pwrss (version 0.3.1)

pwrss.f.reg: 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)

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

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

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)