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).
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.
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.
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.
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