Finally, compute a P value answering this question: If all the values were really sampled from a Gaussian population, what is the chance of randomly obtaining an outlier so far from the other values? If the P value is small, you conclude that the deviation of the outlier from the other values is statistically significant, and most likely from a different population.

Next, standardize this value by dividing by some measure of scatter, such as the SD of all values, the SD of the remaining values, or the range of the data. This can be the difference between the outlier and the mean of all points, the difference between the outlier and the mean of the remaining values, or the difference between the outlier and the next closest value. All the methods first quantify how far the outlier is from the other values. Statisticians have devised several methods for detecting outliers. Assuming you answered no to all three questions above, you have justification to exclude it from your analysis. If this probability is small, then you will conclude that the outlier is not from the same distribution as the other values. If the values really were all sampled from a Gaussian distribution, what is the chance that you would find one value as far from the others as you observed? Statistical calculations, however, can answer this question: No mathematical calculation can tell you for sure whether the outlier came from the same, or a different, population than the others.

Graphpad prism 5 statistics guide