The T-Test in Dissertation & Thesis Research

 

     In dissertation or thesis research, there are two types of inferential statistics: parametric and nonparametric tests. Which type you use for your data depends on the type of measurement scale used and how your collected data are distributed.

T-Test Assumptions

     The t-test is a parametric statistic and perhaps one of the simplest analyses used in dissertation and thesis research. Prior to using the t-test, you must make sure that your data does not violate any of the three assumptions underlying the t-test:

  1. The scores in your data represent a random sample from the population under study.
  2. The distribution of the mean of your sample is normal.
  3. The variances of the different groups studied are very similar.
     If your data violates one or more of these assumptions, you may be committing a Type I error more or less often than the alpha probability you set (either .01 or .05). This bias may undermine the value of the t-test, and therefore, the results of your dissertation.

Types of T-Tests

     The t-test is used when your data has only two levels of the independent variable. There is a t-test for dissertations involving experimental designs with randomized groups (independent samples), and another t-test for dissertations with experimental designs involving correlated groups (matched pairs or within-subjects designs). Knowing what kind of sample you have is key to selecting the appropriate t-test for your analyses.

     Let's say that your dissertation involves two groups of people. If you obtained your subjects from multiple locations and assigned each person to be in one group or the other randomly, say through the use of a random numbers table, then you would use the t-test for independent samples in your analysis. If, however, your dissertation is looking at men versus women in an undergraduate introductory psychology course at your school, you must use the t-test for correlated samples in your analysis.

Independent Samples

     For example, let's suppose that your dissertation involves two random groups of people, an experimental group and a control group. You are examining whether seeing a recording artist's face influences how people rate his/her song. All of your subjects listen to the same song. The experimental group sees the artist's face before hearing the song, while the control group does not. You then collect data from the two groups about how well they liked the song on a scale of 1-7. For your analysis, you compute the mean of each group and find that the experimental group's mean is 5.9, while the control group's mean is 4.6.

     For this analysis, you would use the t-test for independent means. The crux of your paper is determining whether the 1.3 difference between these means is a statistically-reliable difference or if the means are different because of sampling error.

Correlated Samples

     Using the above example, let's say your work involved one group of subjects, but each subject listened to the song first, without seeing the artist's face, then rated how much they liked it. Then, the same subject saw the artist's face and listened to the song again. For your analysis, you would use the t-test for correlated samples, because each person in your sample made two observations. Obviously, the ratings for this sample are correlated, because they came from the same individual. This type of experimental design is called a "within-subjects" design.

Calculating Degrees of Freedom

     Once you have calculated the t-score for your groups, you need to know whether these t values are large enough to assume that the difference you found between the two groups is significant. Most statistical packages used for analyses (SPSS, etc.) will provide an alpha level for you. If, for your dissertation, you have set your significance level at .05, any alpha smaller than this means that you have significant findings. Dissertation committees and dissertation chairs love significant results!

     If you do not have a statistical package, you must first find the degrees of freedom for your sample. For the first example given (the between-subjects design), the degrees of freedom is the number of subjects minus two (N-2). You can then use a t-test table, found in most statistics books, to determine the "critical value" of t. If the t value you obtained in your sample is greater than or equal to the t-score in the table matching your degrees of freedom for your sample, then the difference between your two groups' means are statistically different at the alpha level you set.

     If you cannot find a table that has the degrees of freedom you have for your sample, you can use the next lowest degrees of freedom in the table that you have. This strategy is particularly appropriate if your sample is very large and the degrees of freedom for your t-test is quite a bit larger than those found in a table. Another option is to use a statistical calculator to see if the t-value you got for your results is significant.

     In sum, if your dissertation or thesis involves two groups with only two levels of the independent variable, the t-test may be the ideal statistic for your analysis. Choose the appropriate t-test for your analysis based on whether your samples are independent or correlated.

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