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I here explain different types of contrasts in repeated measures ANOVA. These are available in SPSS and R.
1. Polynomial Contrasts
Purpose: Test for linear, quadratic, cubic, etc., trends in the means across the repeated measures.
Use Case: When the levels of the within-subject factor are ordered (e.g., time points or doses).
Example: If you measure performance at 3 time points (T1, T2, T3), a linear contrast tests if the mean increases or decreases steadily, while a quadratic contrast tests for a curve (e.g., increase then decrease).
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2. Deviation Contrasts
Purpose: Compare each level of the within-subject factor to the overall mean of all levels.
Use Case: When you want to know whether a particular condition differs significantly from the average of all conditions.
Example: Compare each teaching method (A, B, C) to the average effect across all three methods.
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3. Simple Contrasts
Purpose: Compare each level of the within-subject factor to a reference level (usually the first or last).
Use Case: When you have a control or baseline condition and want to compare each other condition to it.
Example: Compare scores at Week 2 and Week 3 to Week 1 (baseline).
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4. Repeated Contrasts
Purpose: Compare each level of the within-subject factor to the previous level.
Use Case: To test sequential changes (e.g., from one time point to the next).
Example: Compare performance at Week 2 to Week 1, then Week 3 to Week 2.
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5. Helmert Contrasts
Purpose: Compare each level of the factor to the mean of subsequent levels.
Use Case: To examine whether early levels differ from the average of what comes next.
Example: Compare Week 1 to the average of Week 2 and Week 3; then compare Week 2 to Week 3.
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6. Difference Contrasts
Purpose: Compare each level to the mean of preceding levels.
Use Case: The reverse of Helmert; used when later levels are to be compared to previous ones.
Example: Compare Week 3 to the average of Week 1 and Week 2.
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Each should be based on your research questions and your research goal, as I summarised below:
For trends across time → Polynomial or Repeated
To compare to a control → Simple
To compare sequentially → Repeated
To compare each to average → Deviation
To test theoretical contrasts → Use Custom Contrasts (manually specify contrast weights)
BY Research Methods in AL
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