In conducting One way analysis of Variance, which of the following test statistics would be used?
F
One-way Analysis of Variance (ANOVA) is used to test whether the means of three or more groups differ. The clue is right in its name — 'analysis of variance'.
ANOVA works by comparing two estimates of variance: the variance between the group means and the variance within the groups. When you form a ratio of two variances, the sampling distribution that results is the F-distribution, and the test statistic is therefore F (named after R. A. Fisher). A large F value means the differences between group means are large relative to the scatter inside the groups, signalling a genuine difference.
Why the others are wrong: the Z statistic is used for means or proportions of large samples when the population standard deviation is known; the t statistic compares means of one or two groups with small samples; chi-square is used for categorical/frequency data such as tests of independence and goodness-of-fit. None of these is the ratio-of-variances test that ANOVA requires.
Correct answer: F
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