2

According to CLT, the SE is the SD of the distribution of several samples means. This SE depends on each sample mean, the SD of each sample and N (the size of each sample which I test). Since there is no relation to the number of samples, why can't I add all the samples to get a more precise estimated average, more precise SD and more precise SE ?

Numerical example - If I have 5 samples of 100 observations each, I can calculate each SD, mean ... But why can't I just add all of the 5 samples to get a big one sample of 500 ? Once I calculate the mean and SD of this big sample - It will be much more precise.

Bottom line - since we know how the mean of samples is distributed, why cant we find the parameters just according to one big sample ? Is there any importance for samples number?

kjetil b halvorsen
  • 77,844
Amit
  • 21
  • 2
    I don't follow this question. Even the initial phrase "If the distribution of the population mean depends on the sample mean" seems not to make sense (how would the mean of the population depend on the sample mean in any way? Why would it have a distribution?) and it seems like the rest has some similar issues. You will have to find a way to clarify the question or perhaps it would be better to ask about each of your premises (the sequence of "facts" that your question relies on). – Glen_b Aug 30 '20 at 00:32
  • How do you wind up with your five samples? My initial reaction was that you should combine them, though it will depend on the data collection (five different points in time, for instance). – Dave Aug 30 '20 at 06:38
  • Ok... leta say I had 100 samplea of 1000 observs each. All are independet and under same circumstances. I can just create the histogram of the samples means or I can add them all toghether and calculate the SE according to se (which is sd of means diatribution) is std/ sqrt(n). It even sounds to be better to add them all together since I would have a much bigger n. I just can't see the advantage of have "many samples" instead of one big sample – Amit Aug 30 '20 at 07:15
  • https://stats.stackexchange.com/questions/412606/central-limit-theorem-only-needs-sample-size-n – Glen_b Aug 30 '20 at 08:41
  • thanks. So bottom line - it is better to add all small sapmles to one, right ? – Amit Aug 30 '20 at 10:05

0 Answers0