Can someone tell me in simple terms about Standard Error of the Mean?

Question

I have to explain the importance of standard error of the mean and I kind of get it but don't...a standard error I have is .5094. Is this significant in predicting the sample pop. to the general population, or does that not really tell much?

Answer 1

Standard error (SE) is a measure of spread of distributed data. When that data is based on mean values, those mean values can also have a SE because they, too, have a spread.

Whether your SE = .5094 is statistically significant depends on the number of mean data points you have and on the level of significance you chose for your hypothesis test. Your null hypo is probably H0: m = M; where m is the mean of your sampled means and M is the mean of the population of means.

If you chose a level of confidence of .90, then if your calculated m fell outside plus or minus 2 SE from M, your null hypo fails so you can conclude that H0 is NOT true. In which case, the alternative hypo H1: m <> M is not disproved. Unless there is error, one might even say m <> M is true.

If your sampled m falls within plus or minus 2 SE @ .90 LOC, then you can conclude your null hypo is true and the alternate is not true. All these conclusions are based on the presumption there are no Type I and II errors.

Bottom line, what you gave us in your question is necessary, but not sufficient information to tell if your given SE is significant or not.