power_lm: 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 regression analysis

Description

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

Usage

power_lm(
  PRE = 0.02,
  PC = 1,
  PA = 2,
  sig_level = 0.05,
  power = 0.8,
  power_ul = 1,
  n_ul = 1.45e+09,
  n = NULL
)

Arguments

PRE	Proportional Reduction in Error. PRE = The square of partial correlation. Cohen (1988) suggested >=0.02, >=0.13, and >=0.26 as cut-off values of PRE for small, medium, and large effect sizes, respectively.
PC	Number of parameters of model C (compact model) without focal predictors of interest. Non-integer PC would be converted to be an integer using as.integer().
PA	Number of parameters of model A (augmented model) with focal predictors of interest. Non-integer PA would be converted to be an integer using as.integer(). as.integer(PA) should be larger than as.integer(PC).
sig_level	Expected significance level for effects of focal predictors.
power	Expected statistical power for effects of focal predictors.
power_ul	The upper limit of power below which the minimum sample size is searched. 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(). as.integer(n_ul) should be at least as.integer(PA) + 1.
n	The current sample size. Non-integer n would be converted to be an integer using as.integer(). Non-NULL as.integer(n) should be at least as.integer(PA) + 1.

Details

power_ul and n_ul determine the total times of power_lm()'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_lm() will keep running and gradually raise the sample size to n_ul until the sample size pushes the power level to power_ul. When PRE is very small (e.g., less than 0.001) and power is larger than 0.8, a huge increase in sample size only brings about a trivial increase in power, which is cost-ineffective. To make power_lm() 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 sample size n is not given, the following results would be returned: ⁠[[1]]⁠ PRE; ⁠[[2]]⁠ f_squared, Cohen's f_squared derived from PRE; ⁠[[3]]⁠ PC; ⁠[[4]]⁠ PA; ⁠[[5]]⁠ sig_level, expected significance level for effects of focal predictors; ⁠[[6]]⁠ power, expected statistical power for effects of focal predictors; ⁠[[7]]⁠ power_ul, the upper limit of power; ⁠[[8]]⁠ n_ul, the upper limit of sample size; ⁠[[9]]⁠ minimum, the minimum sample size n_i required for focal predictors to reach the expected statistical power and significance level, and corresponding df_A_C(the df of the numerator of the F-test, i.e., the difference of the dfs between model C and model A), df_A_i(the df of the denominator of the F-test, i.e., the df of the model A at the sample size n_i), F_i(the F-test of PRE at the sample size n_i), p_i(the p-value of F_i), lambda_i(the non-centrality parameter of the F-distribution for the alternative hypothesis, given PRE and n_i), power_i(the actual power of PRE at the sample size n_i); ⁠[[10]]⁠ prior, a prior power table with increasing sample sizes (n_i) and power(power_i).

If sample size n is given, the following results would also be returned: Integer n, the F_test of PRE at the sample size n with df_A_C, df_A (the df of the model A at the sample size n), F (the F-test of PRE at the sample size n), p (the p-value of F-test at the sample size n), and the post-hoc power analysis with lambda_post (the non-centrality parameter of F at the sample size n), and power_post (the post-hoc power 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

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

Examples

power_lm()
print(power_lm())
plot(power_lm())

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