The Test of Significance for the Correlation Coefficient
The Test of Significance for the Correlation Coefficient
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DOI：
10.1080/01621459.1931.10503208
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发表时间：
1931-06
影响因子：
3.7
通讯作者：
E. S. Pearson
中科院分区：
文献类型：
--
作者：
E. S. Pearson
In applying the methods of statistical analysis it is generally our aim to discriminate between two or more alternative hypotheses regarding the factors which have controlled certain observed events, which form what we term a sample, or samples. If the process is examined in a little detail it will be found that the procedure may be described as follows:(a) We define a hypothesis to be tested.(b) We choose the criterion (or criteria) whose numerical value, derivable from the observations, is most suitable for testing the hypothesis. In doing this we recognize that the criterion is not a single valued expression even if the hypothesis be true, but will vary from one sample of observations to another.(c) We therefore refer the observed value of the criterion to this sampling distributi0n-eg to a normal probability scale, a x2 probability scale, etc.-and so obtain a measure of the likelihood of the hypothesis.(d) Finally, if judged on this probability scale the observed criterion is not exceptional, we conclude that upon the information available there are no grounds for discarding the hypothesis; or if the value prove exceptional we consider the possibility of alternative hypotheses.The step (a) requires in general only a little careful thinking, but (b) leads us into an interesting field at present not fully explored. Here we must first decide upon the principles by which to determine what we mean by a “suitable” criterion. The importance of this problem seems fist to have been realized by R. A. Fisher; it has also been considered from a slightly different aspect by J. Neyman and the present writer. 2 When (b) has been settled it becomes a question of mathematics, which may or may not be within our powers of solution, to determine the sampling distribution of the criterion. These steps in reasoning may be illustrated in the case of the test for significance of the product-moment correlation coefficient between
