The analysis of variance (ANOVA) tests hypotheses about the population variance.

Question

The analysis of variance (ANOVA) tests hypotheses about the population variance.

BlackTom AI · Accepted Answer

Consider the core purpose of ANOVA in hypothesis testing. 
Option 1: 'True' claims that ANOVA tests hypotheses about population variance. This is misleading because the fundamental question in a standard ANOVA is about whether several population means are equal, not about the variances themselves. The ANOVA F statistic compares the variance between group means to the variance within groups to assess mean differences. While variances are involved in the calculation, the null hypothesis pertains to equal means across groups, not to equal variances. 
Option 2: 'False' states that ANOVA tests hypotheses about population variance. Although variances enter into the calculation of the F statistic, the primary hypothesis tested by one-way ANOVA is about the equality of population means. If the concern were about variances specifically, other tests (for example, tests for variance like Levene's test or Bartlett's test) would be more appropriate, not standard ANOVA. 
In sum, the standard ANOVA framework is built around mean comparisons across groups, and therefore the statement in Option 1 mischaracterizes its focus. The assertion in Option 2 aligns with the typical interpretation of ANOVA as a test of means rather than variances.

The analysis of variance (ANOVA) tests hypotheses about the population variance.

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