**One-Sample (and Dependent-Sample) t Test
{From the Institute of Phonetic Sciences (IFA):
http://www.fon.hum.uva.nl/}**

This is the standard test for matched-pairs. It is also
the yard-stick for calculating the relative efficiency of other tests. The
Student-*t* test is the most sensitive test for interval data, but it also
requires the most stringent assumptions.

Other names for this test include: Paired-sample *t*
test, Repeated-measures *t* test, and Correlated *t* test.

This parametric test is used in the following situations:

- To test the hypothesis that a single sample is drawn from a population having a given mean;
- To test the hypothesis that the mean difference between matched pairs of observations is zero; and
- To test the hypothesis that the mean difference between two repeated measures (e.g., pretest and posttest) on the
sameindividuals is zero.

*H _{0}: *For 1, above, the mean value equals some hypothesized
value; for 2 above, the mean value of the difference (between pairs or between
repeated measures) is

*Assumptions: *The difference is Normal distributed. If there is any reason to doubt this
assumption, use another, distribution-free, test (e.g.,
Wilcoxon Matched-Pairs Signed-Ranks Test).

*Scale: *Interval

*Procedure: *For matched pairs and repeated measures compute the
difference (*D* = *x - y*, where *x* = the first measure, or
first member of a pair, and* y* = the second measure, or second member of a
pair). For a single sample, *D* = the sample values for each member of the
sample.

Calculate the mean (*M*) and standard deviation (*SD*)
of the *D*'s, determine the number of individuals in the sample *(*n*)*,
and* *degrees of freedom (*df = n -*1). The test is given by

*t* = [ (*M-C*) / *SD* ) * sqrt( *N* )

where *C* = some hypothesized value for a one-sample test,
and *C = *0 for the matched-pairs and repeated measures situation.

The significance of *t* for different
values* *of *df *can be determined by comparing the computed value of
*t* with critical values of *t,* for various alpha levels, found in *
t* Tables in many introductory statistics books.

When *df* > 30, the distribution of *t* can be
approximated by a standard score,* z*, and compared to probabilities found
in the
Standard Normal Distribution.

You can also compute the *t* test by clicking here:
**
Student t test one sample and for dependent samples.**