For example: We’re interested about operation time for a product. Operation time for previous batches are available. From that list of batches (samples) we selected 30 batches. Here, each batches comprises of no of sets (i.e. no of observations), meaning sets of unit (product) make one batch.
No of observation in a sample may be 30, in another 25 observations. Here’s my question, we need to take same no of observation in each sample for sampling distribution?
We took the mean of values for no of observations for each sample. Then we measured the mean of sample mean to obtain mean of sampling distribution. Is it correct ?
TIA
Mynur -
If I understand your situation, you do not look at paired observations, but just separate sets of numbers. So, no the sample sizes do not need to be equal, but I recall looking into something like this in the past, I think, and it was the most efficient use of data if sample sizes are equal.
But it also sounds like you may be combining some 'batches.' If they represent the same population, then I guess such combinations make up one big sample. If not, and they are different, then if you are saying you are averaging their means, I don't know what that would represent.
Perhaps the following may be of interest to you:
https://newonlinecourses.science.psu.edu/stat100_1/node/57/
Cheers - Jim
Thanks for your generous reply.
“If they represent the same population, then I guess such combinations make up one big sample.”
Yes, Samples are from the same population. I used the word “batch” and “sample” interchangeably. Each sample consists of number of observations, I took the mean of those observations for each sample. This way obtained 30 different values for 30 samples. Then, calculated the mean of these sample values to estimate population mean (mean of sample mean). Is it correct approach to estimate population mean from sampling distribution prospective?
If you are saying you have several samples from the same population, under the same circumstances, so that it really is the same population, then it sounds like you should combine those samples as one big sample. Otherwise, if you take subsamples of various sizes, and average their means, then you effectively weight different sample members arbitrarily.
If there are several samples of varying size present then k-mean algorithm or root mean square algorithm may provide efficient result.
I would like to extend above reply (@James Knaub), what if samples are drawn from the same population but under different circumstances (i.e. data collected from different machine rather than single machine). Then also previous suggesstion (combine those samples as one big sample) apply?
Thanks, always.
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