1. 110/10/2015Slide 1 The homework problems on comparing central tendency and variability extend our focus on central tendency and variability to a comparison of the central tendency and variability of a variable for two or more groups. The goal of comparing central tendency is to make a statement about which group tends to have higher or lower scores than the other group. The goal of comparing variability is to identify which group is more diverse, i.e. is more spread out around the measure of central tendency. As we did with the previous assignment, our first task is to examine the skewness of the variable we want to compare for all groups in the distribution. Based on our appraisal of skewness, we will determine that the mean/standard deviation or median/interquartile range are more appropriate measures.

2. 210/10/2015Slide 2 Using the appropriate statistic, we will compare the measures of central tendency for each group to determine which group had the higher or lower score, implying that they had more or less of the characteristic measured by the variable we are analyzing. Using the appropriate statistic, we will compare the measures of variability for each group to determine which group had more diverse scores, i.e. the larger measure of dispersion.

3. 3 Comparing Central Tendency and Variability Homework Problems

4. 4 Comparing Central Tendency Homework Problems - 1 The problem includes a table to be completed from the statistical output, and narrative statements that might be included in a description of the central tendency and variability of the distribution of a quantitative variable. The notes provide information about the data set to use (GSS2000R.SAV), the variables used in the analysis: news, tvhours, netime, and sex.

5. 5 Comparing Central Tendency Homework Problems - 2 In this set of problems, the paragraph about the number of missing and valid cases has been completed so that we can focus on the task of comparing central tendency and variability.

6. 6 Comparing Central Tendency Homework Problems - 3 Our first task is to compute skewness for each of the variables to identify which measure of central tendency we will compare. To compute the measures of central tendency and dispersion in SPSS, select the Descriptive Statistics > Explore command from the Analyze menu. We will make our decision about which measures of central tendency and variability to report based on the skewness of all the cases that are not missing, ignoring the skewness of the individual groups in the comparison.

7. 7 Comparing Central Tendency Homework Problems - 4 Move the variables for the analysis (news, tvhours, and netime) to the Dependent List list box. Click on the OK button to produce the output. We only request the tables of statistics by marking the Statistics option button. We accept the default descriptive statistics and listwise deletion of missing data.

8. 8 Comparing Central Tendency Homework Problems - 5 The Case Processing Summary confirms that 68 cases were used in the analysis. The descriptive statistics for each variable are shown in a separate panel of the table.

9. 9 Comparing Central Tendency Homework Problems - 6 The descriptive statistics for each variable are shown in a separate panel of the table.

10. 10 Comparing Central Tendency Homework Problems - 7 The variable is not badly skewed. The group comparisons are based on the mean and standard deviation. Frequency of reading the newspaper is a quantitative variable, so it is legitimate to compute the mean, standard deviation, median, IQR, and skewness for it. We transfer the skewness from the SPSS output to table 1, rounding to 2 decimal places.

11. 11 Comparing Central Tendency Homework Problems - 8 The variable is badly skewed. The group comparisons are based on the median and interquartile range. Hours watching TV is a quantitative variable, so it is legitimate to compute the mean, standard deviation, median, IQR, and skewness for it. We transfer the skewness from the SPSS output to table 1, rounding to 2 decimal places.

12. 12 Comparing Central Tendency Homework Problems - 9 Time spent on the internet is a quantitative variable, so it is legitimate to compute the mean, standard deviation, median, IQR, and skewness for it. We transfer the skewness from the SPSS output to table 1, rounding to 2 decimal places. The variable is badly skewed. The group comparisons are based on the median and interquartile range.

13. 13 Comparing Central Tendency Homework Problems - 10 Now that we evaluated skewness for all variables, we compute the descriptive statistics for the groups in the comparison. We can modify the last Explore command to produce the output we want. Click on the Recall dialog tool button.

14. 14 Comparing Central Tendency Homework Problems - 11 Select the Explore command from the drop- down menu when we click on the dialog recall tool button..

15. 15 Comparing Central Tendency Homework Problems - 12 To compute group descriptive statistics, add the group variable, sex, to the Factor List. Click on the OK button to generate the output.

16. 16 Comparing Central Tendency Homework Problems - 13 The SPSS output now shows a breakdown of the number of valid cases by sex. There is a separate panel for each category of sex for each quantitative variable in the table of statistics.

17. 17 Comparing Central Tendency Homework Problems - 14 Frequency of reading the newspaper is a quantitative variable, so it is legitimate to compute the mean, standard deviation, median, IQR, and skewness for it. We transfer the values from the SPSS output to table 1, rounding to 2 decimal places in all of the numbers. Mean, standard deviation, median, and interquartile range are entered in the table for both groups.

18. 18 Comparing Central Tendency Homework Problems - 15 Hours per day watching TV is a quantitative variable, so it is legitimate to compute the mean, standard deviation, median, IQR, and skewness for it. We transfer the values from the SPSS output to table 1, rounding to 2 decimal places in all of the numbers. Mean, standard deviation, median, and interquartile range are entered in the table for both groups.

19. 19 Comparing Central Tendency Homework Problems - 16 Total hours spent on the internet is a quantitative variable, so it is legitimate to compute the mean, standard deviation, median, IQR, and skewness for it. We transfer the values from the SPSS output to table 1, rounding to 2 decimal places in all of the numbers. Mean, standard deviation, median, and interquartile range are entered in the table for both groups.

