# Graphically illustrate the concept of power.

### Description

Create graphs of a normal test statistic under the null and alternative hypotheses to graphically show the idea of power.

### Usage

1 2 3 | ```
power.examp(n = 1, stdev = 1, diff = 1, alpha = 0.05, xmin = -2, xmax = 4)
run.power.examp(hscale=1.5, vscale=1.5, wait=FALSE)
run.power.examp.old()
``` |

### Arguments

`n` |
The sample size for the test statistic. |

`stdev` |
The standard deviation of the population. |

`diff` |
The true difference in means (alternate hypothesis). |

`alpha` |
The type I error rate to use for the test. |

`xmin` |
The minimum x value to show on the graph. |

`xmax` |
The maximum x value to show on the graph. |

`hscale` |
Controls width of plot, passed to |

`vscale` |
Controls height of plot, passed to |

`wait` |
Should R wait for the window to close. |

### Details

This function will draw 2 graphs representing an upper-tailed test of hypothesis.

The upper panel represents the test statistic under the
null hypothesis that the true mean (or mean difference) is 0. It then
also shows the upper tail area equal to `alpha`

and the rejection
region for the test statistic.

The lower panel shows the normal distribution for the test statistic
under the alternative hypothesis where the true mean (or mean
difference) is `diff`

. Using the rejection region from the upper
panel it shades the upper tail area that corresponds to the power of
the test.

Both curves are affected by the specified `stdev`

and sample size
`n`

.

The function `run.power.examp`

will in addition create a Tk
slider box that will allow you to interactively change the values of
`stdev`

, `diff`

, `alpha`

, and `n`

to dynamically
see the effects of the change on the graphs and on the power of the
test.

This can be used to demonstrate the concept of power, show the effect of sample size on power, show the inverse relationship between the type I and type II error rates, and show how power is dependent on the true mean (or difference) and the population standard deviation.

### Value

`power.examp`

invisibly returns the power computed.

`run.power.examp`

returns a list with the parameter settings and
the power if `wait`

is TRUE.

`run.power.examp.old`

does not return anything meaningful.

### Author(s)

Greg Snow 538280@gmail.com

### See Also

`power.t.test`

### Examples

1 2 3 | ```
power.examp()
power.examp(n=25)
power.examp(alpha=0.1)
``` |