Creation date: 08/03/98
Authored by:
Craig Henderson

### Question:

How do I test contrasts in a repeated measures analysis using SAS or SPSS?

In repeated measures analyses, typically, there are three types of contrasts of interest to the researcher: (a) polynomial contrasts which tests the polynomial trend in the data, (b) profile contrasts which test successive pairwise differences (e.g., mean1 - mean2, mean2-mean3, etc.), and reference contrasts which compare all means to a specified reference group (e.g., mean1 - mean2, mean1 - mean3, etc.). In addition SAS and SPSS allow the researcher to define contrasts of interest to their specific research design (e.g., mean2 - mean4, (mean1+mean2)/2 - mean3, etc.).

In SAS release 6.11 or higher:

```/* Polynomial Contrasts */```

```{Data step}; PROC GLM DATA={NAME OF YOUR DATA SET}; MODEL {YOUR DV(s)} REPEATED {YOUR WITHIN SUBJECT EFFECT} POLYNOMIAL; RUN;```

```/* Profile Contrasts */```

```{Data step}; PROC GLM DATA={NAME OF YOUR DATA SET}; MODEL {YOUR DV(s)} REPEATED {YOUR WITHIN SUBJECT EFFECT} PROFILE; RUN;```

```/* Reference Contrasts */```

```{Data step}; PROC GLM DATA={NAME OF YOUR DATA SET}; MODEL {YOUR DV(s)} REPEATED {YOUR WITHIN SUBJECT EFFECT} CONTRAST (1); RUN;```

```The contrast (1) statement assumes that the reference category is the first level of your repeated measures factor.```

```/* Researcher-Defined Contrasts */```

```This involves setting up a contrast matrix with the MANOVA statement and the <M = >option. An example is provided in which the second level of a four level repeated measures factor is contrasted with the third level:```

```{Data step}; PROC GLM DATA={NAME OF YOUR DATA SET}; MODEL {A B C D} REPEATED PERIOD; ```MANOVA H=_ALL_ M=(0 1 -1 0) PREFIX=DIFF;``` RUN;```

```The <H => option specifies that all effects are to be tested, the <M => option defines the effects to be contrasted, and the <prefix = diff> option supplies a label for this contrast. For additional contrasts, provide a comma at the end of each line followed by the next row of the contrast matrix.```

```In mixed models (i.e., models containing one or more within subjects or random factors and one or more between subjects or fixed factors), the above syntax would need to be modified with the appropriate CLASS and MODEL statements.```

In SPSS:

```****Polynomial Contrasts```

```GLM {YOUR DV(s)} /WSFACTOR = {YOUR WITHIN SUBJECTS FACTOR}{NUMBER OF LEVELS OF YOUR WITHIN SUBJECTS FACTOR} POLYNOMIAL /METHOD = SSTYPE {YOUR SELECTION} /CRITERIA = ALPHA(.05) /WSDESIGN.```

```****Profile Contrasts```

```GLM {YOUR DV(s)} /WSFACTOR = {YOUR WITHIN SUBJECTS FACTOR} REPEATED /METHOD = SSTYPE {YOUR SELECTION} /CRITERIA = ALPHA(.05) /WSDESIGN.```

```****Reference Contrasts```

```GLM {YOUR DV(s)} /WSFACTOR = {YOUR WITHIN SUBJECTS FACTOR} SIMPLE(1) /METHOD = SSTYPE {YOUR SELECTION} /CRITERIA = ALPHA(.05) /WSDESIGN.```

```The simple (1) statement assumes that the reference category is the first level of your repeated measures factor.```

```****Researcher-Defined Contrasts```

```This involves setting up a contrast matrix with the MMATRIX statement. An example is provided in which the second level of a four level repeated measures factor is contrasted with the third level:```

```GLM {A B C D} /WSFACTOR = {PERIOD} /METHOD = SSTYPE {3} /CRITERIA = ALPHA(.05) /WSDESIGN /MMATRIX B 1 C -1. ```

```For additional contrasts, provide a semicolon at the end of each line followed by the next contrast.```