Within-subject contrasts are statistical methods used in analysis involving repeated measurements on the same individuals. Within-subject contrasts gives you, as default, linear and quadratic contrasts for the within factor.
Understanding Within-Subject Contrasts
When you have data collected from the same participants under different conditions or at multiple time points (this is the "within-subject factor"), you might want to understand the pattern of change or difference across these conditions/time points. Contrasts help you test specific hypotheses about these patterns.
Default Contrasts: Linear and Quadratic
As highlighted by the reference, the standard contrasts provided for a within-subject factor are typically:
- Linear Contrast: This tests if there is a consistent straight-line trend across the levels of the within-subject factor. For example, does a dependent variable steadily increase or decrease over time?
- Quadratic Contrast: This tests if there is a curved relationship, specifically a parabolic shape (like an upside-down U or a U shape). This could indicate, for instance, that a variable initially increases then decreases, or vice versa, across the levels of the within-subject factor.
Why Use Linear and Quadratic Contrasts?
You would typically report either or both of these contrasts if you had a hypothesis about the within-subject factor having a linear and/or quadratic effect on the dependent variable.
- Linear Effect Hypothesis: You expect the dependent variable to change by a relatively constant amount for each step or level of the within-subject factor.
- Quadratic Effect Hypothesis: You expect the rate of change to itself change over the levels of the within-subject factor, suggesting acceleration or deceleration in the trend.
These contrasts allow researchers to move beyond simply saying "there was a difference" and instead describe the nature or shape of that difference across the repeated measures.
