i know what a sampling distribution is, but i have to answer the question "how do we use a sampling distribution" & I am unsure how we actually use it considering it is just theoretical? I mean it is based on an infinite n.o of statistics. Apart from the Standard Error I was unsure how we actually use it?
Also, there was another question that asked about comparing against the correct sampling distribution - does this mean the type of statistic, like the sampling distribtution of the mean, or median.
And finally, is a t distribution an example of a sampling distribution or is it something completely separate.
my mind is struggling with this concept can anyone help.
Since nobody answered yet... here my attempt, although I encourage others to correct me or explain things more clear.
The idea is that when you estimate a population parameter, for example when you use the average of a sample you've observed to estimate the population mean, there will always be an amount of uncertainty as to wether your estimate is good/accurate in representing the population from which you've drawn your sample. Based on the sample/data you've drawn you don't have information about this accuracy (although you will use your data to estimate this accuracy).
With regard to the sampling distribution of your estimate (e.g. average), you expect this to approach the true population sample, since you sample an infinite amount of times. Due to the known statistical properties of the sampling distribution (i.e. that it equals the population standard deviation divided by the square root of the population size), you can derive an estimate for the standard error there is on your estimate (in this example average). You will use the sample standard deviation of your data to estimate the population standard deviation and than divide it by the square root of n to eventually get the standard error representing the accuracy of your estimate.
So why the sampling distribution is so important, I think, is that the statistical properties of this distribution are known, i.e. its shape. The shape of the sampling distribution of your estimate serves as a way to quantify the amount of error/inaccuracy to expect from that estimate. Although you can also use the formula to estimate standard error without thinking, the sampling distribution serves as a way to know where this comes from, so it is indeed a theoretical construct, although you could also simulate a sampling distribution.
With regard to your second question I don't exactly know what you mean. The sampling distribution that is relevant pertains to the test statistic you use (test statistic by which I mean the statistic you use to answer your hypothesis, e.g. mean if you're interested in group differences).
A t-distribution is indeed a sampling distribution of the T-ratio. The T-ratio being the ratio of the observed error of your estimate (i.e. the estimate subtracted by the unknown parameter --> this parameter you can set to 0 to test the 0 hypotheses) and the anticipated size of its error as expressed by standard error of your estimate.
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