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

## Description

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

## Usage

 ```1 2 3 4 5 6``` ```minEffect.SLR(n, power, sigma.x, sigma.y, alpha = 0.05, verbose = TRUE) ```

## Arguments

 `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.

## 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 ~ 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 stwxq@channing.harvard.edu

## 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.

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

## Examples

 ```1 2``` ``` minEffect.SLR(n = 100, power = 0.8, sigma.x = 0.2, sigma.y = 0.5, alpha = 0.05, verbose = TRUE) ```

### Example output

``` 0.68071
```

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