20. 20 Comparing Central Tendency Homework Problems - 17 The second paragraph focuses on the comparison of central tendency and variability of reading the newspaper for males and females. We first look at the skewness of the distribution to decide which we will report. If the skewness is between -1.0 and + 1.0, we report the mean and standard deviation. If the skewness is -1.0 or smaller, or +1.0 or greater, we report the median and interquartile range. Since the skewness for reading the newspaper (-.90) is between -1.0 and +1.0, we report the mean and standard deviation.

21. 21 Comparing Central Tendency Homework Problems - 18 Since we decided to report the mean and standard deviation, we select M from the first drop down box. The APA notation for mean is M. The APA notation for median is Mdn. We enter the value for the mean from Table 1 (4.07) into the text box.

22. 22 Comparing Central Tendency Homework Problems - 19 The next part of the sentence states the comparison of the average frequency of reading the newspaper for males and females. We will come back to this answer after we have entered the mean for females.

23. 23 Comparing Central Tendency Homework Problems - 20 Since we decided to report the mean and standard deviation, we select M from the second drop down box. When we compare groups, we compare the same measures of central tendency and variability. We enter the value for the mean from Table 1 (3.64) into the text box.

24. 24 Comparing Central Tendency Homework Problems - 21 The mean for males is 4.07, while the mean for females is 3.64. In our sample, males read the newspaper more frequently than females.

25. 25 Comparing Central Tendency Homework Problems - 22 The next sentence compares the variability or diversity of scores in the distribution for males to the diversity of scores for females. We will defer this answer until we enter the measures of variability for the groups.

26. 26 Comparing Central Tendency Homework Problems - 23 Since we decided to report the mean and standard deviation, we select SD from the first drop down box. The APA notation for standard deviation is SD. The APA notation for interquartile range is IQR. We enter the value for the standard deviation from Table 1 (1.07) into the text box.

27. 27 Comparing Central Tendency Homework Problems - 24 Since we decided to report the mean and standard deviation, we select SD from the second drop down box. When we compare groups, we compare the same measures of central tendency and variability. We enter the value for the standard deviation from Table 1 (1.42) into the text box.

28. 28 Comparing Central Tendency Homework Problems - 25 The standard deviation for males is 1.07, while the standard deviation for females is 1.42. In our sample, the variability or diversity in the distribution of scores for males is less than that for females.

29. 29 Comparing Central Tendency Homework Problems - 26 The third paragraph focuses on the comparison of central tendency and variability of watching TV for males and females. Since the skewness for watching TV (2.06) is greater than +1.0, we report the median and interquartile range.

30. 30 Comparing Central Tendency Homework Problems - 27 Since we decided to report the median and interquartile range, we select Mdn from the first drop down box. The APA notation for median is Mdn. We enter the value for the median from Table 1 (3.00) into the text box.

31. 31 Comparing Central Tendency Homework Problems - 28 We enter the value for the median from Table 1 (2.00) into the text box. We select Mdn from the second drop down box. When we compare groups, we compare the same measures of central tendency and variability.

32. 32 Comparing Central Tendency Homework Problems - 29 The median for males is 3.00, while the median for females is 2.00. In our sample, males watched more hours of TV than females.

33. 33 Comparing Central Tendency Homework Problems - 30 We enter the value for the interquartile range from Table 1 (3.00) into the text box. Since we decided to report the median and interquartile range, we select IQR from the first drop down box. The APA notation for interquartile range is IQR.

34. 34 Comparing Central Tendency Homework Problems - 31 Since we decided to report the median and interquartile range, we select IQR from the second drop down box. When we compare groups, we compare the same measures of central tendency and variability. We enter the value for the interquartile range from Table 1 (3.00) into the text box.

35. 35 Comparing Central Tendency Homework Problems - 32 The interquartile range for males is 3.00, and the interquartile range for females is 3.00. In our sample, the variability or diversity in the distribution of scores for males was equally diverse to that for females.

36. 36 Comparing Central Tendency Homework Problems - 33 The fourth paragraph focuses on the comparison of central tendency and variability of hours spent on the internet for males and females. Since the skewness for time spent on the internet (3.88) is greater than +1.0, we report the median and interquartile range.

37. 37 Comparing Central Tendency Homework Problems - 34 Since we decided to report the median and interquartile range, we select Mdn from the first drop down box. The APA notation for median is Mdn. We enter the value for the median from Table 1 (5.00) into the text box.

38. 38 Comparing Central Tendency Homework Problems - 35 We enter the value for the median from Table 1 (5.50) into the text box. We select Mdn from the second drop down box. When we compare groups, we compare the same measures of central tendency and variability.

39. 39 Comparing Central Tendency Homework Problems - 36 The median for males is 5.00, while the median for females is 5.50. In our sample, males spent fewer hours on the internet compared to females.

40. 40 Comparing Central Tendency Homework Problems - 37 We enter the value for the interquartile range from Table 1 (11.25) into the text box. Since we decided to report the median and interquartile range, we select IQR from the first drop down box. The APA notation for interquartile range is IQR.

41. 41 Comparing Central Tendency Homework Problems - 38 Since we decided to report the median and interquartile range, we select IQR from the second drop down box. When we compare groups, we compare the same measures of central tendency and variability. We enter the value for the interquartile range from Table 1 (9.20) into the text box.

42. 42 Comparing Central Tendency Homework Problems - 39 The interquartile range for males is 11.25, and the interquartile range for females is 9.20. In our sample, the variability or diversity in the distribution of scores for males was more diverse compared to that for females.

43. 43 Comparing Central Tendency Homework Problems - 40 Having entered answers for all the blanks, we click on the Submit button to request grading.

44. 44 Comparing Central Tendency Homework Problems - 41 The green shading for the answers and the green checkmarks indicate that the answers entered are correct.