Why does Prism report the standard errors (SE) of best-fit parameters, while some other programs report standard deviations?

Prism reports the standard error (SE) of best fit parameters determined by nonlinear regression (and the slope and intercept of linear regression).

When you look at a group of numbers, the standard deviation (SD) and standard error of the mean (SEM) are very different.

• The SD tells you about the variability or scatter of the values.
• The SEM tells you about how precisely you have determined the mean. The SEM can be thought of as "the standard deviation of the mean" -- if you were to repeat the experiment many times, the SEM (of your first experiment) is your best guess for the standard deviation of all the measured means that would result.

But when you look at a best-fit parameter from regression, the terms "standard error"and "standard deviation" really mean the same thing. Prism calls that value "Std. Error" or SE, the most conventional label. Others call it SD. Just as the SEM is the standard deviation of the mean, the SE for a best-fit parameter is the SD of values for the best-fit parameters that you would see if you repeated the experiment lots of times.

To summarize: When analyzing a list of values, the SD and SEM are very different. When performing linear or nonlinear regression, the SE of a best-fit parameter can also be called the SD of that parameter. There is no distinction between SD and SE in this case, but the term SE is used more often. It would be a mistake, however, to call it the SEM, as the M stands for mean. The SE of a slope, or the SE of an intercept, or the SE of the logarithm of EC50 are not SEMs.

Related: Why doesn't Prism report the SE of the EC50 fit from dose response curves.