Consider performing a one-way ANOVA on two different datasets, each containing the heights of students from three samples. Notice that in both datasets, all three samples have equal sample sizes. Here, we can state the null hypothesis that the mean heights of all three samples are equal. The alternative hypothesis is that at least one of the means is different from the rest. First, calculate the sample means and sample variances for both datasets. Observe that only the means of the first samples in both datasets differ substantially, but the sample variances are identical. Next, calculate the F statistic for both datasets and find the P-values. The different means of the first samples in both datasets cause a substantial change in the variance between samples. However, the variance within samples remains identical, as it doesn't require the sample mean during calculation. The different values of variance between samples in both datasets affect the F statistic, leading to different results. So, we can conclude that the F statistic is substantially affected by the sample mean.