A singularity of statistics is that one of the methods to compare means is called Analysis of Variance (ANOVA, hereinafter). The reason is that this test is carried out by comparing two types of variation. ANOVA is a general method for studying sources of variation in responses. The comparison of several means is called factorial Analysis of Variance. It is a factor because the response variable (in our example, GMD of the piglets), is only influenced by another variable (in our example, the content of fishmeal in the diet). The test of Analysis of Variance to compare various means is called the F test.
The F statistic used to compare various means has the following form:
F = variation among sample means/variation among individuals of the same sample
The F statistic only takes positive or zero values. It will be zero when the means are all equal. In fact, the effect of chance creates some differences between the sample means, even when the population means are the same. Thus, when the null hypothesis is true, we expect F to take values close to one. As the sample means are further apart, the value of F becomes larger.
The large values of F constitute a reliable test against the null hypothesis, leaving us thinking that the correct hypothesis is the alternative, the one that contemplates that some of the sample means are not equal to the others.