Descriptive Statistics
3
SPSS ACTIVITIES
Descriptive Statistics
ACTIVITY 1 Examining Data Suppose a group of researchers administered a 15-item questionnaire that asked subjects to rate how often they engage in various types of physical activity on a five-point scale. From the questionnaire, the researchers obtained the 65 scores in Table 3.2, which will be used as data for this activity.
Procedures and Questions A. Call the data column “testscr” and label it “Scores.” Remember that
this is numerical data. The last column in the Variable View box should be labeled Scale. B. Go to the Data View box to enter all 65 scores. C. Next, click on Graphs in the top menu, select Legacy Dialog, and then se-
lect Histogram. D. In the Histogram screen, move the highlighted scores into the Variable box
by using the arrow, and click OK. A frequency histogram will appear. E. We want to change the intervals a bit. To do this, double-click on the graph
itself. A Chart Editor screen will appear. F. Double-click on the Y-axis. A Properties screen will appear. G. Click on Scale. Change the Major increment to 1, so that the Y-axis will
show a scale with increments of 1. Data set.
TABLE
3.2
49
45
41
49
46
47
47
49
50
50
39
51
35
48
37
46
44
44
52
53
49
40
48
42
48
49
47
49
44
38
51
47
53
45
48
47
43
46
49
50
48
48
45
46
49
48
46
48
52
54
52
36
51
47
45
47
43
47
46
50
44
55
48
50
53
1
H. Click Apply. I. Close the Properties window. J. Next, double-click on the histogram. In the Properties screen, click on
Binning, if it is not already highlighted. K. Click on Custom and change the number of intervals to 21. L. Click on Interval width and enter 1. This will change the bars to be just 1
score wide. M. Click on Apply. N. Close the Properties screen and the Chart Editor screen. This should pro-
duce a histogram. O. Next, in the Analyze menu, select Descriptive Statistics and then select Fre-
quencies… Highlight Scores in the Frequencies screen and move it over to the box on the right. Then, click on Statistics… and check Quartiles and Cut Points For 10 equal groups. Also, add percentiles for 10 and 90 by typing 10 in the box and clicking on Add and then typing 90 in the box and clicking on Add again. Click Continue. Click OK. P. Use the two tables that appear to answer these questions:
Q
1. What percentage of the subjects scored exactly 50 on the questionnaire? 2. What percentage of the subjects scored 42 on the questionnaire? 3. What questionnaire scores correspond to the 10th, 25th, 50th, 75th, and 90th percentiles, respectively?
Q. Finally, go to Analyze→Descriptive Statistics→Frequencies. In the Frequen-
cies screen, move Scores to the box on the right (it may already be there), and click on Statistics. Uncheck the Quartiles and Cut Points For boxes. Highlight 10 in the Percentiles box, and click on Remove. Highlight 90 in the Percentiles box, and click on Remove. This will remove the previous commands so that we can now insert new ones. Enter 0 and 100 in the Percentiles box. Click on the boxes for Standard Deviation, Variance, SE mean, Skewness, Kurtosis, Mean, and Median. Click on Continue and then on OK. Answer the following questions: Q
4. What are the values for the standard deviation, variance, and standard error of the mean? 5. Describe the data in terms of skewness and kurtosis. 6. What is the value of the mean? 7. What is the value of the median?
8. Do your answers to questions 6 and 7 agree or disagree with your observation about the skewness from above? Why or why not? 9. What score does SPSS equate with a percentile rank of 100? 10. What score does SPSS equate with a percentile rank of 0?
ACTIVITY 2 Calculating Descriptive Statistics Suppose a group of researchers was interested in comparing the VO2max of elite bicycle riders and sedentary individuals, and they gathered the data shown in Table 3.3 on the VO2max values of the two groups of subjects.
