This document proves that the F statistic can be obtained by squaring t-test values, or that equivalent t-test values may be obtained by extracting the positive square roots of F values. Proof to varying degrees of completeness and accessibility has been given by other scholars, but generally these prior statements, particularly those available to students of education or psychology, focus on the special case, when sample sizes are equal. No source could be found that provided a complete, detailed proof of the general case that was understandable to students of applied statistics. This document seeks to give a clear step-by-step proof, with a numerical example worked out, and a plan is provided for proving the special case. It is felt the reader should be able to follow the proof of the general case, and should therefore have little difficulty in translating the acquired knowledge into proving the special case. (MP)