# WMWssp: Sample size calculation for the Wilcoxon-Mann-Whitney test. In WMWssp: Wilcoxon-Mann-Whitney Sample Size Planning

## Description

This function calculates the sample size for a given power, type-I error rate and allocation rate t = n_1/N. Additionally, the actual achieved power can be simulated.

## Usage

 ```1 2``` ```WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2, simulation = FALSE, nsim = 10^4) ```

## Arguments

 `x` prior information for the first group `y` prior information for the second group `alpha` two sided type I error rate `power` power `t` proportion of subjects in the first group; or use t = "min" to use optimal proportion rate `simulation` TRUE if a power simulation should be carried out `nsim` number of simulations for the power simulation

## Value

Returns an object from class WMWssp containing

 `result` A dataframe with the results. `t` The allocation rate which was used. `alpha` The type-I error rate which was used. `simulation` The achieved power in a simulation. `power` The power which was used. `N` The sample size needed.

## References

Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.

Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.

## Examples

 ```1 2 3 4 5 6 7 8``` ```# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # calculate sample size ssp <- WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2) summary(ssp) ```

### Example output

```Wilcoxon-Mann-Whitney Sample Size Calculation

Summary
Call: WMWssp
Type-I error (two-sided): 0.05
Power: 0.8

Results
alpha (2-sided)                0.0500000
Power                          0.8000000
Estimated relative effect p    0.3491124
N (total sample size needed) 111.3719511
t=n1/N                         0.5000000
n1 in Group 1                 55.6859755
n2 in Group 2                 55.6859755
N rounded                    112.0000000
n1 rounded                    56.0000000
n2 rounded                    56.0000000
```

WMWssp documentation built on July 9, 2019, 5:03 p.m.