4-Linear-Regression-Rsquared: Linear Regression: R-squared or R-squared Difference (F Test)

In pwrss: Statistical Power and Sample Size Calculation Tools

Linear Regression: R-squared or R-squared Difference (F Test)

Description

Calculates statistical power or minimum required sample size (only one can be NULL at a time) to test R-squared deviation from 0 (zero) in linear regression or to test R-squared difference between two linear regression models. The test of R-squared difference is often used to evaluate incremental contribution of a set of predictors in hierarchical linear regression.

Formulas are validated using Monte Carlo simulation, G*Power, and tables in PASS documentation.

Usage

pwrss.f.reg(r2 = 0.10, f2 = r2 /(1 - r2),
            k = 1, m = k, alpha = 0.05,
            n = NULL, power = NULL, verbose = TRUE)

Arguments

r2	expected R-squared (or R-squared change)
f2	expected Cohen's f-squared (an alternative to r2 specification). f2 = r2 / (1 - r2)
k	(total) number of predictors
m	number of predictors in the subset of interest. By default m = k, which implies that one is interested in the contribution of all predictors, and tests whether R-squared value is different from 0 (zero)
n	sample size
power	statistical power (1-\beta)
alpha	probability of type I error
verbose	if FALSE no output is printed on the console

Value

parms	list of parameters used in calculation
test	type of the statistical test (F test)
df1	numerator degrees of freedom
df2	denominator degrees of freedom
ncp	non-centrality parameter
power	statistical power (1-\beta)
n	sample size

References

Bulus, M., & Polat, C. (in press). pwrss R paketi ile istatistiksel guc analizi [Statistical power analysis with pwrss R package]. Ahi Evran Universitesi Kirsehir Egitim Fakultesi Dergisi. https://osf.io/ua5fc/download/

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Examples

# EXample 1: A researcher is expecting that
# three variables together explain 15 percent of the variance
# in the outcome (R-squared = 0.15).
pwrss.f.reg(r2 = 0.15, k = 3,
            alpha = 0.05, power = 0.80)

# Example 2: A researcher is expecting that
# adding two more variables will increase R-squared
# from 0.15 (with 3 predictors) to 0.20 (with 3 + 2 predictors)
# k = 5 (total number of predictors)
# m = 2 (predictors whose incremental contribution to R-squared change is of interest)
pwrss.f.reg(r2 = 0.05, k = 5, m = 2,
            alpha = 0.05, power = 0.80)

pwrss documentation built on April 12, 2023, 12:34 p.m.