betapower {BetaPASS} | R Documentation |

## Find Power with Beta distribution

### Description

Find the power for a given sample size when testing the null hypothesis that the means for the control and treatment groups are equal against a two-sided alternative.

### Usage

```
betapower(mu0, sd0, mu1.start, mu1.end = NULL, mu1.by = NULL,
ss.start, ss.end = NULL, ss.by = NULL, sig.level = 0.05,
trials = 100, seed = 1, link.type="logit",
equal.precision=TRUE, sd1 = NULL)
```

### Arguments

`mu0` |
mean for the control group |

`sd0` |
standard deviation for the control group |

`mu1.start` |
starting value of mean for the treatment group under the alternative mu1 |

`mu1.end` |
ending value of mean for the treatment group under the alternative mu1 |

`mu1.by` |
step length of mean for the treatment group under the alternative mu1 |

`ss.start` |
starting value of sample size |

`ss.end` |
ending value of sample size |

`ss.by` |
step length of sample size |

`sig.level` |
significant level of test; default value is 0.05 |

`trials` |
number of trials |

`seed` |
seed used in the simulation |

`link.type` |
type of link used in the beta regression. Default value is "logit", or you can use "all" or choose one or more of the following: "logit", "probit", "cloglog", "cauchit", "log", "loglog" |

`equal.precision` |
equal dispersion parameter assumption in simulation |

`sd1` |
standard deviation for the treatment group. Only applicable when equal.precision = FALSE |

### Details

betapower function allows you to control the number of trials in the simulation,
the sample sizes used, and the alternative means.
You can fix the alternative and vary sample size to match a desired power;
You can fix the sample size and vary the alternative to see which will match a desired power;
You can vary both;
Start with a small number of trials (say 100) to determine the rough range of sample sizes or alternatives;
Use a larger number of trials (say 1000) to get better estimates.

The plot function will return different plots depends on "by" statement.
Type of link used in the beta regression. You can choose one or more of the following: "logit", "probit", "cloglog", "cauchit", "log", "loglog", "all"

by = "linktype": return graphs that plot power against mu1,
where mu1 is the mean for the treatment group under the alternative.
The number of plots will vary depending on the number of link types selected with the last plot showing power based on Wilcoxon Rank Sum Test.
The first one or several plots show comparisons of power with different sample size, using GLM method with one or several link types.
The last plot shows a comparison of the power with different sample size using Wilcoxon Rank Sum Test.
Y-axis denotes power and X-axis denotes mu1, the mean for the treatment group under the alternative.

by = "samplesize": return a number of plots equal to the number of sample sizes tested.
Each plot compares power calculated with different link types and the Wilcoxon Rank Sum Test.
Y-axis denotes power and X-axis denotes mu1, the mean for the treatment group under the alternative.

by = "mu1": return a number of plots equal to the number of mu1 used in the procedure.
Each plot compares power calculated with different link types and the Wilcoxon Rank Sum Test.
Y-axis denotes power and X-axis denotes sample size.

### Value

Return a betapower object including basic settings (mean and standard deviation for the control group, significant level, number of trials and link types), and a matrix of estimated power with given sample size and mu1.

`beta regression(link name)` |
estimated power using beta regression method; it will return the power with every links if you use link.type = "all" statement. |

`Wilcoxon` |
estimated power from Wilcoxon Rank sum test. |

`sample size` |
sample size. |

`mu1` |
mean for the treatment group under the alternative. |

### Examples

```
BPmat <- betapower(mu0 = 0.56, sd0 = 0.255, mu1.start = .70, mu1.end = .75, mu1.by = .05,
ss.start = 30, ss.end = 50, ss.by = 20, trials = 100)
## show the results
BPmat
## add plot
plot(BPmat, link.type = "logit", by = "mu1")
```

*BetaPASS*version 1.1-2 Index]