Correlation Coefficients Testing-ECO6416

# Correlation Coefficients Testing-ECO6416 - random sampling...

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Correlation Coefficients Testing The Fisher's Z-transformation is a useful tool in the circumstances in which two or more independent correlation coefficients are to be compared simultaneously. To perform such a test one may evaluate the Chi-square statistic: χ 2 = Σ [(n i - 3).Z i 2 ] - [ Σ (n i - 3).Z i ] 2 / [ Σ (n i - 3)], the sums are over all i = 1, 2, . ., k. Where the Fisher Z-transformation is Z i = 0.5[Ln(1+r i ) - Ln(1-r i )], provided | r i | 1. Under the null hypothesis: H 0 : All correlation coefficients are almost equal. The test statistic χ 2 has (k-1) degrees of freedom, where k is the number of populations. An Application: Consider the following correlation coefficients obtained by
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Unformatted text preview: random sampling form ten independent populations. Population P i Correlation r i Sample Size n i 1 0.72 67 2 0.41 93 3 0.57 73 4 0.53 98 5 0.62 82 6 0.21 39 7 0.68 91 8 0.53 27 9 0.49 75 10 0.50 49 Using the above formula χ 2-statistic = 19.916, that has a p-value of 0.02. Therefore, there is moderate evidence against the null hypothesis. In such a case, one may omit a few outliers from the group, then use the Test for Equality of Several Correlation Coefficients JavaScript. Repeat this process until a possible homogeneous sub-group may emerge....
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