pwrss.f.rmanova {pwrss}

Repeated Measures Analysis of Variance (F test)

Description

Calculates statistical power or minimum required sample size for one-way Repeated Measures Analysis of Variance (RM-ANOVA).

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

Usage

pwrss.f.rmanova(eta2 = 0.10, f2 = eta2/(1 - eta2),
                corr.rm = 0.50, n.levels = 2, n.rm = 2,
                epsilon = 1, alpha = 0.05,
                type = c("between","within","interaction"),
                n = NULL, power = NULL, verbose = TRUE)

Arguments

eta2

expected (partial) Eta-squared

f2

expected Cohen's f-squared (an alternative to eta2 specification). f2 = eta2 / (1 - eta2)

corr.rm

expected correlation between repeated measures. For example, for pretest/posttest designs, this is the correlation between pretest and posttest scores regardless of group membership. The default is 0.50

n.levels

number of levels (groups). For example, for randomized controlled trials with two arms (treatment/control) it takes a value of 2

n.rm

number of measurements. For example, for pretest/posttest designs it takes a value of 2. When there is a follow-up test it takes a value of 3

epsilon

non-sperhicity correction factor, default is 1 (means no violation of sphericity). Lower bound for this argument is epsilon = 1 / (n.rm - 1)

n

total sample size

power

statistical power (1-\beta)

alpha

probability of type I error

type

the effect to be tested: "between", "within", or "interaction". The type of the effect depends on the hypothesis test. If the interest is in the group effect after controlling for the time effect use "between"; if the interest is the time effect after controlling for the group membership use "within"; if the interest is in the group x time interaction use "interaction"

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/

Examples

######################################################
# pretest-posttest design with treatment group only  #
######################################################

# a researcher is expecting a difference of Cohen's d = 0.30
# between posttest and pretest score translating into
# Eta-squared = 0.022
pwrss.f.rmanova(eta2 = 0.022,  n.levels = 1, n.rm = 2,
                corr.rm = 0.50, type = "within",
                alpha = 0.05, power = 0.80)

# paired t-test approach
pwrss.t.2means(mu1 = 0.30, mu2 = 0,
               sd1 = 1, sd2 = 1,
               paired = TRUE, paired.r = 0.50,
               alpha = 0.05, power = 0.80)

##########################################################
# posttest only design with treatment and control groups #
##########################################################

# a researcher is expecting a difference of Cohen's d = 0.50
# on the posttest score between treatment and control groups
# translating into Eta-squared = 0.059
pwrss.f.rmanova(eta2 = 0.059,  n.levels = 2, n.rm = 1,
                type = "between",
                alpha = 0.05, power = 0.80)

# independent t-test approach
pwrss.t.2means(mu1 = 0.50, mu2 = 0,
               sd1 = 1, sd2 = 1,
               alpha = 0.05, power = 0.80)

#############################################################
# pretest-posttest design with treatment and control groups #
#############################################################

# a researcher is expecting a difference of Cohen's d = 0.40
# on the posttest score between treatment and control groups
# after controlling for the pretest translating into
# partial Eta-squared = 0.038
pwrss.f.rmanova(eta2 = 0.038,  n.levels = 2, n.rm = 2,
                corr.rm = 0.50, type = "between",
                alpha = 0.05, power = 0.80)

# regression approach
p <- 0.50 # proportion of subjects in treatment group
pwrss.t.reg(beta1 = 0.40, r2 = 0.25, k = 2,
            sdx = sqrt(p*(1-p)),
            alpha = 0.05, power = 0.80)

# a researcher is expecting an interaction effect
# (between groups and time) of Eta-squared = 0.01
pwrss.f.rmanova(eta2 = 0.01,  n.levels = 2, n.rm = 2,
                corr.rm = 0.50, type = "interaction",
                alpha = 0.05, power = 0.80)