GraphPad Home Library Power of completed experiments with "not significant" results How power analyses complement analyses of confidence intervals. All results should be accompanied by confidence intervals showing how well you have determined the differences (ratios, etc.) of interest. Power analysis can complement the confidence interval. Consider this example. We determined the number of alpha2-adrenergic receptors on platelets of people with and without hypertension. Here are the results: Controls Hypertensives Number of subjects 17 18 Mean receptor number (receptors/platelet) 263 257 Standard Deviation 87 59 Because the mean receptor number was almost the same in the two groups, the P value is very high. These data provide no evidence that the mean receptor number differs in the two groups. While it is tempting to just stop with the conclusion that the results are "not statistically significant" (as we did in this study published 20 years ago), there are two ways to go further. One approach, is to interpret confidence intervals and the other is to do power analysis. The 95% confidence interval for the difference between group means extends from -45 to 57 receptors/platelet. Once we accept the assumptions of the t test analysis, we can be 95% sure that this interval contains the true difference between mean receptor number in the two groups. To put this in perspective, you need to know that the average number of receptors per platelet is about 260, do the 95% CI extends each direction about 20%. The interpretation of the confidence interval (like the power analysis) must be in a scientific context. Here are two approaches to interpreting this confidence interval. You could say: The CI includes possibilities of a 20% change each way. A 20% change is huge. With such a wide CI, the data are inconclusive. Could be no change. Could be big decrease. Could be big increase. Or: The CI tells us that the true difference is unlikely to be more than 20% in each direction. Since we are only interested in changes of 50%, we can conclude that any difference is, at best, only 20% or so, which is biologically trivial. These are solid negative results. Both statements are sensible. It all depends on your scientific interpretation of a 20% change. Statistical calculations can only compute probabilities. It is up to you to put these in a scientific context. As with power calculations, different scientists may interpret the same results differently. The power analysis approach is based on having an alternative hypothesis in mind. You can then ask what was the probability that an experiment with the sample size actually used would have resulted in a statistically significant result if your alternative hypothesis were true. For this example, the experimental design had a 80% chance (power) to detect a true difference between means of 72.28 sites/platelet and a 90% chance (power) to detect a difference of 83.65 sites/platelet. If your goal is simply to explain your results, the confidence interval approach is enough. If you goal is to criticize a study of others, or plan a future similar study, it might help to do a power analysis as well as interpret the confidence interval. Confidence intervals and power analyses are based on the same assumptions, so the results are just different ways of looking at the same thing. You don't get additional information by performing a power analysis on a completed study, but a power analysis can help you put the results in perspective.