If you decide to use randomized block ANOVA and fail to reject the null hypothesis for the main factor, you should perform a one- way ANOVA to be sure the blocking factor is not covering up the difference in population means for the main factor.

Question

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If the main factor is not significant in the randomized block ANOVA, it is possible that the blocking factor is masking the effect of the main factor. Performing a one-way ANOVA without the blocking factor can help determine if there is a significant difference in population means for the main factor.

If You Decide to Use Randomized Block ANOVA and Fail