5-ANOVA-and-ANCOVA: Analysis of (Co)Variance (F test)

In pwrss: Statistical Power and Sample Size Calculation Tools

Analysis of (Co)Variance (F test)

Description

Calculates statistical power or minimum required sample size for one-way, two-way, or three-way ANOVA/ANCOVA. Set n.covariates = 0 for ANOVA, and n.covariates > 0 for ANCOVA. Note that in each case, the effect size (partial) (eta2 or f2) should be obtained from the relevant model.

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

Usage

pwrss.f.ancova(eta2 = 0.01, f2 = eta2 / (1 - eta2),
               n.way = length(n.levels),
               n.levels = 2, n.covariates = 0, alpha = 0.05,
               n = NULL, power = NULL, verbose = TRUE)

Arguments

eta2	expected Eta-squared
f2	expected Cohen's f2 (an alternative to eta2 specification). f2 = eta2 / (1 - eta2)
n.way	1 for one-way, 2 for two-way, 3 for three-way ANOVA or ANCOVA. The default takes its value from the length of n.levels
n.levels	number of levels (groups) in each factor. For example, for two factors each having two levels (groups) use e.g. c(2,2), for three factors each having two levels (groups) use e.g. c(2,2,2)
n.covariates	number of covariates in the ANCOVA model
n	total sample size
alpha	probability of type I error
power	statistical power (1-\beta)
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	total 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

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

# a researcher is expecting a difference of
# Cohen's d = 0.50 between treatment and control
# translating into Eta-squared = 0.059

# estimate sample size using ANOVA approach
pwrss.f.ancova(eta2 = 0.059, n.levels = 2,
               alpha = 0.05, power = .80)

# estimate sample size using regression approach(F test)
pwrss.f.reg(r2 = 0.059, k = 1,
            alpha = 0.05, power = 0.80)

# estimate sample size using regression approach (t test)
p <- 0.50 # proportion of sample in treatment
pwrss.t.reg(beta1 = 0.50, r2 = 0,
            k = 1, sdx = sqrt(p*(1-p)),
            alpha = 0.05, power = 0.80)

# estimate sample size using t test approach
pwrss.t.2means(mu1 = 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)

pwrss.f.ancova(eta2 = 0.03, n.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)
pwrss.f.reg(r2 = 0.03, k = 3, m = 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 (n.cov = 1)
# translating into Eta-squared = 0.048

pwrss.f.ancova(eta2 = 0.048, n.levels = 2, n.cov = 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)

pwrss.f.ancova(eta2 = 0.02, n.levels = c(2,2), n.cov = 1,
               alpha = 0.05, power = .80)

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