powerMediation (version 0.2.3)

minEffect.SLR: Minimum detectable slope

Description

Calculate minimal detectable slope given sample size and power for simple linear regression.

Usage

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

Arguments

n

sample size.

power

power for testing if $\lambda=0$ for 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 minimum absolute detectable effect; FALSE means not printing minimum absolute detectable effect.

Value

• lambda.a
  minimum absolute detectable effect.
• res.uniroot
  results of optimization to find the optimal minimum absolute detectable effect.

Details

The test 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

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

Examples

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