t-test for Two Groups

 

So far we have looked at only counts or frequencies, or at the mean of a single sample. These types of statistics are useful, but limited in what they can tell us.  For example, suppose that a client believes that income is an important variable in determining who will buy her product.  She has two segments, she believes that each sample has the same average income.  A sample of both segments is taken and segment one is found to have an average income of $50,000, the second segment has an average income of $52,400.  Does she really have one segment?

 

The null hypothesis here is that there is no differences between group means:  H0 = (M1-M2) = 0

Essentially the value of a t-test is simply the number of standard errors a sample mean is away from the hypothesized mean.

 

 

Where SE is the sampling error, or the standard deviation of a distribution of the differences between means:

 

 

Since the standard deviation of the population is not known, it has to be estimated by the sample itself, hence the need for a t-test.  Each t-test has a degree of freedom, it is simply (n1 + n2 –2).

 

What to do:

 

  1. Get the file called Trust.sav from the web site.  Use this for your data.
  2. Test to see if order of placing “trust” and level of “teaching” at the beginning at a different effect than placing it towards the end.  This is from a questionnaire handed out in another class.  This form measured how much trust a student had in an instructor, but the answer could be swayed by where the questions were asked relative to other questions. In “form” 1, the questions were asked up front, in “form” 2, they were asked at the back.  “Trust” is how much trust the student had, and “teach” is how good a teacher the student perceived the instructor to be.
  3. Do the following

Analyze

            Compare means

                        Independent Samples T Test

                                    [put “form” into Group Variables: 1 is front, 2 is back]

                                    [put “trust” “teach” and “gpa” into Test Variables(s)]

  1. Explain your results, tell me what your results mean.
  2. Do the same problem again, but this time see if female and males are different on the same variables.  Explain what it means.