6.7.8. Phi Distribution
We should point out that phi is not a distribution as such, but a multi-parameter relationship based on the noncentral F-distribution.
The following two procedures are provided here as an alternative to OC Curves published by Pearson and Hartley (1951).
Here the significance level (α) can be any value between 0 and 1, whereas the OC Curves are limited to α = 0.05 and α = 0.01. Also, the accuracy of calculations here is far higher.
6.7.8.1. Phi Distribution
The user is expected to enter:
· Phi
· Numerator Degrees of Freedom
· Denominator Degrees of Freedom
· Confidence Level
and the program will output the estimated power of the test (1 – β).
Example
Figure B.1d on p. AppB 862 from Zar, J. H. (2010). Select Statistics 1 → Sample Size and Power Estimation → Phi Distribution and the Phi Distribution option. Enter the following data at the next dialogue:
Sample Size and Power Estimation:
Phi Distribution
|
Phi = |
3.0000 |
|
Numerator Degrees of Freedom = |
4.0000 |
|
Denominator Degrees of Freedom = |
20.0000 |
|
Confidence Level = |
0.9900 |
|
Power of the Test = |
0.9899 |
6.7.8.2. Inverse Phi Distribution
The user is expected to enter:
· Power of the Test
· Numerator Degrees of Freedom
· Denominator Degrees of Freedom
· Confidence Level
and the program will output the estimated 
.
Example
Figure B.1g on p. AppB 865 from Zar, J. H. (2010). Select Statistics 1 → Sample Size and Power Estimation → Phi Distribution and the Inverse Phi Distribution option. Enter the following data at the next dialogue:
Sample Size and Power Estimation:
Inverse Phi Distribution
|
Power of the Test = |
0.9050 |
|
Numerator Degrees of Freedom = |
7.0000 |
|
Denominator Degrees of Freedom = |
12.0000 |
|
Confidence Level = |
0.9500 |
|
Phi = |
1.9980 |