08-02-2016, 04:37 PM
The t test is used to compare two means or treatments. Many experiments involve more than two treatments, and for such experiments the F test is used. The F test is based on the ratio of two variances. It is used to determine whether two independent estimates of variance can be assumed to be estimates of the same variance. If treatments are significantly different, the variation in treatment means will be greater than the variation due to random differences among individuals. This ratio was called F by George W. Snedecor in honor of Ronald A. Fisher, a pioneer in the use of mathematical statistics in agriculture. In the analysis of variance, the F test is used to test equality of means; that is, to answer the question, "can it reasonably be assumed that the treatment means resulted from sampling populations with equal means?" The two variances which are estimates of are calculated from sample means and by pooling the variances from the samples. If estimates of F were calculated many times for a series of samples drawn from a population of normally distributed variates (therefore, no difference between the variances would be expected), and the frequency of the F values obtained were plotted, an F distribution would result. Distributions of F can be found on the web at http://members.aoljohnp71/pdfs.html Note that the F distribution is not symmetrical as was the t distribution and that only positive values are considered. If you think about the ratio of the variances, it is apparent that if there is no difference between the variances (Ho is true), the ratio would be 1. If an unusual sample had been drawn so that the sample mean variance was larger than the pooled variance, the ratio would be a number greater than 1.