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The t Test for Related Samples
The t Test for Related Samples Program Transcript
MATT JONES: As its name implies, the independent samples t-test has the assumption of the independence of observations. But that's not always the case. Sometimes we take multiple observations of the same unit of analysis, such as a person, over time. In this case, we'll use a paired sample t-test, sometimes referred to as the dependent sample t-test. Let's go to SPSS to see how we do this.
To perform the paired sample t-test in SPSS, we once again go to Analyze, Compare Means, and down to the Paired Sample T-test. SPSS doesn't require much information here;; only the pair of variables of which we would like to test. We have a simulated data set here for statistical anxiety of students. Students were provided with an instrument that measures their anxiety around statistical topics on a number of different constructs-- teachers, interpretation, asking for help, worth, and self-conceptualization.
They were given the test at the beginning of the class and at the conclusion of a class. Hence, why in the value labels we see pre-test and post-test. As a teacher, I might have some interest in determining whether students felt more comfortable with me or had lowering anxiety over time. This is perfect for a paired sample t- test. To perform this paired sample t-test, we'll go to Analyze, Compare Means, the Paired Sample T-test.
SPSS doesn't ask for much information;; only the pair of variables of which I would like to test. In this case, teacher pre-test and teacher post-test. So this is a classic before and after. The first piece of output I obtain from the paired sample t-test are some descriptive statistics, specifically around the pairwise comparison I'm looking at, which is the teacher subscale pre-test and post-test.
I see that there is mean on the pre-test of 17.32 and on the post-test, an 18.44. So it appears, at least from a descriptive sense, that there is a higher mean on the post-test than the pre-test. On the instrument, higher scores on an item or the subscale indicate higher levels of anxiety for that specific attitude. Except for this specific subscale, fear of statistics teachers, where higher scores actually indicate lower levels of anxiety.
So if post scores are higher than pre scores, that means on average, students feel lower levels of anxiety and more positive attitude about their statistics teacher. I can see here, at least from a descriptive sense, that that appears to be the case. But from the sample, I am performing a test of statistical significance. Next to the mean, I'm provided with the sample size 25-- 25 observations pre-test and 25 observations post-test, all the same person-- the standard deviation for the pre-test and the post-test, and the standard error of the mean.
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The t Test for Related Samples
Next, let's go down and interpret the paired sample test itself. We can see that on average, there was a difference of 1.12 units on the scale with a standard deviation of 2.50. From the 95% confidence interval, we see that the true difference is somewhere between 2.15 and 0.085. We have a t-statistic of 2.235 and an associated p-value of 0.035.
At the 0.05 level, the results are statistically significant and we can say that there is a significant difference between pre-test scores and post-test scores. Therefore, we can reject the null hypothesis that there is no difference. On average, it appears on the post-test, students had lower levels of anxiety about their statistics teacher.
This last example illustrated that students felt more comfortable with statistics as time progressed and specifically felt less anxious about their statistics instructor. I certainly hope this example rings true for you, and that you feel comfortable or at least don't self-identify as being anxious about statistics at the conclusion of this course. I encourage you to review your textbook, review the videos, ask your instructor for help, and also research the resources here available at Walden University to help you succeed.
©2016 Laureate Education, Inc. 2