變異數分析（Analysis of Variance）中進行F考驗時，常遭遇以何者為誤差項（分母）的困擾。本研究從均方期望值（expectations of mean squares）的成分因素（components），找尋少一成分因素的均方期望值為分母。本文探討了單因子相依樣本、二、因子獨立樣本、二因子相依樣本、二因子混合設計、階層設計及拉丁方格設計等較常用的研究設計。最後則討論無法直接從直線模式的成份因素決定誤差項時，其處理的方式。

　　　　　One of the important problems in the analysis of variance is to determine the proper denominators for F statistics. The test statistics is a ratio of mean squares that is chosen such that the components of the expected value of the numerator mean square is more one component than the expected value of the denominator mean square. This reseach introduced the rules that produced the expected mean squares for any model and some examples as follows: one way randomized block design, two way completely randomized design, two way randomized block design, two way fixed model design, completely randomized hierachical design, and latin square design. The possible solutions of no exact test statistics for some effect in the designs were discussed also.