The F-test of the randomized block design of the analysis of variance requires that the random variable of interest must be normally distributed and the population variances must be equal. When the random variable is not normally distributed, we can use:

A) one-way ANOVA
B) two-way ANOVA
C) chi-square test
D) binomial square test
E) Friedman test

When the random variable of interest is not normally distributed, the Friedman test is a non-parametric alternative that can be used instead of the F-test of the randomized block design. The Friedman test is used to analyze repeated measures data where each subject receives multiple treatments or conditions. It ranks the data within each block and performs a chi-square test on the resulting ranked data. Therefore, the correct choice is E) Friedman test.