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

    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.

Assumptions:
    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).

Scale:
    Interval

Procedure:
    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.

Approximation:
    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.