# Conduct and Interpret an Independent Sample T-Test

What is the Independent Sample T-Test?

The independent samples t-test is a test that compares two groups on the mean value of a continuous (i.e., interval or ratio), normally distributed variable.  The model assumes that a difference in the mean score of the dependent variable is found because of the influence of the independent variable that distinguishes the two groups.

The t-test family is based on the t-distribution, because the distribution of differences in means for a normally distributed variable approximates the t-distribution. The t-test is sometimes also called Student’s t-test. Student is the pseudonym used by W.S. Gosset in 1908 in his published paper on the t-distribution based on his empirical findings on the height and the length of the left middle finger of criminals in a local prison.

The independent samples t-test compares two independent groups of observations or measurements on a single characteristic. The independent samples t-test is the between-subjects analog to the dependent samples t-test, which is used when the study involves a repeated measurement (e.g., pretest vs. posttest) or matched observations (e.g., older vs. younger siblings).

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Examples of typical questions that the independent samples t-test answers are as follows:

• Medicine – Has the quality of life improved for patients who took drug A as opposed to patients who took drug B?
• Sociology – Are men more satisfied with their jobs than women?
• Biology – Are foxes in one specific habitat larger than in another?
• Economics – Is the economic growth of developing nations larger than the economic growth of the first world?
• Marketing: Does customer segment A spend more on groceries than customer segment B?

The Independent Samples T-Test in SPSS

Our research question for this independent samples t-test example is as follows:

Does the standardized test score for math, reading, and writing differ between students who failed and students who passed the final exam?

In SPSS, the independent samples t-test is found under Analyze > Compare Means > Independent Samples T Test

In the dialog box of the independent samples t-test, we select the variables with our standardized test scores as the three test variables; the grouping variable is the outcome of the final exam (pass = 1 vs. fail = 0).  The groups need to be defined by clicking on the button Define Groups… and entering the values of the independent variable that distinguish the groups.

The dialog box Options… allows us to define how missing cases shall be managed (either exclude them listwise or analysis by analysis).  We can also define the width of the confidence interval that is used to test the difference of the mean scores in this independent samples t-test.

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