power_r: Conduct post-hoc and prior power analysis, and plan the...

In Keng: Knock Errors Off Nice Guesses

Conduct post-hoc and prior power analysis, and plan the sample size for r.

Description

Conduct post-hoc and prior power analysis, and plan the sample size for r.

Usage

power_r(
  r = 0.2,
  sig_level = 0.05,
  power = 0.8,
  power_ul = 1,
  n_ul = 1.45e+09,
  n = NULL
)

Arguments

r	Pearson's correlation. Cohen(1988) suggested >=0.1, >=0.3, and >=0.5 as cut-off values of Pearson's correlation r for small, medium, and large effect sizes, respectively.
sig_level	Expected significance level.
power	Expected statistical power.
power_ul	The upper limit of power. power_ul should be larger than power, and the maximum power_ul is 1.
n_ul	The upper limit of sample size below which the minimum required sample size is searched. Non-integer n_ul would be converted to be an integer using as.integer(). n_ul should be at least 3.
n	The current sample size. Non-integer n would be converted to be an integer using as.integer(). n should be at least 3.

Details

Power_r() follows Aberson (2019) approach to conduct power analysis. power_ul and n_ul determine the total times of power_r()'s attempts searching for the minimum required sample size, hence the number of rows of the returned power table prior and the right limit of the horizontal axis of the returned power plot. power_r() will keep running and gradually raise the sample size to n_ul until the sample size pushes the power level to power_ul. When r is very small and power is larger than 0.8, a huge increase of sample size only brings about a trivial increase in power, which is cost-ineffective. To make power_r() omit unnecessary attempts, you could set power_ul to be a value less than 1 (e.g., 0.90), and/or set n_ul to be a value less than 1.45e+09 (e.g., 10000).

Value

A Keng_power class, also a list. If n is not given, the following results would be returned: ⁠[[1]]⁠ r, the given r; ⁠[[2]]⁠ d, Cohen's d derived from r; Cohen (1988) suggested >=0.2, >=0.5, and >=0.8 as cut-off values of d for small, medium, and large effect sizes, respectively; ⁠[[3]]⁠ sig_level, the expected significance level; ⁠[[4]]⁠ power, the expected power; ⁠[[5]]⁠ power_ul, The upper limit of power; ⁠[[6]]⁠ n_ul, the upper limit of sample size; ⁠[[7]]⁠ minimum, the minimum planned sample size n_i and corresponding df_i (the df of t-test at the sample size n_i, df_i = n_i - 2), SE_i (the SE of r at the sample size n_i), t_i (the t-test of r), p_i (the p-value of t_i), delta_i (the non-centrality parameter of the t-distribution for the alternative hypothesis, given r and n_i), power_i (the actual power of r at the sample size n_i); ⁠[[8]]⁠ prior, a prior power table with increasing sample sizes (n_i) and power(power_i). ⁠[[9]]⁠ A plot of power against sample size n.

If sample size n is given, the following results would also be returned: Integer n, the t_test of r at the sample size n with df, SE of r, p (the p-value of t-test), and the post-hoc power analysis with delta_post (the non-centrality parameter of the t-distribution for the alternative hypothesis), and power_post (the post-hoc power of r at the sample size n).

By default, print() prints the primary but not all contents of the Keng_power class. To inspect more contents, use print.AsIs() or list extracting.

References

Aberson, C. L. (2019). Applied power analysis for the behavioral sciences. Routledge.

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

Examples

power_r(0.2)
print(power_r(0.04))
plot(power_r(0.04))

Keng documentation built on April 4, 2025, 1:37 a.m.