ancova: Power Analysis for One-, Two-, Three-Way ANOVA/ANCOVA Using...

In pwrss: Statistical Power and Sample Size Calculation Tools

Power Analysis for One-, Two-, Three-Way ANOVA/ANCOVA Using Effect Size (F-Test)

Description

Calculates power or sample size for one-way, two-way, or three-way ANOVA/ANCOVA. Set k.cov = 0 for ANOVA, and k.cov > 0 for ANCOVA. Note that in the latter, the effect size (eta.squared should be obtained from the relevant ANCOVA model, which is already adjusted for the explanatory power of covariates (thus, an additional R-squared argument is not required as an input).

Note that R has a partial matching feature which allows you to specify shortened versions of arguments, such as k or k.cov instead of k.covariates.

Formulas are validated using G*Power and tables in PASS documentation.

Usage

power.f.ancova(eta.squared,
               null.eta.squared = 0,
               factor.levels = 2,
               k.covariates = 0,
               n.total = NULL,
               power = NULL,
               alpha = 0.05,
               ceiling = TRUE,
               verbose = TRUE,
               pretty = FALSE)

Arguments

eta.squared	(partial) eta-squared for the alternative.
null.eta.squared	(partial) eta-squared for the null.
factor.levels	integer; number of levels or groups in each factor. For example, for two factors each having two levels or groups use e.g. c(2, 2), for three factors each having two levels (groups) use e.g. c(2, 2, 2).
k.covariates	integer; number of covariates in the ANCOVA model.
n.total	integer; total 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; if FALSE sample size in each cell is not rounded up.
verbose	logical; if FALSE no output is printed on the console.
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.total	total 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.29299/kefad.1209913")}

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

Examples

#############################################
#              one-way ANOVA                #
#############################################

# Cohen's d = 0.50 between treatment and control
# translating into Eta-squared = 0.059

# estimate sample size using ANOVA approach
power.f.ancova(eta.squared = 0.059,
               factor.levels = 2,
               alpha = 0.05, power = .80)

# estimate sample size using regression approach(F-Test)
power.f.regression(r.squared = 0.059,
                   k.total = 1,
                   alpha = 0.05, power = 0.80)

# estimate sample size using regression approach (T-Test)
p <- 0.50 # proportion of sample in treatment (allocation rate)
power.t.regression(beta = 0.50, r.squared = 0,
                   k.total = 1,
                   sd.predictor = sqrt(p*(1-p)),
                   alpha = 0.05, power = 0.80)

# estimate sample size using t test approach
power.t.student(d = 0.50, alpha = 0.05, power = 0.80)

#############################################
#              two-way ANOVA                #
#############################################

# a researcher is expecting a partial Eta-squared = 0.03
# for interaction of treatment (Factor A) with
# gender consisting of two levels (Factor B)

power.f.ancova(eta.squared = 0.03,
               factor.levels = c(2,2),
               alpha = 0.05, power = 0.80)

# estimate sample size using regression approach (F test)
# one dummy for treatment, one dummy for gender, and their interaction (k = 3)
# partial Eta-squared is equivalent to the increase in R-squared by adding
# only the interaction term (m = 1)
power.f.regression(r.squared = 0.03,
                   k.total = 3, k.test = 1,
                   alpha = 0.05, power = 0.80)

#############################################
#              one-way ANCOVA               #
#############################################

# a researcher is expecting an adjusted difference of
# Cohen's d = 0.45 between treatment and control after
# controllling for the pretest (k.cov = 1)
# translating into Eta-squared = 0.048

power.f.ancova(eta.squared = 0.048,
               factor.levels = 2,
               k.covariates = 1,
               alpha = 0.05, power = .80)

#############################################
#              two-way ANCOVA               #
#############################################

# a researcher is expecting an adjusted partial Eta-squared = 0.02
# for interaction of treatment (Factor A) with
# gender consisting of two levels (Factor B)

power.f.ancova(eta.squared = 0.02,
               factor.levels = c(2,2),
               k.covariates = 1,
               alpha = 0.05, power = .80)

pwrss documentation built on Sept. 16, 2025, 9:11 a.m.