6.7.4. Correlation
6.7.4.1. Sample Size for Correlation
The sample size is estimated using the following formula:
where:
· and z is the Fisher’s z transformation of the correlation coefficient r,
· is the onetailed critical value from the standard normal distribution,
· is the (one or) twotailed critical value from the standard normal distribution.
The user is expected to enter:
· Correlation Coefficient
· Power of the test
· Confidence Level
· 1 or 2 tailed test
and the program will output the estimated sample size.
Example
Example 19.5a on p. 388 from Zar, J. H. (2010). Select Statistics 1 → Sample Size and Power Estimation → Correlation and the Sample Size option. Enter the following data at the next dialogue:
Sample Size and Power Estimation: Correlation
Sample Size
Correlation Coefficient = 
0.5000 
Power of the Test = 
0.9900 
Confidence Level = 
0.9500 
1 or 2 Tailed Test = 
2.0000 
Estimated Sample Size = 
63.9136 
6.7.4.2. Power of the Test for Correlation
Power of the test is one minus the pvalue of the following Zstatistic:
where:
and is the (one or) twotailed critical value from tdistribution with n2 degrees of freedom.
The user is expected to enter:
· Sample Size
· Correlation Coefficient
· Confidence Level
· 1 or 2 tailed test
and the program will output the estimated Zstatistic and its pvalue.
Example
Example 19.4 on p. 388 from Zar, J. H. (2010). Select Statistics 1 → Sample Size and Power Estimation → Correlation and the Power of the Test option. Enter the following data at the next dialogue:
Sample Size and Power Estimation: Correlation
Power of the Test
Sample Size = 
12.0000 
Correlation Coefficient = 
0.8700 
Confidence Level = 
0.9500 
1 or 2 Tailed Test = 
2.0000 
Power of the Test: 

ZStatistic = 
2.0300 
2Tail Probability = 
0.9788 