How to Compare Two Correlation Coefficients-ECO6416

How to Compare Two Correlation Coefficients-ECO6416 - How...

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How to Compare Two Correlation Coefficients? Given that two populations have normal distributions, we wish to test for the following null hypothesis regarding the equality of correlation coefficients: H o : ρ 1 = ρ 2 , based on two observed correlation coefficients r 1 , and r 2 , obtained from two random sample of size n 1 and n 2 , respectively, provided | r 1 | 1, and | r 2 | 1, and n 1 , n 2 both are greater than 3. Under the null hypothesis and normality condition, the test statistic is: Z = (z 1 - z 2 ) / [ 1/(n 1 -3) + 1/(n 2 -3) ] ½ where: z 1 = 0.5 Ln [ (1+r 1 )/(1-r 1 ) ], z 2 = 0.5 Ln [ (1+r 2 )/(1-r 2 ) ], and n 1 = sample size associated with r 1 , and n 2 =sample size associated with r 2 . The distribution of the Z-statistic is the standard Normal(0,1); therefore, you may reject H 0 if |Z| 1.96 at the 95% confidence level. An Application: Suppose r 1 = 0.47, r 2 = 0.63 are obtained from two independent random samples of size n 1 =103, and n 2 = 103, respectively. Therefore, the z
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This note was uploaded on 10/06/2011 for the course ECO 6416 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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How to Compare Two Correlation Coefficients-ECO6416 - How...

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