One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the sample means. Thus, two datasets with equal sample sizes can have two different values for variance between samples.
In contrast, it is possible for two different datasets with equal sample sizes to have equal sample variances but different sample means. Since the variance within samples, also called the pooled variance, is calculated as the mean of sample variances, the variance within samples can be equal for two datasets with equal sample sizes.
The computed F statistic value for the two datasets differs since the datasets show unequal values for variance between samples but equal values for variance within samples.
