# Power Analysis with Existing Data Set

I am new to this forum but have found several threads to be highly useful so am posing a question myself.

My data was collected (fish length = factor, fish mercury = response) from several rivers over several years for the purpose of environmental (mercury) monitoring.

What I would like to do is, using the data I have, perform power analysis to determine how many samples should be collected in the future to get the same results. The purpose is to recommend the least number of samples necessary (thus killing the least number of fish). Is this possible and does anyone have a recommendation on how to go about this?

• What sort of statistical software do you or can you use? – Dimitriy V. Masterov Apr 1 '13 at 20:59
• When you say you want "to get the same results" in the future what do you really mean? Is the monitoring to determine the level of mercury in the river, and the fish length is just a nuisance factor to be controlled for? So does that mean what you are looking for is a large enough sample size to detect an increase in X% of mercury, shown in an average increase in fish mercury after controlling for fish length? This is certainly possible. – Peter Ellis Apr 1 '13 at 23:22
• Dimitriy: I can use SPSS or GraphPad Prism. I have access to almost any statistical software that is user-friendly at the university. I am, however, not able to use R well so would prefer to avoid it. – AshP Apr 1 '13 at 23:47
• Peter: Sorry, that was not phrased well. I want to collect a large enough sample size to detect an effect and perform statical tests (the specific test may vary in the future depending who does what with the data). We collect fish using a length-based approach since mercury is thought to be a function of length. Mercury may not increase each year, it is variable, but yes, I am looking for changes (trends) in fish mercury after controlling for length. – AshP Apr 1 '13 at 23:53

Step 1: Estimate the size of the effect you have gotten in your current data (e.g., r, Cohen's D)

Step 2: Get G*Power

Step 3: Using G*Power, calculate the required sample size given the size of the effect you have, the level of alpha (.05 usually), and the amount of power you want (.80 is common).

If you outline the specific type of analysis you did and want to do, I can guide you a bit further.

• Thank you! Are these tests only possible to perform in R? What do you mean by "size of the effect"? And what do you mean by "specific type of analysis"? Do my previous comments answer that question? – AshP Apr 1 '13 at 23:55
• This would be an approximation, but seems to ignore the fact that that effect size is an estimate; the actual effect size in the population could be smaller -- if you want to have a particular level of confidence in detecting the actual effect size in the population, the uncertainty in the effect size estimate would need to be considered. It would lead to a slightly larger sample size for a given power. – Glen_b Apr 2 '13 at 4:04
• Lets say for example you are interested in looking at how length correlates with mercury levels. You already have data on this, so you can determine the approximate size of the effect between these variables. Lets say the correlation is .50. GPower tell me that you need approximately 21 cases (fish) to have an 80% chance to statistically support this relationship in a future sample. This is a pretty layman explanation and perhaps a bad example, but that is the crux. You can calculate for t-tests, ANOVAs, etc. in GPower. – Behacad Apr 2 '13 at 13:55
• Also, I will mention that G*Power can help you identify the size of the effect using values often outputted by SPSS and other programs. If you say what specific statistical analysis you are doing (e.g., t-test, ANOVA, regression, correlation, chi-square) we can guide you more specifically. – Behacad Apr 2 '13 at 20:25

If you have access to Stata, you can trying using the user-written command powerreg. It does multiple linear regression power analysis. There's a nice example of how to use it at the UCLA ATS site.