minEffect.SLR: Minimum detectable slope
In powerMediation: Power/Sample Size Calculation for Mediation Analysis

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

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

`n`	sample size.
`power`	power for testing if λ=0 for the simple linear regression y_i=gamma+lambda x_i + epsilon_i, epsilon_i ~ 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.

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 ~ N(0, sigma^2_{e})

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

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.

Weiliang Qiu stwxq@channing.harvard.edu

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

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