2-Two-Means: Difference between Two Means (t or z Test for Independent or...

In pwrss: Statistical Power and Sample Size Calculation Tools

Difference between Two Means (t or z Test for Independent or Paired Samples)

Description

Calculates statistical power or minimum required sample size (only one can be NULL at a time) to test difference between two means. For standardized mean difference (Cohen's d) set mu1 = d and use defaults for mu2, sd1, and sd2. If pooled standard deviation (psd) is available set sd1 = psd.

Formulas are validated using Monte Carlo simulation, G*Power, http://powerandsamplesize.com/, and tables in PASS documentation.

Usage

pwrss.t.2means(mu1, mu2 = 0, margin = 0,
               sd1 = ifelse(paired, sqrt(1/(2*(1-paired.r))), 1), sd2 = sd1,
               kappa = 1, paired = FALSE, paired.r = 0.50,
               alpha = 0.05, welch.df = FALSE,
               alternative = c("not equal","greater","less",
                               "equivalent","non-inferior","superior"),
               n2 = NULL, power = NULL, verbose = TRUE)

pwrss.z.2means(mu1, mu2 = 0, sd1 = 1, sd2 = sd1, margin = 0,
               kappa = 1, alpha = 0.05,
               alternative = c("not equal", "greater", "less",
                               "equivalent", "non-inferior", "superior"),
               n2 = NULL, power = NULL, verbose = TRUE)

Arguments

mu1	expected mean in the first group
mu2	expected mean in the second group
sd1	expected standard deviation in the first group
sd2	expected standard deviation in the second group
paired	if TRUE paired samples t test
paired.r	correlation between repeated measures for paired samples (e.g., pretest and posttest)
n2	sample size in the second group (or for the single group in paired samples)
kappa	n1/n2 ratio (applies to independent samples only)
power	statistical power (1-\beta)
alpha	probability of type I error
welch.df	if TRUE uses Welch's degrees of freedom adjustment when groups sizes or variances are not equal (applies to independent samples t test only)
margin	non-inferority, superiority, or equivalence margin (margin: boundry of mu1 - mu2 that is practically insignificant)
alternative	direction or type of the hypothesis test: "not equal", "greater", "less", "equivalent", "non-inferior", or "superior"
verbose	if FALSE no output is printed on the console

Value

parms	list of parameters used in calculation
test	type of the statistical test (z or t test)
df	degrees of freedom
ncp	non-centrality parameter
power	statistical power (1-\beta)
n	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/

Chow, S. C., Shao, J., Wang, H., & Lokhnygina, Y. (2018). Sample size calculations in clinical research (3rd ed.). Taylor & Francis/CRC.

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

Examples

# independent samples t test

## difference between group 1 and group 2 is not equal to zero
## estimated difference is Cohen'd = 0.25
pwrss.t.2means(mu1 = 0.25, mu2 = 0, power = 0.80,
                alternative = "not equal")

## difference between group 1 and group 2 is greater than zero
## estimated difference is Cohen'd = 0.25
pwrss.t.2means(mu1 = 0.25, mu2 = 0, power = 0.80,
                alternative = "greater")

## mean of group 1 is practically not smaller than mean of group 2
## estimated difference is Cohen'd = 0.10 and can be as small as -0.05
pwrss.t.2means(mu1 = 0.25, mu2 = 0.15,
                margin = -0.05, power = 0.80,
                alternative = "non-inferior")

## mean of group 1 is practically greater than mean of group 2
## estimated difference is Cohen'd = 0.10 and can be as small as 0.05
pwrss.t.2means(mu1 = 0.25, mu2 = 0.15,
                margin = 0.05, power = 0.80,
                alternative = "superior")

## mean of group 1 is practically same as mean of group 2
## estimated difference is Cohen'd = 0
## and can be as small as -0.05 and as high as 0.05
pwrss.t.2means(mu1 = 0.25, mu2 = 0.25,
                margin = 0.05, power = 0.80,
                alternative = "equivalent")


#  dependent samples (matched pairs) t test

## difference between time 1 and time 2 is not equal to zero
## estimated difference between time 1 and time 2 is Cohen'd = -0.25
pwrss.t.2means(mu1 = 0, mu2 = 0.25, power = 0.80,
                paired = TRUE, paired.r = 0.50,
                alternative = "not equal")

## difference between time 1 and time 2 is less than zero
## estimated difference between time 1 and time 2 is Cohen'd = -0.25
pwrss.t.2means(mu1 = 0, mu2 = 0.25, power = 0.80,
                paired = TRUE, paired.r = 0.50,
                alternative = "less")

## mean of time 1 is practically not smaller than mean of time 2
## estimated difference is Cohen'd = -0.10 and can be as small as 0.05
pwrss.t.2means(mu1 = 0.15, mu2 = 0.25, margin = 0.05,
                paired = TRUE, paired.r = 0.50, power = 0.80,
                alternative = "non-inferior")

## mean of time 1 is practically greater than mean of time 2
## estimated difference is Cohen'd = -0.10 and can be as small as -0.05
pwrss.t.2means(mu1 = 0.15, mu2 = 0.25, margin = -0.05,
                paired = TRUE, paired.r = 0.50, power = 0.80,
                alternative = "superior")

## mean of time 1 is practically same as mean of time 2
## estimated difference is Cohen'd = 0
## and can be as small as -0.05 and as high as 0.05
pwrss.t.2means(mu1 = 0.25, mu2 = 0.25, margin = 0.05,
                paired = TRUE, paired.r = 0.50, power = 0.80,
                alternative = "equivalent")

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