One-Sample (and Dependent-Sample) t Test
{From the Institute of Phonetic Sciences (IFA):}

    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:

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

H0: 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 zero.

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.