10 more values) and are using standard deviations for their normal use of "standard error" reporting then use just either because the difference between them is negligible compared to other inaccuracies in calculating standard error values. Okay, so that is which one to use but why? Quick Explanation When the mean is calculated from the n data, there are only n-1 degrees of freedom left to calculate the spread of the data. It would be cheating to use the other degree of freedom again. Essentially, the mean used is not the real mean but a estimate of the mean based on samples of data found in the experiment. This estimate is, of course, biased towards fitting the found data because that is how you got it. Therefore estimating how widely spread around the real mean the data samples are by calculating how spread around the estimated mean they are is going to give a value biased slightly too low. Using n-1 instead of n compensates. Longer Explanation For this, one has to go back two levels; back beyond the use of standard deviation and the derivation of the formulae and think why it is used at all. As with all applied mathematics, there is nothing intrinsically magical about the definitions. They are simply chosen because they are useful. Neither standard deviations as error estimations nor means as averages are the only options available for their tasks. However their combination of ease of calculation, ease of algebraic manipulation & easily understandable