ayahhanda

Lesson 3:

Computing a T-Test for Between-Subjects Designs

Purpose

This test is used to examine the effects of one independent variable on one or more dependent variables and is restricted to comparisons of two conditions or groups (two levels of the independent variable). The results of this test enable you to determine if two means differ significantly. Two basic experimental designs, between-subjects and within-subjects designs, can be analyzed with a t-test. In this lesson, we will describe how to analyze the results of between-subjects designs. It is important to distinguish between these two types of designs because they require different versions of the t-test. (For those of you who are familiar with statistics and SPSS, the Independent Samples T-Test is used with between-subjects designs and the Paired Samples T-Test is used with within-subjects designs.)

A two-group between-subjects design is one in which participants have been randomly assigned to the two levels of the independent variable. In this design, each participant is assigned to only one group, and consequently, the two groups are independent of one another. For example, assume that you are interested in studying the effects of two types of drugs (X, Y) on reaction time. If you randomly assign some participants to the Drug X group and other participants to the Drug Y group, then you are using a between-subjects design. (In a within-subjects design, all participants would receive both levels of the drug.)

An Example: Parental Involvement Experiment

Assume that you studied the effects of parental involvement (independent variable) on students' grades (dependent variable). Half of the students in a third grade class were randomly assigned to the parental involvement group. The teacher contacted the parents of these children throughout the year and told them about the educational objectives of the class. Further, the teacher gave the parents specific methods for encouraging their children's educational activities. The other half of the students in the class were assigned to the no-parental involvement group. The scores on the first test were tabulated for all of the children, and these are presented below.

Data Sheet for Parental Involvement Experiment

Student	Parental Involvement Condition	Test 1
01	Involvement	78.6
02	Involvement	64.9
03	Involvement	100.0
04	Involvement	83.7
05	Involvement	94.0
06	Involvement	78.2
07	Involvement	76.9
08	Involvement	82.0
09	No involvement	81.0
10	No involvement	69.5
11	No involvement	73.8
12	No involvement	66.7
13	No involvement	54.8
14	No involvement	69.3
15	No involvement	73.5
16	No involvement	79.4

Creating Your Data File: Key Point

There is a key point to keep in mind when creating a data file for an independent samples t-test. That is, that you must create a column for your independent variable condition. In this case, that is the parental involvement condition, and you should create a numeric code that allows SPSS to know the parental involvement condition that the score is in. So, the first part of your data file might look like the one below, with three variables--one for student number, one for parental involvement condition (using a code of "1" for involvement and "2" for no involvement), and score on Test 1. Remember, that in creating the data file, you should create a variable Label for each variable and Value label for the parental involvement variable. Your variable view file should look something like the one below.

Variable View File for the Parental Involvement Experiment

Computing the t-test for the Parental Involvement Experiment

Step 1. Click on Analyze, then Compare Means, then Independent Samples T-Test.

Step 2. Now, move the dependent variable (in this case, labeled "test1") into the Test Variable field.

Step 3. Move your independent variable (in this case, "involve") into the Grouping Variable field. You should be aware that Grouping Variable stands for your independent variable.

Step 4. You will notice that there are question marks in the parentheses following your independent variable in the Grouping Variable field. This is because you need to define the particular groups that you want to compare. To do so, click on Define Groups, and indicate the numeric values that each group represents. In this case, you will want to put a "1" in the field labeled Group 1 and a "2" in the field labeled Group 2. Once you have done this, click on Continue. Your independent-samples t-test screen should look like that below.

Independent Samples t-test Figure

Step 5. Now click on OK to run the t-test. You may also want to click on Paste in order to create a record of what you have done.

Output from the t-test Procedure

As you can see below, the output from a t-test procedure is relatively straightforward.

Output from Independent Samples t-test

The first table lists the number of participants (N), mean, standard deviation, and standard error of the mean for both of your groups. Notice that the value labels are printed as well as the variable labels for your variables.
The second table initially presents you with an F-test (Levene's test for equality of variances) that evaluates the basic assumption of the t-test that the variances of the two groups are approximately equal (homogeneity of variance). If the F value reported here is very high and the significance level is very low--usually lower than .05 or .01), then the assumption of homogeneity of variance has been violated. If this is the case, you should use the t-test in the lower half of the table, whereas if you have not violated the homogeneity assumption, you should use the t-test in the upper half of the table.
In this particular case, you can see that we have not violated the homogeneity assumption, and we should use the t of 2.356, degrees of freedom of 14, and the significance level of .034. Thus, our data show that parental involvement has a significant effect on grades, t(14) = 2.356, p < .05.

Further Practice: Extending the Parental Involvement Experiment

Assume that the course had three tests and you wished to examine the effects of parental involvement on all three tests as well as a final term average. So, to do this, assume that the test score you already have in your data file is the score from the first test. Add the Test 2 and Test 3 scores (shown below in the data file) for each of the 16 students. Once you have done this, try to get SPSS to perform four t-tests--one for each of the three term grades and one for the final grade average. (Note that you can get SPSS to calculate the term average with the Transform Compute menu.)

Datafile with the Addtion of Tests 2 and 3

If you have problems working through this example, you should look at the steps below.

Step 1. To create a new variable that represents the average of all three tests, click on Transform, then Compute. Type in the name of the variable that you wish to create (e.g., "average") in the Target Variable field. In the Numeric Expression field, type (or click on the appropriate characters) the expression that represents the average. In this case, you might type the following expression

Target Variable	Numeric Expression
average	(test1 + test2 + test3)/3

Note that the three test scores are included within parentheses. This is necessary because SPSS first performs operations that are within parentheses, and that we want to add all the numbers before dividing. Make sure that you also create a label for your new variable. Once you have created the proper expression, click on OK, and this should take you to the SPSS data editor where you should see a new column that represents the average of the three test scores.

Step 2. Now click on Statistics, then Compare Means, then Independent Samples t-test. You should then move the four dependent variables (test1, test2, test3, average) into the Test Variable field. Next, move the independent variable (i.e., involve) into the Grouping Variable field. Next, click on Define Groups and indicate the two levels of your involve variable. When you are finished, click on OK. The first portion of your output should look like that below.