 t-Test

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Definition

A Hypothesis Test used to compare two population Means or one population mean to a specified value. The term t-test comes from the Student t distribution, created by W.S.Gossett ("Student") in the early 1900's. Use of the t-test depends on satisfaction of the assumption of normality of the population distribution (or of both Populations being compared). In the latter case, the test is further differentiated by asssuming equal or unequal Variances.

The paired t-test is used to evaluate the difference between two Population Means when the data from the two Samples are related on some characteristic. An application of a paired t-test could be evaluating the effectiveness of a training program. Suppose subjects were evaluated before and after training. Rather than using a 2-sample t-test on the before data vs. the after data, a paired t-test should be used to study the difference between the "before" and "after" scores for each subject. Doing so better discerns the impact of the training alone and limits the effect of other variables, such as the smaller within-subject variation.

Application

The different types of t-tests are:
One Sample (One Mean) t-test
Paired Samples t-test (in case of related/matched data)
Two Independent Samples t-test (with pooled variances if the equal variances assumption holds), also called Pooled t-test
Two Independent Samples t-test (where the variances are not pooled if the equal variances assumption does not hold)