SIGNIFICANCE OF DIFFERENCE BETWEEN THE MEANS OF 2 NON-NORMAL SAMPLES
SIGNIFICANCE OF DIFFERENCE BETWEEN THE MEANS OF 2 NON-NORMAL SAMPLES
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DOI：
10.1093/biomet/37.3-4.399
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发表时间：
1950-01-01
期刊：
影响因子：
2.7
通讯作者：
GAYEN, AK
中科院分区：
文献类型：
--
作者：
GAYEN, AK
If'and x/'are the means of two samples of nl and n2 members drawn from the same population (or from two different populations having equal variance), and if S'and S'are the sample sums of squares about the mean, then the test function xV, n/in2 (n,+ n2-2)(x'-" A/\al+ 2 J 2+ 2 has the'Student't-distribution (Fisher, 1925) with (nl+ n2-2) degrees of freedom provided the variables are normally distributed. But the situation will be different for non-normal variation in the parent distributions. On the basis of some experimental results, ES Pearson (1931) concluded that'in dealing with very small samples (say, if nl+ n2< 20), the use of the t-probability (normal-theory t) scale rather than the normal probability* scale is justified, even if the population varies very considerably from the normal'. Examining the pos-nl nf2 n n2 sible form of the joint characteristic function of x'-E x" and z x'2+ E x" 2 for the popu-
