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 one-tailed critical value from the standard normal distribution,

·      is the (one or) two-tailed 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 p-value of the following Z-statistic:

  

where:

  

  

  

and is the (one or) two-tailed critical value from t-distribution with n-2 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 Z-statistic and its p-value.

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:
Z-Statistic =	2.0300
2-Tail Probability =	0.9788