Between-Within Subjects ANOVA

If we want to test all main effects (factors) and their interactions, like we did before, and we want to add gender to the model, we need to use a different ANOVA test. This is because gender is a between subjects variable - that is each subject is a different gender. And we also have the within subject variables that we had before, so we have to use a Between-Within ANOVA.

 

Between-Within ANOVA in SAS

How this was done.

 
 
                      General Linear Models Procedure
 
                   Repeated Measures Analysis of Variance
 
              Tests of Hypotheses for Between Subjects Effects
 
 
 
Source                  DF    Type III SS   Mean Square   F Value     Pr > F
 
 
 
SEX                      1        49.9468       49.9468      0.42     0.5226
 
 
 
Error                   30      3580.2096      119.3403
 
 
 
 
 
 
 
                               The SAS System                            311
 
                                                 11:25 Friday, June 26, 1998
 
 
 
                      General Linear Models Procedure
 
                   Repeated Measures Analysis of Variance
 
         Univariate Tests of Hypotheses for Within Subject Effects
 
 
 
Source: WORDTYPE
 
                                                               Adj  Pr > F
 
     DF     Type III SS     Mean Square   F Value   Pr > F    G - G    H - F
 
      1      0.41933316      0.41933316      0.20   0.6608    .        .
 
 
 
Source: WORDTYPE*SEX
 
                                                               Adj  Pr > F
 
     DF     Type III SS     Mean Square   F Value   Pr > F    G - G    H - F
 
      1      0.07037487      0.07037487      0.03   0.8572    .        .
 
 
 
Source: Error(WORDTYPE)
 
 
 
     DF     Type III SS     Mean Square
 
     30     64.05267636      2.13508921
 
                               The SAS System                            312
 
                                                 11:25 Friday, June 26, 1998
 
 
 
                      General Linear Models Procedure
 
                   Repeated Measures Analysis of Variance
 
         Univariate Tests of Hypotheses for Within Subject Effects
 
 
 
Source: PRIME
 
                                                               Adj  Pr > F
 
     DF     Type III SS     Mean Square   F Value   Pr > F    G - G    H - F
 
      1      2.81167301      2.81167301      1.87   0.1817    .        .
 
 
 
Source: PRIME*SEX
 
                                                               Adj  Pr > F
 
     DF     Type III SS     Mean Square   F Value   Pr > F    G - G    H - F
 
      1      0.05408118      0.05408118      0.04   0.8509    .        .
 
 
 
Source: Error(PRIME)
 
 
 
     DF     Type III SS     Mean Square
 
     30     45.12436725      1.50414558
 
                               The SAS System                            313
 
                                                 11:25 Friday, June 26, 1998
 
 
 
                      General Linear Models Procedure
 
                   Repeated Measures Analysis of Variance
 
         Univariate Tests of Hypotheses for Within Subject Effects
 
 
 
Source: WORDTYPE*PRIME
 
                                                               Adj  Pr > F
 
     DF     Type III SS     Mean Square   F Value   Pr > F    G - G    H - F
 
      1      5.56550868      5.56550868      4.48   0.0426    .        .
 
 
 
Source: WORDTYPE*PRIME*SEX
 
                                                               Adj  Pr > F
 
     DF     Type III SS     Mean Square   F Value   Pr > F    G - G    H - F
 
      1      0.11018091      0.11018091      0.09   0.7678    .        .
 
 
 
Source: Error(WORDTYPE*PRIME)
 
 
 
     DF     Type III SS     Mean Square
 
     30     37.24083479      1.24136116

Between-Within ANOVA in SAS JMP

Between-Within ANOVA in SPSS

Again we see that only significant effect is the interaction between WORDTYPE*PRIME is significant at the 0.05 level (p= 0.0426), suggesting that both the prime factor and the wordtype factor work together to affect reaction time.