t-test of two independent means

Version 1



    This is the simplest t-test for a significant difference in the means of two independent populations assumed to have equal variance. This test assumes the two samples are of equal size. The test is not adjusted for multiple comparisons.

    For example, this test may be used to determine if the sample mean of measurements in your control group is different enough from the mean of your treatment group to indicate that the populations from which the samples are drawn are likely to be different as well.


    See the forum article where Jonathan Drummey and I collaborated on this calculation here: Statistical analysis of groups of data


    Example Calculation:


    // The calculated fields described below are in the attached workbook.


    // The "Is Treatment different from Control?" field

    // returns the string "Different" if the NULL hypothesis

    // is rejected at the 95% confidence level and "Same" otherwise.

    IF [pValue] < 0.05 THEN "Different"

    ELSE "Same"



    // The "pValue" field finds the likelihood for this two sided test that the

    // critical value, "tcrit", would occur by accident if the two means were the same.

    // It uses an approximation of the normal distribution which itself is an approximation

    // of the student-t distribution which is the distribution of the null hypothesis

    // for this or any other t-test.

    // I use the formula recommended by this paper: http://web2.uwindsor.ca/math/hlynka/zogheibhlynka.pdf.
    2 * ( .5 * exp(-1.2 * power( abs([tcrit]), 1.3) ) )

    // The "tcrit" field finds the test critical value for a t-test of difference of two means.
    ([Average Control Value]-[Average Treatment Value])/([Sxx]*SQRT(2/SIZE()))


    // See the attached Workbook for the remaining fields required to calculate this test.