# ED632G: Research/Applied Educational Psychology

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2 2 Below is the sample data set that we will be using this example. It lists the test scores for 14 students in both their first and second semesters, their average test grades for each semester, and the difference between the test averages of the semesters (the second minus the first). Analyzing data In this example we will create our hypothesis tests, run a paired-t test, and interpret our data according to our test results. Checking for normality We want to know if we have a normally distributed sample in order to run our statistics. In order to do this, we will need to graph a probability plot. We will be graphing the how much students have improved over the semesters. To do this, we must calculate the difference between their second and first semester of average test scores. Select Calc in the top left menu bar to open the Calculator. Next, type in Difference as your new variable to store your data. Then input your expression subtracting the average score of second semester minus the first. Hit OK when finished.

3 3 Your newest variable should be stored in the next column of your worksheet. Graphing Select Graph in the top right left hand corner, then Probability Plot. Select the single option then choose/type in difference to graph. Generally, you want your data points to follow the straight blue line in the center and fall between the two curved outer blue lines. Hypothesis Testing A one tailed hypothesis test is conducted the researcher believes that the students first semester average test scores are lower than the students second semester average test scores. H o : μ Test Avg_Sem 1 = μ Test Avg_Sem 2 H A : μ Test Avg_Sem 1 < μ Test Avg_Sem 2 Now we will compare the matched pair/2 dependent samples (Paired t-test). If the test subjects are matched and paired by certain traits when assigned to the treatment groups, we no longer have independent samples. Each measurement in a treatment group can be reasonably paired with a measurement in the other treatment group, which is decided before the experiment was run. The data will be placed into 2 columns with each row corresponding to a paired data set. For this example each of the individual student s first semester average test score is in a same row with his or her second semester average test score. To test if there is a significant difference between the two semesters we run the paired-t test in Minitab.

4 4 To run a paired-t test, select Stat from the menu in the top left corner, then find Basis Statistics. Under basic statistics should be the option Paired t Choose this and input your two samples. The order of your samples should match your hypothesis tests. In order to run a one sided test, you must choose options then whether you want to test if your first average is greater than, less than, or not equal to your second average (this is dependent upon your hypothesis tests). Results Here is the output for the paired-t test:

5 5 Here is the interpretation of/conclusion for these results: We can see that the p-value for the test is well below our cutoff of 0.05 (alpha level) and so we would reject the null hypothesis and conclude there is significant evidence that the average of students first semester test scores was less than the average of their second semester test scores. There is statistical evidence to say that students average second semester scores were greater than their average first semester scores.

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