Friedmans ANOVA

Question 1

What is Friedman’s ANOVA?

Answer 1

A non-parametric test used to compare 3 or more related groups (within-subjects design) when assumptions of repeated measures ANOVA are violated.

Question 2

When is Friedman’s ANOVA used?

Answer 2

When you have ordinal/ranked data, repeated measures design, and non-normal distribution.

Question 3

What is the non-parametric alternative to a repeated measures t-test?

Answer 3

Wilcoxon Signed-Rank Test.

Question 4

What is Friedman’s ANOVA an alternative to?

Answer 4

Repeated Measures One-Way ANOVA.

Question 5

What assumption of RM ANOVA does Friedman’s ANOVA avoid?

Answer 5

Normality assumption

Question 6

What are your three options if normality is violated in RM ANOVA?

Answer 6

1) Continue if robust
2) Transform data
3) Use a non parametric test

Question 7

How can normality be tested in JASP?

Answer 7

Shapiro-Wilk test, skewness, kurtosis, histograms, Q-Q plots.

Question 8

What does a significant Shapiro-Wilk test indicate?

Answer 8

Data significantly deviate from normal distribution.

Question 9

What indicates normality in a histogram?

Answer 9

Rough symmetric, bell shaped distribution

Question 10

What indicates normality in a Q-Q plot?

Answer 10

Data points closely follow the diagonal line.

Question 11

What is sphericity?

Answer 11

The assumption that variances between all repeated conditions are equal.

Question 12

How do you test sphericity?

Answer 12

Mauchly’s Test of Sphericity.

Question 13

What do you do if sphericity is violated in RM ANOVA?

Answer 13

Apply Greenhouse-Geisser or Huynh-Feldt correction.

Question 14

What are the components of the Friedman test formula?

Answer 14

N = participants
k = number of conditions
Ri = sum of ranks per condition

Question 15

What are the degrees of freedom for Friedman’s ANOVA?

Answer 15

df = k − 1

Question 16

What distribution is used to determine significance in Friedman’s ANOVA?

Answer 16

Chi-square distribution.

Question 17

What must the test statistic exceed to be significant (df = 2)?

Answer 17

5.99 (critical value at p < .05).

Question 18

How do you report Friedman’s ANOVA?

Answer 18

χ²(df) = value, p = value, Kendall’s W = value.

Example: χ²(2) = 7.6, p = .022, Kendall’s W = .382

Question 19

What is Kendall’s W?

Answer 19

Effect size for Friedman’s ANOVA measuring agreement between rankings.

Question 20

What is the range of Kendall’s W?

Answer 20

0 to 1 (0 = no effect, 1 = perfect agreement).

Question 21

What does a higher Kendall’s W indicate?

Answer 21

Stronger effect / greater differences between conditions.

Question 22

Which descriptive statistic is reported with Friedman’s ANOVA?

Answer 22

Median.

Question 23

What type of post-hoc tests are used after significant Friedman’s ANOVA?

Answer 23

Pairwise comparisons (e.g., Conover’s post hoc test).

Question 24

When is the Mann-Whitney U test used?

Answer 24

When comparing ranked scores of two independent groups with non-normal data

Question 25

When is the Kruskal-Wallis test used?

Answer 25

When you have one IV with three or more levels in a between-subjects design.

Question 26

What design does Friedman’s ANOVA use?

Answer 26

Within-subjects (repeated measures) design.