The test statistic $\text { one-way } \mathrm { ANOVA } \text { is } \mathrm { F } = \frac { \text { variance between samples } } { \text { variance within samples } }$ . Describe variance within samples and variance between samples. What relationship between variance within samples and variance between samples would result in the conclusion that the value of F is significant?

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The Answer is Variance between samples measures the variation between the sample means, that is the variation due to the treatment. The variance within the samples depends solely on the sample variances and is a measure of pooled variation. The F ratio compares the two. If the F ratio is relatively close to 1, the two variances are about the same, and we conclude that there are no significant differences among the sample means. When the value of F is excessively large (that is, greater than 1), we conclude that the variation among the samples is not the same and that the means are not equal.