當母體變異數未知且相等時，我們令各母體平均數與所有母體的總平均數之間的最大距離為一測度，它用來檢定母體是否為處方等價，其中等價在實驗設計裡代表處理效應是不存在的。在虛無假設成立下，達到最大水準之均數組合，稱為最大水準均數組合。然而，在均數組合下，水準是與未知平均數、變異數完全獨立的。因此一旦知道虛無假設，我們就可以透過數值方法求得檢定的p值。之後，我用一個實驗設計例子來進行檢定並加以分析。

A distance statistic from the grand mean is proposed to test a null hypothesis of equivalence of treatments, where the "equivalence" stands for an event of treatment means falling into a negligible region around the grand mean. Least favorable mean configuration (LFMC) to guarantee
the maximum level at a null hypothesis is searched. It has been found that the level of the test is fully independent of the unknown means and variances. For a given null hypothesis, the p-value of the test can be evaluated by numerical method. An example to demonstrate the use of the test is given.

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