size.mean: Sample Size Determination

Description

This function performs sample size determination the one-sample and two-sample t-tests, proportions, and Pearson product-moment correlation coefficients based on precision requirements (i.e., type-I-risk, type-II-risk and an effect size).

Usage

size.mean(delta, sample = c("two.sample", "one.sample"),
          alternative = c("two.sided", "less", "greater"),
          alpha = 0.05, beta = 0.1, write = NULL, append = TRUE,
          check = TRUE, output = TRUE)
size.prop(pi = 0.5, delta, sample = c("two.sample", "one.sample"),
          alternative = c("two.sided", "less", "greater"),
          alpha = 0.05, beta = 0.1, correct = FALSE, write = NULL,
          append = TRUE, check = TRUE, output = TRUE)
size.cor(rho, delta,
         alternative = c("two.sided", "less", "greater"),
         alpha = 0.05, beta = 0.1, write = NULL, append = TRUE,
         check = TRUE, output = TRUE)

Arguments

delta: a numeric value indicating the minimum mean difference to be detected, \(\delta\).
sample: a character string specified in the function size.mean or size.prop specifying a one- or two-sample t-test or a proportion test, i.e., "two.sample" (default) for a two-sample test and "one.sample" for a one-sample test.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
alpha: a numeric value indicating the type-I-risk, \(\alpha\).
beta: a numeric value indicating the type-II-risk, \(\beta\).
write: a character string naming a text file with file extension ".txt" (e.g., "Output.txt") for writing the output into a text file.
append: logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check: logical: if TRUE (default), argument specification is checked.
output: logical: if TRUE (default), output is shown.
pi: a numeric value specified in the function size.prop indicating the true value of the probability under the null hypothesis in the one-sample test \(\pi\).0 or a number indicating the true value of the probability in group 1 in the two-sample test \(\pi\).1.
rho: a numeric value specified in the function size.cor indicating the correlation coefficient under the null hypothesis \(\rho\).0.
correct: logical: if TRUE, continuity correction is applied.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. John Wiley & Sons.

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R.Chapman & Hall/CRC.

Examples

Run this code

#----------------------------------------------------------------------------
# Example 1: One- and two-sample t-test

# Example 1a: One-sample t-test
# H0: mu = mu.0, H1: mu != mu.0
# alpha = 0.05, beta = 0.2, delta = 0.5
size.mean(delta = 0.5, sample = "one.sample",
          alternative = "two.sided", alpha = 0.05, beta = 0.2)

# Example 1b: One-sided two-sample test
# H0: mu.1 >= mu.2, H1: mu.1 < mu.2
# alpha = 0.01, beta = 0.1, delta = 1
size.mean(delta = 1, sample = "two.sample",
          alternative = "less", alpha = 0.01, beta = 0.1)

#----------------------------------------------------------------------------
# Example 2: One- and two-sample test for proportions

# Example 2a: Two-sided one-sample test
# H0: pi = 0.5, H1: pi != 0.5
# alpha = 0.05, beta = 0.2, delta = 0.2
size.prop(pi = 0.5, delta = 0.2, sample = "one.sample",
          alternative = "two.sided", alpha = 0.05, beta = 0.2)

# Example 2b: One-sided two-sample test
# H0: pi.1 <=  pi.1 = 0.5, H1: pi.1 > pi.2
# alpha = 0.01, beta = 0.1, delta = 0.2
size.prop(pi = 0.5, delta = 0.2, sample = "two.sample",
          alternative = "greater", alpha = 0.01, beta = 0.1)

#----------------------------------------------------------------------------
# Example 3: Testing the Pearson product-moment correlation coefficient

# H0: rho = 0.3, H1: rho != 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2
size.cor(rho = 0.3, delta = 0.2, alpha = 0.05, beta = 0.2)

# H0: rho <= 0.3, H1: rho > 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2
size.cor(rho = 0.3, delta = 0.2,
         alternative = "greater", alpha = 0.05, beta = 0.2)