Introduction to Mathematical Statistics

Cover Introduction to Mathematical Statistics
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Because each term of the mean squared deviation of the means is squared and hence necessarily positive any accidental fluctuations of the means of the arrays in data of essentially zero correlation increase the value of rj. Since there are no com- pensating flunctuations, the result is that small values of tj are quite likely to be too large and hence the statistical significance of rj for data of a small degree of correlation is open to ques- tion. The degree of correlation in such cases canno...t be greater than the value of 77 would indicate and it may be less. It must be evident from the nature of the error that for material show- ing a considerable degree of correlation the error from this source is negligible. As discussed in Chapter VII, in perfectly correlated data the frequencies of each array are concentrated in a single class or subgroup of the array. According to the shape of the re- gression curve two cases can arise for perfectly correlated data, as the following imaginary distributions illustrate.

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