Although the word "sampling" seems to imply the word "sample," sampling distributions are actually more closely related to a population model distribution of sample statistics.A sampling distribution is the most basic concept underlying all statistical tests. It is the relative frequency distribution that would be obtained if all possible samples of a particular sample size were taken. It makes it possible to attach probability to inferences made from statistics to parameters. In fact, almost all inferential statistics are based on sampling distributions.

A sampling distribution is what it would be like if
an individual repeatedly took samples of size "n" from a population
distribution and computed a particular statistic each time he/she took a sample.
This would create a sampling distribution for that statistic. Discussion
of Its Application A very common use of sampling
distributions is in regard to the mean. The sampling distribution of the
mean is simply the distribution of means of an infinite number of random samples
drawn under certain conditions.For example, if
a sample of 15 is taken from a population (n = 15) and a statistic, such as
the mean, is calculated for that sample and this process is repeated again and
again, then this is a sampling distribution of that statistic (here, the sampling
distribution of the mean).Although the particulars
of sampling distributions may differ between designs and from statistic to statistic,
the underlying concept remains the same. For example, s^{ 2},
or the sample variance, is an unbiased estimate of the population variance.
In other words, if one repeated samples from the population and repeatedly finds
s^{ 2} , the average value of s^{ 2} will approach the population
variance. The shape of the sampling distribution
for s^{ 2} is positively skewed and, therefore, it is likely to underestimate
the population variance especially when examined separately or when it is a
small sample. The sampling distribution
can also be applied to such sample statistical techniques as the median, range,
correlation coefficient, and proportions. standard
error

Every statistic has a sampling distribution and every sampling distribution has a standard error. The standard error, or standard deviation of the distribution, reflects the variability one would expect to see in the values of a specific statistic over repeated trials. As the sample size increases, the standard error decreases.

The central limit theorem is an important concept when discussing the sampling distribution of a mean. It relates the parameters of a sampling distribution of the mean to the population model. It states that a sampling distribution of the mean tends toward a normal distribution as "n" tends toward infinity. more topics