Simple slopes analysis is commonly used to evaluate moderator or interaction effects in multiple linear regression models. In usual practice, the moderator is treated as a fixed value when the standard error of simple slopes is estimated. The usual method used for choosing the conditional value of moderator (i.e., at one sample SD below, one SD above, and at the mean) makes the moderator a random variable and therefore renders the standard error suspect. In this study I examined whether the standard error used in post hoc probing for interaction effect is a biased estimator of the population variance when moderator is a random variable. I conducted Monte Carlo simulations to evaluate the variance of the simple slope under a variety of conditions corresponding to a 5 (sample size, N) x 5 (variance of focal predictor, x) x 5 (variance of moderator, z) x 4 (levels of r, the correlation between x and z) x 5(model fit, R 2) x 4 (population slope for interaction, b xz) factorial design. I present circumstances under which usual practice yields an "almost" unbiased estimator and conditions when the estimator is more severely biased and less so.
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