2. POL 242 Introduction to Research Methods Assignment One Tutorial Descriptive Statistics June 2, 2011 Anthony Sealey anthony.sealey@utoronto.ca http://individual.utoronto.ca/sealey

3. Agenda (1) Introduction (2) Review (i) Types of Variables (ii) Principal Descriptives (iii) Webstats (3) Descriptives in Webstats (4) Exercise in Webstats

4. Introduction

5. Please be sure to sign the attendance form.

6. Research Questions Review of Types of Variables

7. Research Questions Review of Principal Descriptives

8. Research Questions 1. Measures of Central Tendency

9. Research Questions “Pick a number …”

10. Research Questions “… close counts.”

11. Research Questions 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

12. n where ‘n’ denotes the number of elements    x i _______ n Mean (x) = (1+2+3+4+5+6+7+8+9+10) 10 Mean = Mean = 5.5 i = 1 _

13. Research Questions 1, 2, 3, 4, 5, 6, 7, 8, 9, 100

14. Research Questions Median: After arranging the data from highest to lowest, the median is the value in the middle.

15. Research Questions “… close doesn’t count.”

16. Research Questions 1, 2, 2, 3, 4, 5, 6, 7, 8, 9

17. Research Questions Mode: The value that occurs with the highest frequency (i.e. the value that appears most often).

18. Research Questions 2. Measures of Dispersion

19. Research Questions 1, 2, 3, 4, 5

20. n where ‘x’ denotes the Mean    (x i – x) 2 _________________ n – 1 (1-3) 2 +(2-3) 2 +(3-3) 2 +(4-3) 2 +(5-3) 2 5 – 1 Mean = Mean = 2.5 i = 1 Variance (s 2 ) = _ _

21. where ‘s 2 ’ denotes the Variance Variance(s) = Standard Deviation √ (s2)√ (s2) √  Variance (  ) = 1.58114 Variance (  ) ≈

22. Research Questions Descriptive Statistics Measures of Central TendencyMeasures of Dispersion MeanMedianModeVarianceStandard ()() (  2) Deviation (  ) Nominal Data Type Ordinal Interval Ratio When to use key descriptive statistics:

23. Research Questions Review of Webstats

24. There are four basic steps to the analysis of a variable in Webstats: (1) Select a dataset. (2) Run a ‘frequency’ to understand how the variable is coded. (3) Refine the variable. (4) Perform the analysis.

25. In today’s tutorial we’ll use the 2006 CES to consider three variables: (1) A citizen’s province. (2) Citizen’s preferences for or against income redistribution. (3) Citizen’s evaluations of the competence of political leaders.

26. Research Questions I strongly recommend going to my site, downloading the ‘code’ file and following along: http://individual.utoronto.ca/sealey

27. Research Questions Step One: Select the dataset Go to the course website located at: http://groups.chass.utoronto.ca/pol242/ Go to: Webstats > Start Webstats. In section 1, select ‘CES 2006’. In section 3, select ‘Syntax Method’. Hit.

28. Research Questions Step Two: Run a Frequency Let’s begin with the ‘province’ variable. To run a frequency, use this code: fre VAR = province. Given that this variable has no missing values and does not require a recode, we can skip the third step (‘refine the variable’) and go to the fourth (‘perform the analysis’).

29. Research Questions Moving on to the next variable …

30. Research Questions The question wording for ‘cps_f6’ in the 2006 iteration of the Canadian Elections Study:

31. Research Questions Step Two: Run a Frequency Since we’ve already selected the dataset, we don’t need to repeat step one. To run a frequency, use this code: fre VAR = cps_f6.

32. Research Questions Step Three: Refine the Variable Notice the ‘don’t know’ and ‘refused’ responses. These responses take on the values of ‘8’ and ‘9’ respectively. We’ll want to code them as missing, and then rerun the frequency: missing values cps_f6 (8,9). fre VAR = cps_f6.

33. Research Questions And finally …

34. Research Questions The ‘cps_h2b0’ and ‘cps_h2d0’ variables in the 2006 iteration of the Canadian Elections Study asks about respondent’s perceptions of levels of political leaders’ competence. In today’s tutorial, we’ll focus on the two most successful political leaders in the 2011 election.

35. Smiling Jack

36. Smiling Stephen

37. Research Questions Step Two: Run a Frequency Since we’ve already selected the dataset, we don’t need to repeat step one. To run frequencies, use this code: fre VAR = cps_h2b0. fre VAR = cps_h2d0.

38. Research Questions Step Three: Refine the Variables Notice the ‘don’t knows’ are coded as ‘98’. To code them as missing, use this code: missing values cps_h2b0 (98). fre VAR = cps_h2b0. missing values cps_h2d0 (98). fre VAR = cps_h2d0.

39. Research Questions Descriptives in Webstats

40. Research Questions Once we’ve refined our variables, the final step is to perform the analysis. To obtain descriptive statistics, we do this by simply adding some extra code at the end of our frequency command.

41. Research Questions Step Four: Perform the Analysis Suppose we want to find the mode of the ‘province’ variable; in order to do this, we simply add ‘ /statistics=mode ’ at the end of our frequency command: fre VAR = province/statistics=mode.

42. Research Questions If we want other descriptive statistics, simply include the appropriate code at the end of the frequency command. For example, if we want to know the median, mean, variance and standard devation, simply add ‘ /statistics=median mean variance stddev ’ at the end of our frequency command.

43. Research Questions Use appropriate descriptives for each level of measurement. For nominal variables, find the mode: fre VAR = province/statistics=mode. For ordinal variables, find the mode and median: missing values cps_f6 (8,9). fre VAR = cps_f6/statistics=mode median.

44. Research Questions For interval/ratio variables, find the mode, median, mean, variance and standard deviation: missing values cps_h2b0 (98). fre VAR = cps_h2b0/statistics = mode median mean variance stddev.

45. Research Questions We can use the means and standard deviations of similar variables to compare them. For example, if we want to compare perceptions of Jack’s and Stephen’s competence, use this code: missing values cps_h2b0 (98). fre VAR = cps_h2b0/statistics = mean stddev. missing values cps_h2d0 (98). fre VAR = cps_h2d0/statistics = mean stddev.

46. Research Questions Once we’ve completed our analysis, we’ll be prepared to ‘tell the story’. In other words, what have we learned from our analysis? When doing this, use the information we’ve gathered from the frequency distribution as well as from the appropriate descriptive statistics.

47. Research Questions Exercise in Webstats

48. Research Questions Exercise Choose a public opinion dataset that you are interested in. Find a variable for each of the nominal, ordinal and (interval or ratio) levels of measurement. Run frequency distributions, refine the variables by declaring missing values and performing necessary recodes and calculate appropriate descriptive statistics for each of the identified variables. What’s the ‘story’ of your analysis? What have you learned?