Which of the following statements about Tukey's HSD is TRUE?

Accepted Answer

It controls the family-wise error rate for all pairwise comparisons.

Question 18

What is the formula for the total sum of squares in ANOVA?

Accepted Answer

$$SS_{Total} = \sum_{i=1}^m \sum_{j=1}^{n_i} (y_{ij} - \bar{y})^2$

Question 19

Which scenario best illustrates the use of a post-hoc test?

Accepted Answer

After finding a significant ANOVA F test for cholesterol-lowering drugs, comparing each pair of drugs to see which differ.

Analysis of Variance (ANOVA): Comparing Multiple Means

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