Cesar Chew at 16:55, 25 November 2014

2014-11-25T16:55:05Z

New page

{{Cat|Power| 1}}

Prerequisites
* [[Significance Testing]], [[Type I and II Errors]], [[Misconceptions]]

==Define power==
* Suppose you work for a foundation whose mission is to support researchers in mathematics education and your role is to evaluate grant proposals and decide which ones to fund.
* You receive a proposal to evaluate a new method of teaching high-school algebra.
* The research plan is to compare the achievement of students taught by the new method with those taught by the traditional method.
* The proposal contains good theoretical arguments why the new method should be superior and the proposed methodology is sound.
* In addition to these positive elements, there is one important question still to be answered: Does the experiment have a high probability of providing strong evidence that the new method is better than the standard method even if, in fact, the new method is actually better?
* It is possible, for example, that the proposed sample size is so small that even a fairly large population difference would be difficult to detect.
* That is, if the sample size is small, then even a fairly large difference in sample means might not be significant.
* If the difference is not significant, then no strong conclusions can be drawn about the population means.
* It is not justified to conclude that the null hypothesis that the population means are equal is true just because the difference is not significant.
* Of course, it is not justified to conclude that this null hypothesis is false. Therefore, when an effect is not significant, the result is inconclusive.
* You may prefer that your foundation's money be used to fund a project that has a higher probability of being able to make a strong conclusion.

* Power is defined as the probability of correctly rejecting a false null hypothesis.
* In terms of our example, it is the probability that given there is a difference between the population means of the new method and the standard method, the sample means will be significantly different.
* The probability of failing to reject a false null hypothesis is often referred to as β.
* Therefore power can be defined as:

:<math> \mbox{power} = \mathbb P\big( \mbox{reject null hypothesis} \big| \mbox{null hypothesis is false} \big) </math>

power = 1 - β.

==Identify situations in which it is important to estimate power==

* It is very important to consider power while designing an experiment.
* You should avoid spending a lot of time and/or money on an experiment that has little chance of finding a significant effect.

== Questions ==

<quiz display=simple >

{Power is:
|type="()"}
- The probability that the null hypothesis is true.
- The probability that the null hypothesis is false.
+ The The probability a false null hypothesis will be rejected.
- The The probability a true null hypothesis will be rejected

{
{{Show Answer|
It is the probability of correctly rejecting a false null hypothesis.
}}
}

{If the power of an experiment is low then
|type="()"}
+ The experiment will likely be inconclusive.
- Any significant findings obtained are suspect.
- The results are skewed

{
{{Show Answer|
With low power, the null hypothesis is unlikely to be rejected. When the null hypothesis is not rejected, the experiment is inconclusive.
}}
}

</quiz>

[[:Category:Power|Power]] | [[Example Calculations]] >

Introduction to Power - Revision history

Cesar Chew at 16:55, 25 November 2014