P o w e r, type one error rate, beta

**True State of the World**

Decision | Ho True |
Ho False |

Reject Ho |
Type I error p = alpha |
Correct decision p = 1 - beta = |

Fail to reject Ho |
Correct decision p = 1 - alpha |
Type II error p = beta |

Power refers to the probability of a test appropriately
rejecting the null hypothesis. In other words rejecting *H*o because
it is false.

Because a type II error, or failure to reject a false null hypothesis, is known as beta, power must equal 1 - beta.

A test with High Power is what you want as a test developer. Your test will have more clout if it has a higher probability of detecting a difference between the compared means. A test with Low Power is not a good instrument to detect differences between compared means.

Most of us are familiar with Type I and Type II errors.
Type I errors occurs when we find a difference that is not really there.
Type II errors occur when we fail to see differences where there actually is
a difference. * How does Power relate to this? *Power
is the probability that we will avoid a Type II error.

Power analysis is used to determine how large an N an experiment needs and to evaluate the worth of an experiment that retains the null hypothesis.

There are three factors that determine the power of an experiment:

1. ** Effect size:** The larger
the effect size, the more likely you are to reject

2. __ The standard error of a difference:__
The smaller

3. __ Alpha:__ As you all
know the higher the alpha level, the more likely you are to reject the null
hypothesis. The conventional alpha level is .05.