STA 144 Week 3 Homework - Zachary Jensen

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Feb 20, 2024

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STA 144 Week 3 Homework Zachary Jensen Professor Lee - STA144-AE January 26, 2024 Work on the following problem set from chapters 5-6 Chapter 5 1. Use Chapter 5 Data Set 2 in the appendix or below to answer Questions 1a and 1b. a. Using SPSS, compute the Pearson product-moment correlation coefficient. b. Construct a scatterplot for these 10 values. Based on the scatterplot, would you predict the correlation to be direct or indirect? Why? Total N umber of Problems Correct (out of a possible 20) Attitude Toward Test Taking (out of a possible 100) 17 94 13 73 12 59 15 80 16 93 14 85 16 66 16 79 18 77 19 91

Answers copied from SPSS: a. b. The correlation would be direct because as the attitude toward test-taking increases the number of problems correct also increases. 2. Use these data to answer Questions 2a and 2b. These data are saved as Chapter 5 Data Set 3 in the appendix. Speed (to complete a 50-yard swim) Strength (number of pounds bench-pressed)

21.6 135 23.4 213 26.5 243 25.5 167 20.8 120 19.5 134 20.9 209 18.7 176 29.8 156 28.7 177 a. using SPSS, compute the Pearson correlation coefficient. Answer copied from SPSS: b. Interpret these data using the general range of very weak to very strong. Also compute the coefficient of determination. How does the subjective analysis compare to the value of r 2 ?

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Answers: Interpreting the data the general range has a strength of very weak because the correlation coefficient is under .30 at .269. Coefficient of determination: (0.269)(0.269) = 0.072 The subjective analysis compares to the value of r squared, which that the variables are not perfectly related. 3. Rank the following correlation coefficients on strength of their relationship ( list the weakest first) (sign does not affect the strength). +0.71 +0.36 -0.45 +0.47 -0.62 Answer: +0.35, -0.45, 0.47, -0.62, +0.71 4. For the following set of data, using SPSS, correlate minutes of exercise with GPA. What do you conclude given your analysis? These data are saved as Chapter 5 Data Set 5 in the appendix. Exercise GPA 25 3.6 30 4.0 20 3.8 60 3.0 45 3.7

90 3.9 60 3.5 0 2.8 15 3.0 10 2.5 Answer copied from SPSS: I conclude that the correlation between exercise and GPA is weak because of the tailed .149. However, there is a positive correlation between the two variables with a value of 1. 5. The coefficient of determination between two variables is .64. Answer the following questions: a. What is the Pearson correlation coefficient? Pearson correlation coefficient: r = (square root) 64 = 0.8 b. How strong is the relationship?

The relationship is strong between the two variables. c. How much of the variance in the relationship between these two variables is unaccounted for? Explained variation: 64% Unaccounted variation: 100% - 64% = 36% 6. Here is a set of 3 variables for each of 20 participants in a study on recovery from a head injury. Use SPSS to create a simple matrix that shows the correlations between each variable. These data are saved as Chapter 5 Data Set 6 in the appendix. Age at Injury Level of Treatment 12-Month Treatment Score 25 1 78 16 2 66 8 2 78 23 3 89 31 4 87 19 4 90 15 4 98 31 5 76 21 1 56 26 1 72 24 5 84 25 5 87 36 4 69 45 4 87 16 4 88 23 1 92

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31 2 97 53 2 69 11 3 79 33 2 69 Answer copied from SPSS: 7. Look at Table 5.4 in your textbook. What type of correlation coefficient would you use to examine the relationship between sex (defined as male or female) and political affiliation? How about family configuration (two-parent or single-parent) and high school GPA? Explain why you selected the answers you did. Answers: The type of correlation I would use to examine the relationship between sex and political affiliation is the phi coefficient because there are two categories ranging from -1 to 1. For family configuration and high school GPA I would use the point biserial correlation due to the binary correlation and continuous variable.

Chapter 6 1. Provide an example of when you would want to establish test–retest and parallel forms reliability. You would establish a test-retest when measuring reliability by giving the same test twice. For example, you would take a group of students a version of a test on one day and then a different version of that same test on a different day and correlate the scores. This is considered a parallel form of reliability because you are measuring using the same or similar group and materials. You use these measures of reliability when finding the consistency of results. 2. You are developing an instrument that measures vocational preferences (what people want to do for a living), and you need to administer the test several times during the year to students who are attending a vocational program. You need to assess the test–retest reliability of the test and the data from two administrations (available as Chapter 6 Data Set 1)—one in the fall and one in the spring. Would you call this a reliable test? Why or why not? By using the measure of test-retest reliability with one test in the fall and one test in the spring to assess students in vocational programs, this would be considered a reliable test. The test is reliable because the scores should be similar as it is a test-retest, and students have already seen the test once before taking it a second time, resulting in similar results. There could still be slight variability but overall there should be constant and reliable results. 3. How can a test be reliable and not valid? Why is a test not valid unless it is reliable? A test can be reliable but not valid when the answers or scores produced are consistent but entirely wrong, making the test very reliable but invalid. A test can only be valid if it is reliable because if there are inconsistent results lacking reliability, then you cannot measure the validity. 4. Here’s the situation. You are in charge of the test development program for state employment, and you need at least two forms of the same test to administer on the same day. What kind of reliability will you want to establish? Use the data in Chapter 6 Data Set 2 in the appendix to

compute the reliability coefficient between the first and second form of the test for the 100 people who took it. Did you reach your goal? (Hint: Use SPSS) In this situation, you would want to establish reliability using Cronbach’s Alpha and a test-retest. You would want to establish a positive reliability coefficient. When putting these values into SPSS, a negative reliability coefficient is produced at -0.196209672. The goal was not reached because of the negative reliability coefficient, proving it to be unreliable. 5. When testing any experimental hypothesis, why is it important that the test you use to measure the outcome be both reliable and valid? It is important that the outcome is both reliable and valid when testing any experimental bodies because you will get an invalid result if an outcome is either unreliable, invalid, or both. You wouldn’t know what is being measured incorrectly because you wouldn’t get a measurement at all because reliability and validity rely on each other to give accurate results. 6. Describe the differences among content, predictive, and construct validity. Give examples of how each of these is measured. Content validity assesses if a measurement measures the entirety of the measure that is being conducted without leaving anything out. This can be measured, for example, by reviewing a test to ensure that it covers the entirety of the topics that need to be on the test. Predictive validity assesses if a measurement has the ability to predict future outcomes. This can be measured by taking a measurement before an event, and then another one after the event occurs to predict what will happen the next time. Construct validity assesses whether or not a test actually measures the construct it is supposed to measure. This can be measured by comparing a test you are conducting with another test that was already conducted to see if it hits the concepts it is supposed to cover.

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STA 144 Week 3 Homework - Zachary Jensen

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