power.SLR {powerMediation}

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 sd(x).

sigma.y

marginal standard deviation of the outcome sd(y). (not the marginal standard deviation sd(y|x))

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. For one-sided tests, please double the significance level. For example, you can set alpha=0.10 to obtain one-sided test at 5% significance level.

Author(s)

Weiliang Qiu [e-mail]

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)