Testing linear hypotheses illustrated by a simple example in correlation

The development of a criterion suitable for testing the significance of a correlation or regression coefficient is used as an illustration of the manner in which a research problem is bound to the selection of the particular data appropriate to collect and a fitting type of statistical analysis of the latter. The translation of the original inquiry into a problem of testing linear hypotheses is the means by which these two aspects of an investigation are held together. This presentation is offered as a plan which might be useful for some research workers in determining appropriate criteria for testing their particular hypotheses.