pwrss (version 0.3.1)

pwrss.z.2props: Difference between Two Proportions (z Test)

Description

Calculates statistical power or minimum required sample size (only one can be NULL at a time) to test difference between two proportions.

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

Usage

pwrss.z.2props(p1, p2, margin = 0, arcsin.trans = FALSE, kappa = 1, alpha = 0.05,
               alternative = c("not equal","greater","less",
                               "equivalent","non-inferior","superior"),
               n2 = NULL, power = NULL, verbose = TRUE)

Value

parms

list of parameters used in calculation

test

type of the statistical test (z test)

ncp

non-centrality parameter

power

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

n

sample size for the first and second group

Arguments

p1

expected proportion in the first group

p2

expected proportion in the second group

arcsin.trans

if TRUE uses arcsine transformation, if FALSE uses normal approximation (default)

kappa

n1/n2 ratio

n2

sample size in the second group. Sample size in the first group can be calculated as n2*kappa. By default, n1 = n2 because kappa = 1

power

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

alpha

probability of type I error.

margin

non-inferority, superiority, or equivalence margin (margin: boundry of p1 - p2 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

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

# Example 1: expecting p1 - p2 smaller than 0
## one-sided test with normal approximation
pwrss.z.2props(p1 = 0.45, p2 = 0.50,
               alpha = 0.05, power = 0.80,
               alternative = "less",
               arcsin.trans = FALSE)
## one-sided test with arcsine transformation
pwrss.z.2props(p1 = 0.45, p2 = 0.50,
               alpha = 0.05, power = 0.80,
               alternative = "less",
               arcsin.trans = TRUE)

# Example 2: expecting p1 - p2 smaller than 0 or greater than 0
## two-sided test with normal approximation
pwrss.z.2props(p1 = 0.45, p2 = 0.50,
               alpha = 0.05, power = 0.80,
               alternative = "not equal",
               arcsin.trans = FALSE)
## two-sided test with arcsine transformation
pwrss.z.2props(p1 = 0.45, p2 = 0.50,
               alpha = 0.05, power = 0.80,
               alternative = "not equal",
               arcsin.trans = TRUE)

# Example 2: expecting p1 - p2 smaller than 0.01
# when smaller proportion is better
## non-inferiority test with normal approximation
pwrss.z.2props(p1 = 0.45, p2 = 0.50, margin = 0.01,
               alpha = 0.05, power = 0.80,
               alternative = "non-inferior",
               arcsin.trans = FALSE)
## non-inferiority test with arcsine transformation
pwrss.z.2props(p1 = 0.45, p2 = 0.50, margin = 0.01,
               alpha = 0.05, power = 0.80,
               alternative = "non-inferior",
               arcsin.trans = TRUE)

# Example 3: expecting p1 - p2 greater than -0.01
# when bigger proportion is better
## non-inferiority test with normal approximation
pwrss.z.2props(p1 = 0.55, p2 = 0.50, margin = -0.01,
               alpha = 0.05, power = 0.80,
               alternative = "non-inferior",
               arcsin.trans = FALSE)
## non-inferiority test with arcsine transformation
pwrss.z.2props(p1 = 0.55, p2 = 0.50,  margin = -0.01,
               alpha = 0.05, power = 0.80,
               alternative = "non-inferior",
               arcsin.trans = TRUE)

# Example 4: expecting p1 - p2 smaller than -0.01
# when smaller proportion is better
## superiority test with normal approximation
pwrss.z.2props(p1 = 0.45, p2 = 0.50, margin = -0.01,
               alpha = 0.05, power = 0.80,
               alternative = "superior",
               arcsin.trans = FALSE)
## superiority test with arcsine transformation
pwrss.z.2props(p1 = 0.45, p2 = 0.50, margin = -0.01,
               alpha = 0.05, power = 0.80,
               alternative = "superior",
               arcsin.trans = TRUE)

# Example 5: expecting p1 - p2 greater than 0.01
# when bigger proportion is better
## superiority test with normal approximation
pwrss.z.2props(p1 = 0.55, p2 = 0.50, margin = 0.01,
               alpha = 0.05, power = 0.80,
               alternative = "superior",
               arcsin.trans = FALSE)
## superiority test with arcsine transformation
pwrss.z.2props(p1 = 0.55, p2 = 0.50, margin = 0.01,
               alpha = 0.05, power = 0.80,
               alternative = "superior",
               arcsin.trans = TRUE)

# Example 6: expecting p1 - p2 between -0.01 and 0.01
## equivalence test with normal approximation
pwrss.z.2props(p1 = 0.50, p2 = 0.50, margin = 0.01,
               alpha = 0.05, power = 0.80,
               alternative = "equivalent",
               arcsin.trans = FALSE)
# equivalence test with arcsine transformation
pwrss.z.2props(p1 = 0.50, p2 = 0.50, margin = 0.01,
               alpha = 0.05, power = 0.80,
               alternative = "equivalent",
               arcsin.trans = TRUE)