power.SLR: Power for testing slope for simple linear regression

In powerMediation: Power/Sample Size Calculation for Mediation Analysis

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=γ+λ x_i + ε_i, ε_i\sim N(0, σ_{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 λ=0 versus the alternative hypothesis λ\neq 0 for the simple linear regressions:

y_i=γ+λ x_i + ε_i, ε_i\sim N(0, σ^2_{e})

Value

power	power for testing if b_2=0.
delta	λσ_x√{n}/√{σ_y^2-(λσ_x)^2}.
s	√{σ_y^2-(λσ_x)^2}.
t.cr	Φ^{-1}(1-α/2), where Φ is the cumulative distribution function of the standard normal distribution.
rho	correlation between the predictor x and outcome y =λσ_x/σ_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)

powerMediation documentation built on March 24, 2021, 1:06 a.m.