What do planned contrasts do with the variance due to group differences?

• A. Planned contrasts partition the variance due to group differences into smaller portions.
• B. They test differences between variances.
• C. They estimate regression coefficients.
• D. They assess normality of residuals.

Answer: (C)

Planned contrasts are a way to test specific hypotheses about group means by forming linear combinations of those means with chosen weights. Those weights define a contrast value that represents a particular difference you want to examine. In regression terms, this contrast corresponds to estimating a regression coefficient for a dummy-coded design that compares the groups in that precise way. The contrast’s estimated value tells you the size and direction of the difference between the groups under study, and its statistical significance is tested using the usual error variance from the model.

So the key idea is that planned contrasts yield an estimate of a regression coefficient that captures the specified difference among group means. The other options describe broader variance partitioning, comparing variances, estimating regression coefficients in a different sense, or assessing residual normality, none of which pin down what a planned contrast provides.