Procedures and Questions A. Change the number of decimal places if desired. B. Under Graphs in the top tool bar, select Legacy Dialogs
and then select Histogram. Enter the data for the elite bicycle riders in the Variable box to be used for the graph. Click OK. C. Let’s make some changes to the histogram to change its
appearance. You might experiment with the commands to discover some of the many possibilities for presenting your information. Double-click on the histogram and go to the Chart editor. Double-click on a value on the X-axis to open the Properties screen. Change the size of the values on the X-axis from a preferred size of 8 to 12. Click Apply. Next, click on Scale at the top of the Properties screen. Change Minimum to 65, Maximum to 79, and Major Increment to 1. Click Apply. D. Close the Properties screen and return to the Chart Edi-
tor. Click on the icon under the word SanSerif. (It looks like a normal curve.) Then close the screen that pops up. Next, double-click on the histogram and change the bin size from automatic to custom, and change interval width to 1. Click Apply. Click Close. E. Change the size of the increments on the Y-axis by dou-
ble-clicking on a number on the Y-axis. Change the preferred size from 8 to 12 in the text screen. Click Apply. Click Close. F. Click on the graph, copy it, and paste it to MS Word.
Give the graph an appropriate name.
TABLE
3.3
Data set.
ELITE
SEDENTARY
74 73 71 76 69 71 73 68 75 74 70 78 71 71 68 74 75 69 73 74 70 76 73 67 74 67 70 73 69 74
32 40 35 42 30 29 24 35 41 28 30 43 35 40 32 35 29 41 32 40 30 28 35 30 41 27 42 32 29 35
G. Go to Analyze→Descriptive Statistics→Descriptives. Move the elite
VO2max values into the Variable box. Click on Options and select all boxes (not bubbles). Click Continue and then OK. Q
11. What is the highest value? 12. What is the lowest value? 13. What is the range? 14. What is the mean? 15. What is the standard deviation? 16. What is the sum of the 30 values? 17. What is the variance? 18. What is the skewness? 19. What is the kurtosis?
H. Determine the same descriptive statistics for the sedentary individuals. I. Manipulate your Data View screen by using cut and paste to put all the data
in one column. Determine the same descriptive statistics for the combined data. Q 20. If you graphed these data, what word would best describe the shape of the curve? 21. Describe in words the main differences between the two distributions (elite vs. sedentary), basing your comparison on appropriate descriptive statistics.
SPSS ACTIVITIES
Descriptive Statistics
ACTIVITY 1 Examining Data Suppose a group of researchers administered a 15-item questionnaire that asked subjects to rate how often they engage in various types of physical activity on a five-point scale. From the questionnaire, the researchers obtained the 65 scores in Table 3.2, which will be used as data for this activity.
Procedures and Questions A. Call the data column “testscr” and label it “Scores.” Remember that
this is numerical data. The last column in the Variable View box should be labeled Scale. B. Go to the Data View box to enter all 65 scores. C. Next, click on Graphs in the top menu, select Legacy Dialog, and then se-
lect Histogram. D. In the Histogram screen, move the highlighted scores into the Variable box
by using the arrow, and click OK. A frequency histogram will appear. E. We want to change the intervals a bit. To do this, double-click on the graph
itself. A Chart Editor screen will appear. F. Double-click on the Y-axis. A Properties screen will appear. G. Click on Scale. Change the Major increment to 1, so that the Y-axis will
show a scale with increments of 1. Data set.
TABLE
3.2
49
45
41
49
46
47
47
49
50
50
39
51
35
48
37
46
44
44
52
53
49
40
48
42
48
49
47
49
44
38
51
47
53
45
48
47
43
46
49
50
48
48
45
46
49
48
46
48
52
54
52
36
51
47
45
47
43
47
46
50
44
55
48
50
53
1
H. Click Apply. I. Close the Properties window. J. Next, double-click on the histogram. In the Properties screen, click on
Binning, if it is not already highlighted. K. Click on Custom and change the number of intervals to 21. L. Click on Interval width and enter 1. This will change the bars to be just 1
score wide. M. Click on Apply. N. Close the Properties screen and the Chart Editor screen. This should pro-
duce a histogram. O. Next, in the Analyze menu, select Descriptive Statistics and then select Fre-
quencies… Highlight Scores in the Frequencies screen and move it over to the box on the right. Then, click on Statistics… and check Quartiles and Cut Points For 10 equal groups. Also, add percentiles for 10 and 90 by typing 10 in the box and clicking on Add and then typing 90 in the box and clicking on Add again. Click Continue. Click OK. P. Use the two tables that appear to answer these questions:
Q
1. What percentage of the subjects scored exactly 50 on the questionnaire? 2. What percentage of the subjects scored 42 on the questionnaire? 3. What questionnaire scores correspond to the 10th, 25th, 50th, 75th, and 90th percentiles, respectively?
