Lecture 7A: One-way ANOVA

Question 1

What is a key reason for not using multiple t-tests when comparing more than 2 groups/means?

Answer 1

• Cumulative error increases the probability of Type I error.
• Use ANOVA instead

Question 2

What is the formula for cumulative error in independent t-tests?

Answer 2

αΣ = 1 - (1 - α)ᶜ

• c is the no. of comparisons
• as the no. of comparisons increases, the cumulative error increases

Question 3

What are the two sources of variation in one-way ANOVA?

Answer 3

• Between-groups variance (MSB)
• Within-groups variance (MSW)

Question 4

What does the F statistic in one-way ANOVA represent?

Answer 4

F = MSB / MSW

Question 5

In one-way ANOVA, what happens to the F statistic if the sample size is increased?

Answer 5

• Increased MSB (larger differences between groups)
• Decreased MSW (smaller differences within groups)
• F increases

Question 6

What is the significance of the p-value in one-way ANOVA?

Answer 6

It indicates the probability of obtaining an F-value equal to or larger than the F in your study, if the null hypothesis is true (no sig. diff.)

Question 7

What conclusion is reached when p=0.422 in one-way ANOVA?

Answer 7

Do not reject the null hypothesis.

Question 8

What is the purpose of post-hoc tests following one-way ANOVA?

Answer 8

• One-way ANOVA: only determines if statistical significance exists among 3 or more
  means
• Post-hoc ANOVA: determines which specific comparisons are significant

Question 9

Name the types of post-hoc tests mentioned.

Answer 9

• SNK test
• Tukey’s test
• Scheffe test

Question 10

Fill in the blank: In one-way ANOVA, if p < α, we _______ the null hypothesis.

Answer 10

reject