
Step 2: Summary Statistics
Stat > Basic Statistics > Display Descriptive Statistics, Variable= Difference, By variables=Gender
| Gender | |||
|---|---|---|---|
| Group | Sample Size | Mean | Std |
| Female | 16 | 4.313 | 1.352 |
| Male | 16 | 5.250 | 1.483 |
Stat > Basic Statistics > Display Descriptive Statistics, Variable= Difference, By variables=Treatment
| Treatment | |||
|---|---|---|---|
| Group | Sample Size | Mean | Std |
| 1 | 8 | 3.875 | 1.356 |
| 2 | 8 | 4.375 | 1.188 |
| 4 | 8 | 4.625 | 1.061 |
| 3 | 8 | 6.250 | 1.282 |
Step 3: Interaction
Stat > ANOVA > Interactions Plot, Response= Difference, Factors= Gender Treatment

there does not appear to be any interaction. Let's confirm this with the hypothesis test:
Test for Interaction:
Stat > ANOVA > Twoway, Response=Difference, Row Factor=Gender, Column factor=Treatment
1) a=0.05
2) H0: g11=g12=...=g24=0 (no interaction)
3) H0: gij≠0 (some interaction)
4) p-value= 0.724 > a
5) We fail to reject H0, there is no interaction
So we will fit an additive model
Step 4: Hypothesis tests
Stat > ANOVA > Twoway, Response=Difference, Row Factor=Gender, Column factor=Treatment , check box additive model, Graphs > Residual vs. Fits and Normal plot

everything appears fine
Test for Gender:
1) a=0.05
2) H0: a1 = =a2=0 (no difference in the mean for Men and Women)
3) Ha: ai≠0 for some i (some differences in the means of Men and Women)
4) p-value= 0.028 < a
5) We reject H0, there are some differences in the means of Men and Women
Test for Treatment:
1) a=0.05
2) H0: b1 = .. =b4=0 (no difference in the means of different Treatments )
3) Ha: ai≠0 for some i (some differences in the means of different Treatments)
4) p-value= 0.002 < a
5) We reject H0, there are some differences in the means of different Treatments)
Step 5: Multiple Comparison
Which treatment is best? Because there is no interaction this will be the same for both genders. We can therefore do this by ignoring Gender and running a one-way ANOVA of Differences by Treatment, with Tukey's multiple comparison. We find
| 1 | 2 | 4 | 3 |
|---|---|---|---|
| _____ | |||
| _____ | |||