1 IV. 2 groups t-test

3+ groups ANOVA

Group Differences:1 Independent Variable

• IV: male, female• DV: happiness

• There is a difference• Due to chance?

TheoryTheory

• Confidence Interval• 95% within interval

• If Overlap– No real differences

(non-significant)

• If no Overlap– Difference is real

(significant)

TheoryTheory

• Can make significant:

• Move points away(larger between group variation)

TheoryTheory

TheoryTheory

• Can make significant:

• Smaller intervals(less within group variation)

TheoryTheory

• Summarizing theory behind “group differences”:

between group variation

within group variation

• Notice how that translates into formulas:

T-test: independent

T-test: repeated

ANOVA (I’ll show you later)

TheoryTheory

• A single pairwise comparison (e.g., males to females)• Is there a significant difference (e.g., p = .025)• What are group means (e.g., 4.84, 5.61)• What is the effect size (e.g., by hand, website)

2 groups2 groups

• Same as before:

95% CI

Overlap = n.s.

No overlap = sig

• Difference:

Multiple pairwise comparisons

So FIRST see if “overall”

Then SECOND test each pairwise

3+ groups3+ groups

(1) Overall “F”

(2) Post-hoc or Planned Comparisons

• Overall “F”– F = between group variability

within group variability

– Can’t simply start with multiple pairwise comparisons because must control for familywise error

3+ groups3+ groups

(1) Overall “F”

(2) Post-hoc or Planned Comparisons

• Overall “F”– F = between group variability

within group variability

– Can’t simply start with multiple pairwise comparisons because must control for familywise error

3+ groups3+ groups

.95 x .95 x .95 =.857 1-.857=.14

(1) Overall “F”

(2) Post-hoc or Planned Comparisons

• Overall “F”– F = between group variability

within group variability

– Can’t simply start with multiple pairwise comparisons because must control for familywise error

3+ groups3+ groups

1 - (1 - )C = 1 - (1 -.05)3=.14

.95 x .95 x .95 =.857 1-.857=.14

(1) Overall “F”

(2) Post-hoc or Planned Comparisons

• Post-hoc– Testing all possible pairwise comparisons– Control for familywise error (keep alpha=.05)– Many options. I suggest LSD or Tukey

• Planned Comparisons– Testing only specific pairwise comparisons– Must be “apriori hypotheses”– Can do one-tailed tests

3+ groups3+ groups

• Overall F (e.g., p = .003) • Post-hoc (e.g., see table)• What are group means (e.g., see table)• What is the effect size (e.g., by hand, website)

3+ groups3+ groups