The analysis of variance and covariance techniques in relation to the conventional formulas for the standard error of a difference

In this paper it is demonstrated that the analysis of variance techniques yield results equivalent to the calculation oft by means of expressions based on the short or the long formula. It is also shown that the covariance technique gives results equivalent to those obtained by means of the formula fort which should be used with matched groups. The conditions necessary for equivalent results are such that the conventional formulas fort would normally be used rather than the variance or covariance techniques. However, a knowledge of the relationships described in this paper should contribute to one's understanding of the variance and covariance techniques.The relationships described in this paper were brought to the attention of the author by the excellent article of Eugene Shen (8). The proofs given here and the examples are the work of the present author.