pwrss.f.reg {pwrss}

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)