The researcher believes that the population squared multiple correlation is about .
In fact, they are more accurate than necessary because these sample size formulas require a planning value for the population squared multiple correlation and researchers are usually unable to accurately specify this value.
specifically, Equations 1 and 2 clearly describe how the sample size requirement depends on the desired level confidence, the desired precision, and the planning value of the population squared multiple correlation.
First, it is well known that the distribution of sample squared multiple correlation is generally skewed.
To ensure the precision of Helland's (1987) confidence intervals for the squared multiple correlation coefficient, two methods were considered in Bonett and Wright (2011).
In order to demonstrate the features of Bonett and Wright's (2011) sample size procedures in Equations 2 and 3, empirical examinations were performed for precise interval estimation of the squared multiple correlation coefficient.
The determination of sample sizes needed for the chosen precision of the confidence intervals requires the specification of the confidence level, the magnitude of squared multiple correlation coefficient, and the number of predictor variables.
Overall, the presented numerical evidence suggests that the sample size formulas of Bonett and Wright (2011) are not accurate enough to serve as a general method for computing the sample sizes for ensuring precise confidence intervals of squared multiple correlation.
Therefore, their procedures are not recommended for precise interval estimation of squared multiple correlation coefficient in multiple regression analysis.
Sample size planning for the squared multiple correlation coefficient: Accuracy in parameter estimation via narrow confidence intervals.