Sampling Distributions

Sampling distributions are important in statistical tests. They arise from the repeated sampling and successive calculation of a (sample) statistic. An example may clarify the concept:

Example:

Suppose we know the average weight and its standard deviation of 27 year old men in Switzerland (for simplicity let's assume that the average weight is 72.2 kg, and the standard deviation is 5.4 kg). If we now randomly select 40 men and determine their weights, we will obtain a specific mean which is close to the average weight of the whole population. Repeating the selection will result in a somewhat different mean. If this selection were repeated several times, the resulting histogram of the calculated means would be approximately normal even if  the probability distribution of the whole population (in a statistical sense) of all 27 year old men in Switzerland is not normal.

The nature of the distribution of a sample statistic may be determined either mathematically, or at least empirically, by simulating sampling experiments on a computer. Since the properties of a sample statistic depend on its distribution, sampling distributions are used to compare among statistics and to infer knowledge about some test statistic.

There are a few special sampling distributions which are often needed in statistical calculations and statistical tests:

• normal distribution
• chi-square distribution
• t distribution
• F distribution