Power Analysis for Linear Regression: R-squared or R-squared Change (F-Test)

Calculates power or 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 change between two linear regression models. The test of R-squared change 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.

NOTE: The pwrss.f.reg() function and its alias pwrss.f.regression are deprecated, but they will remain available as a wrapper for power.f.regression() during the transition period.

Usage

power.f.regression(r.squared.change = NULL, margin = 0,
                   k.total, k.tested = k.total,
                   n = NULL, power = NULL, alpha = 0.05,
                   ceiling = TRUE, verbose = TRUE, pretty = FALSE)

Arguments

r.squared.change: R-squared (or R-squared change).
margin: margin - ignorable R-squared (or R-squared change).
k.total: integer; total number of predictors.
k.tested: integer; number of predictors in the subset of interest. By default m.tested = k.total, which implies that one is interested in the contribution of all predictors, and tests whether R-squared value is different from 0 (zero).
n: integer; sample size.
power: statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).
alpha: type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).
ceiling: logical; whether sample size should be rounded up. TRUE by default.
verbose: logical; whether the output should be printed on the console. TRUE by default.
pretty: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

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 for the alternative.
null.ncp: non-centrality parameter for the null.
f.alpha: critical value.
power: statistical power \((1-\beta)\).
n: sample size.

References

Bulus, M., & Polat, C. (2023). pwrss R paketi ile istatistiksel guc analizi [Statistical power analysis with pwrss R package]. Ahi Evran Universitesi Kirsehir Egitim Fakultesi Dergisi, 24(3), 2207-2328. doi:10.29299/kefad.1209913

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

Examples

# in the outcome (R-squared = 0.15).
power.f.regression(r.squared = 0.15,
                   k.total = 3, # total number of predictors
                   power = 0.80)
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Linear Regression (F-Test)
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : R-squared = 0 
#>   H1 (Alt. Claim) : R-squared > 0 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Sample Size          = 66  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.199
#>   Statistical Power    = 0.801
#> 

# adding two more variables will increase R-squared
# from 0.15 (with 3 predictors) to 0.25 (with 3 + 2 predictors)
power.f.regression(r.squared.change = 0.10, # R-squared change
                   k.total = 5, # total number of predictors
                   k.tested = 2, # predictors to be tested
                   power = 0.80)
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Hierarchical Linear Regression (F-Test)
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : Change in R-squared = 0 
#>   H1 (Alt. Claim) : Change in R-squared > 0 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Sample Size          = 90  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.199
#>   Statistical Power    = 0.801
#>