Inferential statistics involves mathematical procedures that allow psychologists to make inferences about collected data. For example, these procedures might be used to
estimate the likelihood that the collected data occurred by chance (that is, to make probability predictions)
to draw conclusions about a larger population from which samples were collected
The type of inferential statistical procedure used depends upon the type of measurement scale used as well as the distribution of the data. The procedures are usually used to test hypotheses and establish probability.
Sampling is the process of selecting cases to be tested from a larger population. For example, experimenters could not expect to measure the effects of a new therapeutic drug on every adult male in the population, so they would use a sample that is determined to be representative and unbiased. In inferential statistical procedures, the term probability refers to the likelihood that study results are statistically significant or that they are due to chance factors such as sampling errors. For example, if the significance level is determined to be .05, the researcher knows that the chances are only 5 out of 100, or 1 in 20, that the results were produced by chance factors alone.