minEffect.SLR {powerMediation}

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 sd(x)=\sigma_x.

sigma.y

marginal standard deviation of the outcome sd(y)=\sigma_y. (not the conditional standard deviation sd(y|x))

alpha

type I error rate.

verbose

logical. TRUE means printing minimum absolute detectable effect; FALSE means not printing 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})

Value

lambda.a

minimum absolute detectable effect.

res.uniroot

results of optimization to find the optimal minimum absolute detectable effect.

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

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)