powerMediation (version 0.2.4)

power.SLR: 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.

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 $y$ $=\lambda\sigma_x/\sigma_y$.

Details

The power is for testing the null hypothesis $\lambda=0$ versus the alternative hypothesis $\lambda\neq 0$ for the simple linear regressions: $$y_i=\gamma+\lambda x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{e})$$

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)