In many scientific communications, we are confronted with data showing "no statistically significant difference" between two groups (populations) with respect to a certain variable. The authors often conclude that the two groups are not different regarding that variable. Such a conclusion is not warranted without an indication of the power of the statistical test to detect a clinically important difference. In reality, the two groups referred to almost certainly are at least minutely different. However, whether or not the difference will lead to a statistically significant difference between samples in the study depends on the following: (1) the variability of the variable in the population (which can be estimated using the standard deviation of the same or similar data), (2) the sample size (the number of independent subjects or data points in the samples from each group), and (3) the chosen level of significance (the probability that any difference found
Bourne WM. 'No Statistically Significant Difference': So What? Arch Ophthalmol. 1987;105(1):40–41. doi:https://doi.org/10.1001/archopht.1987.01060010046029
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