Field Ch. 12 - ANOVA

Question 1

What is ANOVA?

Answer 1

• technique for comparing 3+ means
• it’s t-tests on steroids
• Ex: are avg IQ scores different btwn 3 schools?

Question 2

ANOVA Step 1: Summarize & Visualize

Answer 2

• run descriptives and create charts

Question 3

ANOVA Step 2: Null hypothesis

Answer 3

all populations means are equal

this is the null for any ANOVA

Question 4

ANOVA Step 3: Variances

Answer 4

(values found in ‘ANOVA’ table of SPSS output)

SS Between = how far sample means are from each other

mean squares = variance among sample means

SS within = total dispersion within groups

Question 5

ANOVA Step 4: Assumptions

Answer 5

1. independent observations
2. normality (outcome variable distribution, really only required when n < 20 per group)
3. homogeneity of variance (variance w/in sub pops must be equal)

Question 6

ANOVA Step 5: Run analysis

Answer 6

1. Analyze > Compare Means > one-Way ANOVA
2. Post Hoc choices: Tukey
3. Options choices: descriptive + homogeneity + means plot

Question 7

ANOVA Step 6: F-statistic

Answer 7

• How likely is it that the population means are equal?
• Larger F-value = less likely

Larger variance between (MS between) + smaller variance within (MS within) + larger sample sizes = Larger F-value

(all values in the Mean Square column of ‘ANOVA’ table in SPSS output)

Question 8

ANOVA Step 7: Effect Size

Answer 8

eta squared = η2 = How different are the means?

η2 > 0.01 = small effect
η2 > 0.06 = medium effect
η2 > 0.14 = large effect

η2 = SSbetween / SStotal

Question 9

ANOVA Step 8: Post Hoc Tests

Answer 9

Post hoc tests tell us which means are different.

Tukey’s HSD (honestly significant difference)