SmalleyTylerStatsHomeworkWeek3

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California Baptist University *

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Jan 9, 2024

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STA 144 Week 3 Homework 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. Correlations Problems_C orrect Attitude Problems_Corr ect Pearson Correlation 1 .596 Sig. (2-tailed) .069 N 10 10 Attitude Pearson Correlation .596 1 Sig. (2-tailed) .069 N 10 10 b. Construct a scatterplot for these 10 values. Based on the scatterplot, would you predict the correlation to be direct or indirect? Why?

I believe this correlation to be a direct correlation as the numbers most appear to be moving in a positive direction. The higher the students were in confidence was generally reflected as a higher score on the test, although according to the rule of thumb, being that the correlation is only at . 596, it is only a moderately positive correlation. Total Number 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 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. Correlations Speed Strength Speed Pearson Correlation 1 .269 Sig. (2-tailed) .452 N 10 10 Strengt h Pearson Correlation .269 1 Sig. (2-tailed) .452 N 10 10 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 ? This correlation is a weak relationship and the determination would show a very low fit for this model. With only about 7% of variance Coefficient of determination = .269^2. r^2 = 0.072361. 3. Rank the following correlation coefficients on strength of their relationship ( list the weakest first) (sign does not affect the strength). +0.71 1 – +0.36 +0.36 2 – +0.45 -0.45 3 – +0.47 +0.47 4 – -0.62 -0.62 5 – +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.

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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 Correlations Exercis e GPA Exercis e Pearson Correlation 1 .492 Sig. (2-tailed) .149 N 10 10 GPA Pearson Correlation .492 1 Sig. (2-tailed) .149 N 10 10 The analysis of this data set would show a moderate relationship with exercise and GPA. A slight positive correlation in that the more that someone exercised, there was a potential for a higher grade point average. The determination is .242 after squaring .492 and that appears to give us a 24% fit with the model. 5. The coefficient of determination between two variables is .64. Answer the following questions: a. What is the Pearson correlation coefficient? The square root of .64. = 0.8

b. How strong is the relationship? The relationship strong. c. How much of the variance in the relationship between these two variables is unaccounted for? 64% 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 31 2 97 53 2 69 11 3 79

33 2 69 Correlations Age Treatment_L evel TreatmentSc ore Age Pearson Correlation 1 .082 -.154 Sig. (2-tailed) .732 .516 N 20 20 20 Treatment_Le vel Pearson Correlation .082 1 .356 Sig. (2-tailed) .732 .124 N 20 20 20 TreatmentSco re Pearson Correlation -.154 .356 1 Sig. (2-tailed) .516 .124 N 20 20 20 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. Chapter 6 1. Provide an example of when you would want to establish test–retest and parallel forms reliability. a. A test retest would be useful when trying to compare the data of separate groups after a certain period of time. Perhaps a test is given and the data shows a result that is favorable or demonstrates some sort of validity to a hypothesis the researches had, and after a while there is a retest so that they can confirm their findings and make sure that the one off test wasn’t a fluke. A parallel form would be when trying to give out varying tests to different groups and making sure that the outcomes or effectiveness of each test is equal among them as to not mess up the data that is collected. 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

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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? (Hint: Use SPSS) a. 3. How can a test be reliable and not valid? Why is a test not valid unless it is reliable? a. The test may prove to show scores or data reliably and upon retesting or giving out different forms of the test to multiple groups, the data may come back as expected and therefore be reliable. However, the way in which the test was given could be incorrect, the metrics for which the data was based on could be wrong and the way in which the questions, if a survey, were asked could have been asked in a leading fashion. 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) 5. When testing any experimental hypothesis, why is it important that the test you use to measure the outcome be both reliable and valid? This is important because if the test is not reliable, then the ability to retest or continue using the same test are useless. It has to be valid because it needs to be a trusted way of collecting the data with standards. If it the test is not done in a valid fashion then it becomes useless as well. 6. Describe the differences among content, predictive, and construct validity. Give examples of how each of these is measured. Content is focused on a vast sample size encompassing a wide variety of information - This type of test could be seen as perhaps an iq test or a test in school where the goal is to see how well someone has grasped certain information. Predictive is focused on seeing how well future events are matched with the test that was performed. - This could be giving out a survey to high school students that are deciding on what they want to do with their lives and seeing how well that actually played out for them in the long run. Construct Validity is based on testing an idea or behavior. - This could possibly be seen as those psychology tests that everyone seems to be taking online that tells you what your personality is based on the questions you answered.

SmalleyTylerStatsHomeworkWeek3

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