Question

Explain the seeming contradiction in the One-Way ANOVA; namely, that the null hypothesis is about comparing the means of three or more populations, whereas the actual testing of means is about using ANOVA analysis to compare variances. Why is this so?

Answer 1

One - way ANOVA method is utilized to do hypothesis tests when there are as a minimum three populations as for two populations, we can simply do z or t test.

In one-way ANOVA, relating three groups, the alternative hypothesis would be measured correct if, in the population, 2 means are equivalent but the third is dissimilar or all three means contain unlike values

When Null is correct for a one-way ANOVA, variation of the group means is an indication of inherent variation

Inconsistency of subgroup means about the mean of the joint distribution give an indication of inherent variation and variation attributable to action, when there