pwrss (version 1.3.1)

power.f.ancova.keppel: Power Analysis for One-Way ANOVA/ANCOVA Using Means and Standard Deviations (F test)

Description

Calculates power, sample size or effect size for one-way ANOVA/ANCOVA. Set k.covariates = 0 for one-way ANOVA (without any pretest or covariate adjustment). Set k.covariates > 0 in combination with r.squared > 0 for one-way ANCOVA (with pretest or covariate adjustment).

Formulas are validated using the PASS documentation.

Usage

power.f.ancova.keppel(
  mu.vector,
  sd.vector,
  n.vector = NULL,
  p.vector = NULL,
  factor.levels = NULL,
  r.squared = 0,
  k.covariates = 0,
  power = NULL,
  alpha = 0.05,
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)

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 under alternative.

null.ncp

non-centrality parameter under null.

power

statistical power \((1-\beta)\).

n.total

total sample size.

Arguments

mu.vector

vector of adjusted means (or estimated marginal means) for each level of a factor.

sd.vector

vector of unadjusted standard deviations for each level of a factor.

n.vector

vector of sample sizes for each level of a factor.

p.vector

vector of proportion of total sample size in each level of a factor. These proportions should sum to one.

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 or groups use e.g. c(2, 2, 2)

r.squared

explanatory power of covariates (R-squared) in the ANCOVA model. The default is r.squared = 0, which means an ANOVA model would be of interest.

k.covariates

integer; number of covariates in the ANCOVA model. The default is k.covariates = 0, which means an ANOVA model would be of interest.

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 \(\alpha\).

ceil.n

logical; whether sample size should be rounded up. TRUE by default.

verbose

1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.

utf

logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Details

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

References

Keppel, G., & Wickens, T. D. (2004). Design and analysis: A researcher's handbook (4th ed.). Pearson.

Examples

# required sample size to detect a mean difference of
# Cohen's d = 0.50 for a one-way two-group design
power.f.ancova.keppel(mu.vector = c(0.50, 0), # marginal means
                      sd.vector = c(1, 1), # unadjusted standard deviations
                      n.vector = NULL, # sample size (will be calculated)
                      p.vector = c(0.50, 0.50), # balanced allocation
                      k.covariates = 1, # number of covariates
                      r.squared = 0.50, # explanatory power of covariates
                      alpha = 0.05, # Type 1 error rate
                      power = .80)

# effect size approach
power.f.ancova(eta.squared = 0.111, # effect size that is already adjusted for covariates
               factor.levels = 2, # one-way ANCOVA with two levels (groups)
               k.covariates = 1, # number of covariates
               alpha = 0.05, # Type 1 error rate
               power = .80)

# regression approach
p <- 0.50
power.t.regression(beta = 0.50,
                   sd.predictor = sqrt(p * (1 - p)),
                   sd.outcome = 1,
                   k.total = 1,
                   r.squared = 0.50,
                   n = NULL, power = 0.80)