Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 81
Estimates
The Power
The power is the probability of getting a significant result. It is a function of the sample size n, the effect size
δ, the standard deviation of the error σ, and the significance level α. The power tells you how likely your
experiment will detect a difference at a given α-level.
Power has the following characteristics:
• If the true value of the parameter is the hypothesized value, the power should be alpha, the size of the
test. You do not want to reject the hypothesis when it is true.
• If the true value of the parameters is not the hypothesized value, you want the power to be as great as
possible.
• The power increases with the sample size, as the error variance decreases, and as the true parameter gets
farther from the hypothesized value.
The Adjusted Power and Confidence Intervals
You typically substitute sample estimates in power calculations, because power is a function of unknown
population quantities (Wright and O’Brien 1988). If you regard these sample estimates as random, you can
adjust them to have a more proper expectation.
You can also construct a confidence interval for this adjusted power. However, the confidence interval is
often very wide. The adjusted power and confidence intervals can be computed only for the original δ,
because that is where the random variation is. For details about adjusted power see “Computations for
Adjusted Power” on page 685 in the “Statistical Details” appendix
Correlation of Estimates
The Correlation of Estimates command on the Estimates menu creates a correlation matrix for all
parameter estimates.
Example of Correlation of Estimates
1. Open the Tiretread.jmp data table.
2. Select Analyze > Fit Model.
3. Select ABRASION and click Y.
4. Select SILICA and SILANE and click Add.
5. Select SILICA and SILANE and click Cross.
6. Click Run.
7. From the Response red triangle menu, select Estimates > Correlation of Estimates.