Q. Finally, go to Analyze→Descriptive Statistics→Frequencies. In the Frequen-
cies screen, move Scores to the box on the right (it may already be there), and click on Statistics. Uncheck the Quartiles and Cut Points For boxes. Highlight 10 in the Percentiles box, and click on Remove. Highlight 90 in the Percentiles box, and click on Remove. This will remove the previous commands so that we can now insert new ones. Enter 0 and 100 in the Percentiles box. Click on the boxes for Standard Deviation, Variance, SE mean, Skewness, Kurtosis, Mean, and Median. Click on Continue and then on OK. Answer the following questions: Q
4. What are the values for the standard deviation, variance, and standard error of the mean? 5. Describe the data in terms of skewness and kurtosis. 6. What is the value of the mean? 7. What is the value of the median?
8. Do your answers to questions 6 and 7 agree or disagree with your observation about the skewness from above? Why or why not? 9. What score does SPSS equate with a percentile rank of 100? 10. What score does SPSS equate with a percentile rank of 0?
ACTIVITY 2 Calculating Descriptive Statistics Suppose a group of researchers was interested in comparing the VO2max of elite bicycle riders and sedentary individuals, and they gathered the data shown in Table 3.3 on the VO2max values of the two groups of subjects.
Procedures and Questions A. Change the number of decimal places if desired. B. Under Graphs in the top tool bar, select Legacy Dialogs
and then select Histogram. Enter the data for the elite bicycle riders in the Variable box to be used for the graph. Click OK. C. Let’s make some changes to the histogram to change its
appearance. You might experiment with the commands to discover some of the many possibilities for presenting your information. Double-click on the histogram and go to the Chart editor. Double-click on a value on the X-axis to open the Properties screen. Change the size of the values on the X-axis from a preferred size of 8 to 12. Click Apply. Next, click on Scale at the top of the Properties screen. Change Minimum to 65, Maximum to 79, and Major Increment to 1. Click Apply. D. Close the Properties screen and return to the Chart Edi-
tor. Click on the icon under the word SanSerif. (It looks like a normal curve.) Then close the screen that pops up. Next, double-click on the histogram and change the bin size from automatic to custom, and change interval width to 1. Click Apply. Click Close. E. Change the size of the increments on the Y-axis by dou-
ble-clicking on a number on the Y-axis. Change the preferred size from 8 to 12 in the text screen. Click Apply. Click Close. F. Click on the graph, copy it, and paste it to MS Word.
Give the graph an appropriate name.
TABLE
3.3
Data set.
ELITE
SEDENTARY
74 73 71 76 69 71 73 68 75 74 70 78 71 71 68 74 75 69 73 74 70 76 73 67 74 67 70 73 69 74
32 40 35 42 30 29 24 35 41 28 30 43 35 40 32 35 29 41 32 40 30 28 35 30 41 27 42 32 29 35
G. Go to Analyze→Descriptive Statistics→Descriptives. Move the elite
VO2max values into the Variable box. Click on Options and select all boxes (not bubbles). Click Continue and then OK. Q
11. What is the highest value? 12. What is the lowest value? 13. What is the range? 14. What is the mean? 15. What is the standard deviation? 16. What is the sum of the 30 values? 17. What is the variance? 18. What is the skewness? 19. What is the kurtosis?
H. Determine the same descriptive statistics for the sedentary individuals. I. Manipulate your Data View screen by using cut and paste to put all the data
in one column. Determine the same descriptive statistics for the combined data. Q 20. If you graphed these data, what word would best describe the shape of the curve? 21. Describe in words the main differences between the two distributions (elite vs. sedentary), basing your comparison on appropriate descriptive statistics.
