Now Playing: Multiple Regression (2:58)
In a typical multiple regression analysis, the variables are tested by dividing each regression coefficient by its standard error to form a t-statistic. An equivalent F-test for each term may be made by considering the amount of R-squared that is lost if the term is removed from the model. Further, a group of terms may be tested collectively by considering the decrease in R-Squared if the group of terms is removed from the model. It is this decrease in R-Squared that is required as input to determine the necessary sample size in PASS.
Suppose a study is to be conducted to determine the relationship between two hormone levels and heart rate. Several other covariates will be measured on each subject, such as blood pressure and weight, but it is of primary interest to determine whether the two hormone levels (together) correlate with a change in heart rate.
In total, four covariates will be measured. Researchers estimate that those four covariates alone will yield an R-Squared of somewhere between 0.2 and 0.4.
They would like to know the sample size needed to detect increases in R-Squared between 0.05 and 0.15, when the two hormone levels are added as variables (to the other four).
The researchers need a power of 90% and will use an alpha of 0.05.
Some explanation about the reasoning for using the Conditional Power Calculation Method is given in the Option Info section.
The numeric report gives the needed sample sizes for each combination of parameters, line by line.
The values are much easier to compare using the sample size chart at the bottom.
The needed sample sizes are much higher for R-Squared increases that are less than 0.10.