2-Two-Proportions: Difference between Two Proportions (z Test)

In pwrss: Statistical Power and Sample Size Calculation Tools

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)

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

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

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)

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