t Test for Independent Samples
(A worked Problem:  Procedure explained in more detail in Chapter 12)

A psychologist studying the human factors of computer keyoards setus up an experiment to compare twe different keyboard designs.  He measures the number of words per minute typed by one group on Keyboard A and then he measures the number of words typed per minute by another group of people on Keyboard B.  Use the data below to determine if the typing speeds on the two different keyboards are significantly different.

I.  Because we have two independent samples we will use a t test for independent sample means.

II.  We must first state the hypotheses

    A.  The null hypothesis
       

    B.  The research hypothesis
       

III.  Compute the mean and standard deviation of each sample

    A.  Keyboard A

    B.  Keyboard B

IV.  Compute the estimate of the standard error of the mean for each sample

    A.  Keyboard A

    B.  Keyboard B

V.  Compute the estimate of the standard error of the difference between means

VI.  Compute t

VII.  The significance of t

   A.  Compute the degrees of freedom

        df = (n₁-1) + (n₂-1) = (10-1) + (12-1) = 20

    B.  Look up the critical value in Table T using the column for a two-tailed research hypothesis

        C. V. = 2.086

    C.  Conculusion:  because the computed t, 2.817, is greater than the critical value, 2.086, 
            we can reject H_o and accept H₁.  Therefore people type significantly faster on
            Keyboard A than they do on Keyboard B.

Copyright © 2004 by Mark W. Vernoy