When might analysis of covariance be used?

Analysis of covariance (ANCOVA) is particularly useful when groups are not randomly assigned. This statistical method allows for the adjustment of differences among groups, which may arise from variables other than the main treatment or intervention being studied. By controlling for these covariates, researchers can isolate the effect of the independent variable on the dependent variable, thus providing a clearer understanding of the relationship between them.

When groups are not randomly assigned, there might be pre-existing differences that could influence the outcomes. ANCOVA helps to mitigate the impact of these differences by statistically controlling for them, allowing for a more accurate comparison between groups. This makes it an essential tool in observational studies and situations where random assignment is not feasible, ensuring that the results are more reliable.

In contrast, analyzing randomly assigned groups, enhancing coefficients, or norming tests does not specifically relate to the primary function of ANCOVA, which focuses on adjusting for pre-existing differences in non-random assignments.