power.SLR {powerMediation} | R Documentation |
Calculate power for testing slope for simple linear regression.
power.SLR(n, lambda.a, sigma.x, sigma.y, alpha = 0.05, verbose = TRUE)
n |
sample size. |
lambda.a |
regression coefficient in the simple linear regression y_i=\gamma+\lambda x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma_{e}^2). |
sigma.x |
standard deviation of the predictor. |
sigma.y |
standard deviation of the outcome. |
alpha |
type I error rate. |
verbose |
logical. TRUE means printing power; FALSE means not printing power.
|
The power is for testing the null hypothesis \lambda=0 versus the alternative hypothesis \lambda\neq 0 for the simple linear regressions:
y_i=\gamma+\lambda x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{e})
power |
power for testing if b_2=0. |
delta |
\lambda\sigma_x\sqrt{n}/\sqrt{\sigma_y^2-(\lambda\sigma_x)^2}. |
s |
\sqrt{\sigma_y^2-(\lambda\sigma_x)^2}. |
t.cr |
\Phi^{-1}(1-\alpha/2), where \Phi is the cumulative distribution function of the standard normal distribution. |
rho |
correlation between the predictor x and outcome y =\lambda\sigma_x/\sigma_y. |
The test is a two-sided test. Code for one-sided tests will be added later.
Weiliang Qiu stwxq@channing.harvard.edu
Dupont, W.D. and Plummer, W.D.. Power and Sample Size Calculations for Studies Involving Linear Regression. Controlled Clinical Trials. 1998;19:589-601.
minEffect.SLR
,
power.SLR.rho
,
ss.SLR.rho
,
ss.SLR
.
power.SLR(n=100, lambda.a=0.8, sigma.x=0.2, sigma.y=0.5, alpha = 0.05, verbose = TRUE)