For various reasons, cross-sectional tests of linear factor models have employed the returns on portfolios of assets (as opposed to individual securities). There is a good deal of flexibility in how one goes about choosing which portfolios to examine (the experimental design). This article points out that some choices can lead to collinearity among factor loadings with potentially harmful consequences for power. A diagnostic procedure for detecting collinearity is discussed, and several illustrations of the procedure on existing tests of linear factor models are used to illustrate their value to the researcher. Finally, a series of experiments is carried out to validate the diagnostics and to confirm their assessment of the experimental design in the models examined.