# Power Analysis Tutorial

### Statistical Power

The Statistical Data Analysis tutorial page provides a good background for understanding the concept of "statistical power".

In very basic terms, statistical power is the likelihood of achieving
statistical significance, when in fact the "alternative hypothesis" is true. In other words, statistical power is the probability
of obtaining a p-value less than 0.05 (p < 0.05) with a given sample size and a given effect size (e.g. strength of correlation within the "population" of interest).

### Power Analysis Example

Suppose your research hypothesis is that rich people have a better quality of
life than poor people. Assume you have a valid and reliable measure of quality of life and
that the measure is a number between 0 and 100, with 0 being very bad and 100
being very good. Now, suppose that the truth about the entire population of rich
and poor people (if we could test them all) is that rich people score an average
of 75 on the measure and poor people score an average of 35.

Imagine that you do a study of rich people and poor people with a sample size
of 10 in each group, how likely is it that a t-test would produce a
statistically significant result (p < 0.05)? In other words, if we assume a
certain difference between the two groups to be true (35 versus 75 in this
example), we can then ask whether or not a random sample of a given size (e.g.
10 in each group) is sufficient to show statistically that this difference truly
exists.

### Power Analysis and Sample Size

Typically, the smaller the sample size, the larger any difference between group scores will have be in order to achieve statistical significance.

Statistical power analysis is a set of procedures and formulas that allow us to determine how likely we would achieve statistical significance with a particular sample size (given an assumed true difference between groups).

If the likelihood is good (e.g. greater than or equal to an 80% chance), then the sample size is considered adequate.

### Get the Statistics Help you need

When you hire me to handle the statistical considerations for your dissertation
proposal
, I carefully determine which
statistical methods
are appropriate for your study and I perform a power
analysis to justify your sample size. I also
provide ongoing statistical help to
make sure that you fully understand all of the statistics that I used for your
dissertation research.

Simply contact me by phone or email to get started.

Steve Creech

630-936-4771 | Steve@StatisticallySignificantConsulting.com

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