On the Sampling Errors of Correlation Coefficients

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  • 相關係數の誤差に就いて

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As a natural extension of the standard error or, the confidence limits may be conveniently used in the case of small sample. For this purpose, R. A. Fisher's methods are not only somewhat laborious, but also attended by innegligible errors. Utilizing H. E. Soper's table, the auther has calculated two kinds of tables which give the confidence limits for the following values of n (size of sample) and r (observed correlation coefficient), <br>n=5, 6, …25, 50, 100<br>r=0, 0.05, …, 0.95, <br>and has prepared two diagrams corresponding to them. The confidence coefficient of the limits in one table is 1-2Φ (1), and in the other is 1-2Φ (2), where and the errors of calculated numbers are, on the whole, less than 0.005.<br>These tables and diagrams can be used for the following problems:<br>(1) To find the confidence-limits of observed correlation coefficient r.<br>(2) The significance test of r.<br>(3) To test the difference between observed r and its previously assumed value.<br>(4) To test the difference between two observed values r1 and r2.<br>(5) The composition of these r1 and r2.

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