Correlation - HHP Communities Website
5
SPSS ACTIVITIES
Correlation
ACTIVITY 1 Bivarate Correlation The data in Table 5.9 represent the scores on two youth fitness measurements, PACER laps and treadmill-determined VO2max, for 25 subjects. Enter the data into SPSS, and then perform the indicated operations.
TABLE
5.9
Data set.
STUDENT
PACER LAPS
VO2MAX
1
47
33
2
54
49
3
48
40
4
47
44
5
50
48
6
45
36
7
50
35
8
56
50
9
54
46
10
48
37
11
53
40
12
47
39
13
38
32
14
47
42
B. Go to Analyze on the tool bar, select Correlate and then
15
48
39
select Bivariate. Move PACER laps and VO2max into the Variables box, make sure Pearson is checked, and click OK.
16
49
37
17
53
42
18
53
40
19
49
40
20
52
47
21
58
51
22
39
30
23
50
40
24
44
34
25
55
47
Procedures and Questions A. On the tool bar, go to Graphs, Legacy Dialogs, select
Scatter/Dot…, and then select Simple Scatter. Click Define. Move VO2max to the Y-axis and PACER laps to the X-axis. Select Titles… and label the graph appropriately. Click Continue. Click OK. When the graph is displayed, double-click on the graph to open the Chart Editor. In the bottom row of icons, click on the fifth one from the left, Add fit line at total. This brings up a Properties screen. Add a line of best fit to your scattergram. Q 1. What are the following statistics for each of the two tests? a. mean b. standard deviation c. range
Q 2. What is the correlation between PACER laps and VO2max? Explain briefly what this means. (Hint: notice the sign and magnitude.) C. Suppose the researcher decides to give each subject an ad-
ditional five PACER laps because of a timing error. Go back to your data set and add a new column to achieve the researcher’s goal. (Hint: you can do this manually, or you could use the Compute command, under Transform on the tool bar.) Now, go back to Analyze and select Correlate and Bivariate again. Put all three tests in the variables box. Click OK. Q 3. What is the correlation between VO2max and the “corrected” PACER laps? What does this tell you?
D. To help answer the next question, change PACER laps and the “corrected”
PACER laps to z-scores. To do this, go to Analyze→Descriptive Statistics→ Descriptives and move the variables to the right window. Be certain to click on Save standardized values as variables. Q 4. What do you notice about the two sets of z-scores? 5. What is the correlation between PACER laps and the “corrected” PACER laps? What does this and your z-scores tell you?
ACTIVITY 2 Correlation Matrix The data in Table 5.10 represent the scores of 10 students on four different sports rules written exams. Use SPSS to obtain a correlation matrix involving all four exams and descriptive statistics to answer the following questions: TABLE
Procedures and Questions
5.10
Q
Data set.
EXAM 1
EXAM 2
EXAM 3
EXAM 4
49
85
61
43
53
74
54
22
51
78
56
13
49
58
53
30
48
83
62
24
49
70
58
10
49
76
65
39
51
90
63
33
50
84
57
31
52
63
63
22
6. What is the correlation between each examination and each of the other three examinations? 7. (Hint: use Descriptives for questions 7 and 8.) If each of the examinations contained 100 questions, which test was the easiest and which was most difficult? 8. On which exam were the scores most scattered? 9. Which two of the exams have the highest correlation with each other? 10. Which two exams show the least amount of correlation with each other? 11. If a new student took Exam 1 and scored above 50.1, would you predict he would score above or below 59.2 on Exam 3? Why? 12. Construct a scattergram for Exams 1 and 4 by considering Exam 1 as the X variable and Exam 4 as the Y variable. Which person falls closest to the line of best fit on the graph? (Hint: Use Scatter/ Dot under Graphs on the top tool bar, and add a regression line as done above.)
SPSS ACTIVITIES
Correlation
ACTIVITY 1 Bivarate Correlation The data in Table 5.9 represent the scores on two youth fitness measurements, PACER laps and treadmill-determined VO2max, for 25 subjects. Enter the data into SPSS, and then perform the indicated operations.
TABLE
5.9
Data set.
STUDENT
PACER LAPS
VO2MAX
1
47
33
2
54
49
3
48
40
4
47
44
5
50
48
6
45
36
7
50
35
8
56
50
9
54
46
10
48
37
11
53
40
12
47
39
13
38
32
14
47
42
B. Go to Analyze on the tool bar, select Correlate and then
15
48
39
select Bivariate. Move PACER laps and VO2max into the Variables box, make sure Pearson is checked, and click OK.
16
49
37
17
53
42
18
53
40
19
49
40
20
52
47
21
58
51
22
39
30
23
50
40
24
44
34
25
55
47
Procedures and Questions A. On the tool bar, go to Graphs, Legacy Dialogs, select
Scatter/Dot…, and then select Simple Scatter. Click Define. Move VO2max to the Y-axis and PACER laps to the X-axis. Select Titles… and label the graph appropriately. Click Continue. Click OK. When the graph is displayed, double-click on the graph to open the Chart Editor. In the bottom row of icons, click on the fifth one from the left, Add fit line at total. This brings up a Properties screen. Add a line of best fit to your scattergram. Q 1. What are the following statistics for each of the two tests? a. mean b. standard deviation c. range
Q 2. What is the correlation between PACER laps and VO2max? Explain briefly what this means. (Hint: notice the sign and magnitude.) C. Suppose the researcher decides to give each subject an ad-
ditional five PACER laps because of a timing error. Go back to your data set and add a new column to achieve the researcher’s goal. (Hint: you can do this manually, or you could use the Compute command, under Transform on the tool bar.) Now, go back to Analyze and select Correlate and Bivariate again. Put all three tests in the variables box. Click OK. Q 3. What is the correlation between VO2max and the “corrected” PACER laps? What does this tell you?
D. To help answer the next question, change PACER laps and the “corrected”
PACER laps to z-scores. To do this, go to Analyze→Descriptive Statistics→ Descriptives and move the variables to the right window. Be certain to click on Save standardized values as variables. Q 4. What do you notice about the two sets of z-scores? 5. What is the correlation between PACER laps and the “corrected” PACER laps? What does this and your z-scores tell you?
ACTIVITY 2 Correlation Matrix The data in Table 5.10 represent the scores of 10 students on four different sports rules written exams. Use SPSS to obtain a correlation matrix involving all four exams and descriptive statistics to answer the following questions: TABLE
Procedures and Questions
5.10
Q
Data set.
EXAM 1
EXAM 2
EXAM 3
EXAM 4
49
85
61
43
53
74
54
22
51
78
56
13
49
58
53
30
48
83
62
24
49
70
58
10
49
76
65
39
51
90
63
33
50
84
57
31
52
63
63
22
6. What is the correlation between each examination and each of the other three examinations? 7. (Hint: use Descriptives for questions 7 and 8.) If each of the examinations contained 100 questions, which test was the easiest and which was most difficult? 8. On which exam were the scores most scattered? 9. Which two of the exams have the highest correlation with each other? 10. Which two exams show the least amount of correlation with each other? 11. If a new student took Exam 1 and scored above 50.1, would you predict he would score above or below 59.2 on Exam 3? Why? 12. Construct a scattergram for Exams 1 and 4 by considering Exam 1 as the X variable and Exam 4 as the Y variable. Which person falls closest to the line of best fit on the graph? (Hint: Use Scatter/ Dot under Graphs on the top tool bar, and add a regression line as done above.)
