## Discussion: Comparing Two Groups: Independent Sample t Tests

A researcher who wishes to compare two populations often is interested either in estimating the difference between two population means or in testing hypotheses about this difference. In order to accomplish either task, information (in the form of a sample) must be obtained from each population. The sample information then is used to make inferences about the difference between these two population means. The type of *t* test to use when testing hypotheses concerning two population means can depend on several factors. One of these is the method of obtaining samples. For example:

Imagine that a high school developed a new course in reading comprehension for its freshmen. The high school wants to know whether the new course is more effective than the old one. That is, will the mean reading level for freshmen who are given the course be higher than the mean reading level for freshmen who are *not* given the course?

One way to study the question would be to select a group of freshmen, give them the new course, and then compare their scores on a reading examination with the scores of a group of freshmen from the same institution who did not take the new course. The two samples of scores in this case are called **independent**. Another method would be to select one group of students and compare their scores on a reading test *before* they take the new course with their scores on the reading test *after* they take the new course. In this case, the two samples of scores would be called **dependent**, or **paired**.

Two samples are said to be **independent** if the data values obtained from one are unrelated to the values of the other. In the example above, the high school could examine the mean reading level of two independent populations: one that took the new course and one that did not take the new course.

In contrast, the samples are said to be **dependent** if each data value from one sample is paired in a natural way with a data value from the other sample. In the example above, the same population of students took a reading test before the new course and then took a reading test after the new course. Each student would have two scores. These two scores are paired in a natural way—each score came from the same student.

Now, whether we are dealing with dependent samples or independent samples, we compare the means of two populations by focusing on their difference (i.e., Mean1–Mean2). In this course, you will learn how to make inferences about the difference between two population means when the two samples are independent, yielding what was mentioned earlier as an independent samples *t* test.

For this Discussion, you will expand the new dataset that you created in Week 7.

**To Prepare:**

- Based on the US Demographic Information_PA_PS dataset from Week 9, compare income between the red states and the blue states.
- Use your PSPP software, or statistical software of your choice, to help you conduct your independent samples
*t*test of your data for this Discussion. - For students using the PSPP statistical software program, review the Learning Resources document Working with Datasets Job Aid for information about how to complete the tasks identified in the To Prepare and Post activities.

##### By Day 4 (Post First)

**Post** the results of your independent samples* t* test to compare income from the red states to income from the blue states. Next, using the *p* value associated with the *t* test (i.e., *Sig. Two-tailed*), determine whether there is a statistically significant difference in income between blue states and red states. Explain how big this difference is and what this means.

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