Advice: How to interpret a large P value

•	Assess the science. If the study was not designed well, then the results probably won't be informative. It doesn't matter what the P value is.

•	Review the assumptions of the analysis you chose to make sure you haven't violated any assumptions. We provide an analysis checklist for every analysis that Prism does. If you've violated the assumptions, the P value may not be meaningful.

If the P value is large, the data do not give you any reason to conclude that the overall means differ. Even if the true means were equal, you would not be surprised to find means this far apart just by chance. This is not the same as saying that the true means are the same. You just don't have convincing evidence that they differ.

How large could the true difference really be? Because of random variation, the difference between the group means in this experiment is unlikely to be equal to the true difference between population means. There is no way to know what that true difference is. The uncertainty is expressed as a 95% confidence interval. You can be 95% sure that this interval contains the true difference between the two means. When the P value is larger than 0.05, the 95% confidence interval will start with a negative number (representing a decrease) and go up to a positive number (representing an increase).

To interpret the results in a scientific context, look at both ends of the confidence interval and ask whether they represent a difference that would be scientifically important or scientifically trivial. There are two cases to consider:

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The confidence interval ranges from a decrease that you would consider to be trivial to an increase that you also consider to be trivial. Your conclusions is pretty solid. Either the treatment has no effect, or its effect is so small that it is considered unimportant. This is an informative negative experiment.

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One or both ends of the confidence interval include changes you would consider to be scientifically important. You cannot make a strong conclusion. With 95% confidence you can say that either the difference is zero, not zero but is scientifically trivial, or large enough to be scientifically important. In other words, your data really don't lead to any solid conclusions.