Modified z-test as an alternative to Completely Randomized Design

A less time-consuming method named Modified z-test is suggested here as an alternative to one-way ANOVA (completely randomized design) to test hypothesis manually for three or four samples with unequal and equal sample size respectively. Two illustrations taking sets of Microsoft Excel generated random numbers are solved with Modified z-test. Six assumptions of this suggested method are listed. Computed statistics and critical values according to this method and according to completely randomized design are compared and found to be significantly not different.