Previous research has examined moderation effects with traditional analyses such as ANOVA, ANCOVA, moderated regression analysis (MRA), or a combination of MRA and subgroup analysis. However, there exists some confusion in such analyses, because the analyses do not separately consider two possible effects of a moderator on the form and strength of relationship between a focal predictor and a dependent variable. The effect on the form is measured with the interaction effect between the focal predictor and the moderator whereas the effect on the strength is measured with the effect of the moderator on predictability of the focal predictor on the dependent variable. This paper proposes a heterogeneous MRA that allows the moderation effect to be heterogeneous in the population, and shows that it allows one to examine the two possible moderation effects separately. Furthermore, this paper shows that previous research based on the traditional analyses might have incorrectly led to conclusions that there did not exist moderation effects even though the moderation effects were strongly supported by theories. The heterogeneous MRA can examine moderation effects with a data set collected for the traditional analyses. Thus, this paper recommends one to use the heterogeneous MRA together with the traditional analyses.