Analysis of covariance(ANCOVA) is frequently applied in educational research ignoring the fact that when the assumption of the homogeneity of regression slope within group is violated, ANCOVA is not an appropriate procedure any more. Teachers or researchers interested in educational research have used this procedure regardless of the equality of regression slope within group. The purpose of the present study is to present available alternatives to ANCOVA when the within-group regression slopes are heterogeneous: blocking or stratification, Hollingsworth’s F statistic, Johnson-Neyman procedure, Potthoff’s modified Johnson-Neyman procedure, Rogosa’s three alternatives, and Wilcox’s trimmed-mean method. Furthermore, the Potthoff’s modified Johnson-Neyman procedure and the Wilcox’s trimmed-mean method are applied under the unequal slopes condition using one numerical example presented here to introduce teachers or researchers the appropriate alternatives to ANCOVA. This study also insisted that teachers or researchers interested in educational research should know the limitation of ANCOVA and use statistical procedures appropriately.