# ss.SLR: Sample size for testing slope for simple linear regression In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

Calculate sample size for testing slope for simple linear regression.

## Usage

 ```1 2 3 4 5 6 7 8``` ```ss.SLR(power, lambda.a, sigma.x, sigma.y, n.lower = 2.01, n.upper = 1e+30, alpha = 0.05, verbose = TRUE) ```

## Arguments

 `power` power for testing if λ=0 for the simple linear regression y_i=γ+λ x_i + ε_i, ε_i\sim N(0, σ_{e}^2). `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)) `n.lower` lower bound for the sample size. `n.upper` upper bound for the sample size. `alpha` type I error rate. `verbose` logical. `TRUE` means printing sample size; `FALSE` means not printing sample size.

## Details

The test 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

 `n ` sample size. `res.uniroot ` results of optimization to find the optimal sample size.

## 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.

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

## Examples

 ```1 2``` ``` ss.SLR(power=0.8, lambda.a=0.8, sigma.x=0.2, sigma.y=0.5, alpha = 0.05, verbose = TRUE) ```

### Example output

``` 70.79538
```

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