power.SLR {powerMediation}R Documentation

Power for testing slope for simple linear regression

Description

Calculate power for testing slope for simple linear regression.

Usage

power.SLR(n, lambda.a, sigma.x, sigma.y, alpha = 0.05, verbose = TRUE)

Arguments

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.

Details

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})

Value

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.

Note

The test is a two-sided test. Code for one-sided tests will be added later.

Author(s)

Weiliang Qiu stwxq@channing.harvard.edu

References

Dupont, W.D. and Plummer, W.D.. Power and Sample Size Calculations for Studies Involving Linear Regression. Controlled Clinical Trials. 1998;19:589-601.

See Also

minEffect.SLR, power.SLR.rho, ss.SLR.rho, ss.SLR.

Examples

  power.SLR(n=100, lambda.a=0.8, sigma.x=0.2, sigma.y=0.5, 
    alpha = 0.05, verbose = TRUE)


[Package powerMediation version 0.0.6 Index]