pwrss (version 0.3.1)

pwrss.f.ancova: 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)

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

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

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)