Statistic Uses

Among the most frequently used t tests are:

* A test of whether the mean of a normally distributed population has a value specified in a null hypothesis.
* A test of the null hypothesis that the means of two normally distributed populations are equal. Given two data sets, each characterized by its mean, standard deviation and number of data points, we can use some kind of t test to determine whether the means are distinct, provided that the underlying distributions can be assumed to be normal. All such tests are usually called Student's t tests, though strictly speaking that name should only be used if the variances of the two populations are also assumed to be equal; the form of the test used when this assumption is dropped is sometimes called Welch's t test. There are different versions of the t test depending on whether the two samples are
o unpaired, independent of each other (e.g., individuals randomly assigned into two groups, measured after an intervention and compared with the other group[4]), or
o paired, so that each member of one sample has a unique relationship with a particular member of the other sample (e.g., the same people measured before and after an intervention[4]).

If the calculated p-value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis which usually states that the two groups do not differ is rejected in favor of an alternative hypothesis, which typically states that the groups do differ.

* A test of whether the slope of a regression line differs significantly from 0.

Once a t value is determined, a p-value can be found using a table of values from Student's t-distribution.