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

    This is the standard test for two samples. 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.

    H0: Both populations have identical mean values. That is, the difference between the means is zero.

    Both distributions are Normal distributed with identical variances. If there is any reason to doubt these assumptions, use another, distribution-free, test (e.g. the Wilcoxon Test).


    Calculate the Mean values (M1, M2) and standard deviations (SD1 and SD2) of both samples. Calculate

SDg = sqrt{[(n1-1)*SD12 + (n2-1)*SD22]/(n1+n2 - 2)}

        The test statistic is

t = ( M1 - M2 ) / ( SDg * sqrt{ 1 / n1 + 1 / n2 ) }.

    The number of Degrees of Freedom (df) = n1 + n2 - 2.

Level of Significance:
    The significance levels of t for different df are tabulated 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: Independent-sample t test.