If we take a sample of, say, 100 people, we could measure their heights, and find the intend and standard deviation. We can calculate an estimate of the standard error from this single sample distribution to find where the population think of is probable to lie .
If we repeated this sampling and measured promote samples of 100 people from the population, then finding the means for each sample would give a sampling distributions of means. The mean of this sampling distribution estimates the population average, while the standard deviation of this sampling distribution besides estimates the standard error.
This all seems reasonably clear .
now, consider a large number of trials, e.g. 20000 trials of 100 coin flips, where the issue of heads in each test is recorded and the divide of heads obtained in each trial found. To me, it seems less obvious as to what constitutes a sample hera .
Would each one of these 20000 trials be considered as a single sample, so that we have 20000 samples ?
If that’s right, then when we average the fractions of heads found over all 20000 trials, then — just as for the height example — the mean is an estimate of the population mean, and the standard deviation would be an estimate of the standard error.
The alternative I ‘m thinking of would be to treat each determine of 100 coin flips as a one data period, which would give a single big sample distribution of 20000 measurements .
Treating this datum as 20000 individual samples does seem like it should be correct since it ‘s analogous to the height case. however, it does n’t seem immediately intuitive to me. possibly this is because each trial results in a single divide value, rather of dealing with the 100 individual flips of each trial. then, think of the result of each test as a person sample mean seems less obvious hera, as the trial efficaciously yields a single value. On the other hand, I can see that the fraction of heads is effectively a mean respect, where we code heads as 1, tails as 0 and then divide by the total number of flips in a test .
What confuses me further is if we then decide to work with the raw phone number of heads found in each test alternatively of the fraction of heads. The total number of heads in a trial is a single rate, preferably than a think of. however, my think is that the lapp would be genuine : the mean of the 20000 raw numbers of heads would be an estimate of the population mean, and that the standard diversion would estimate the criterion error of the think of. I ‘m not sure if or why this would be the encase though.
edit : truly, I think what I ‘m trying to understand about this :
- If I take repeat trials of a repair number of flips and compile the fraction of heads, do these give a distribution of sample means ? I think from Michael Chernick ‘s answer that this is adjust .
- future, if we look at the distribution of the raw scores of heads obtained in the perennial trials of a fixed total of flips, can this be again considered as a distribution of sample means ? This is precisely the lapp as in 1, except the measured values are multiplied by the sample distribution size. Because of this, I assume the solution is yes, but it good seems a short discordant. When you reframe the data like that, you ‘re using a sum value, rather than the mean number of heads ( the intend being equivalent to the fraction of heads ) .