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Statistical Analysis Of Pre-Test And Post-Test Performance In Introductory Statistics: A Pilot Study

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    Statistical Analysis of Pre - Test and Post - Test Performance in Introductory Statistics: A Pilot Study At the University of Mytholopolois the head of the statistics department wants to find out whether or not 7 basic topics are being adequately learned in introductory statistics courses. A test is written that has 7 questions, one question addressing each of the main topics under consideration. These topics are: 1 - Measurement scales 2 - Measures of central tendency 3 - Standard deviation 4 - Normal curve and empirical rule 5 - t - tests 6 - ANOVA 7 - Correlation and regression This brief test is going to be administered to all students registered in the introductory statistics course at the beginning of the first session and the end of the last session. This is a pre - test/post - test design. But before this full scale data

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    collection effort begins the department is going to test this little instrument. Eight students are selected to use as a test group. The following is a table of the student scores in the pre - test condition and the post - test condition. This final project is asking you to consider 4 different statistical tests. The first is what the department head is looking for, the second is an extension of that with a further breakdown of information, the third is looking for a relationship between two different variables and the fourth is asking what test you would use to predict a student’s score. Student Sex Pre - test Post - test Hours per week studying statistics Matilda F 4 6 15 Franklin M 2 5 18 Lily F 4 7 13 Paul M 3 6 11 Louise F 5 5 7 Golda F 4 6 12

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    Duncan M 2 5 14 Philip M 6 7 9 Answer the following questions about this problem. Preliminary information about the data Question 1. What is the head of the statistics department trying to find out? The head of department is trying to find out whether or not 7 basic topics are being adequately learned in introductory statistics courses. 2. What are the variables of interest? The variable of interest are 1. pre test scores, 2. post test scores, and 3. Number of hours studies weekly. 3. What is the measurement scale of the each of the variables of interest? The measurement scale of pre test scores is ratio.

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    The measurement scale of post test scores is ratio. The measurement scale of number of hours studies weekly is ratio. 4. What is the mean of the pre - test scores? Mean = ( 4 + 2 + 4 + 3 + 5 + 4 + 2 + 6) / 8 = 30/8 = 3.75 5. What is the median of the post - test scores? Median is 6. 6. In both the pre and post test conditions, considering these as a single sample, what is the mode? (There should be 16 values considered.) There are two modes: 5 and 6. 7. What is the range of the hours studied values? The range is 18 – 7 = 11. 8. Can you calculate a mean for the sex of the students involved in this pilot study? Explain your answer. No, we cannot.

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    9. What is the standard deviation of the pre - test scores? Please show all your work. You don't have to do the standard deviation of the post - test scores. 2 2 2 SD = 126 SD = 3.75 1.299 1.3 8 X X n − − =   X X 2 4 16 2 4 4 16 3 9 5 25 4 16 2 4 6 36 2 X  =126 10. Looking at just the pre - test scores, using the empirical rule, is the distribution of these scores normal? Since SD 3.75 1.3 2.45 to 5.05 X  = 

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