{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

How to Compare Two Correlation Coefficients-ECO6416

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

This preview shows pages 1–2. Sign up to view the full content.

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 1 = 0.510, and z 2 = 0.741, with Z-statistics: Z = (0.510 - 0.7)/ [1/(103-3) + 1/(103-3)] ½ = -1.63

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern