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POL 242 Introduction to Research Methods Assignment One Tutorial Descriptive Statistics June 2, 2011 Anthony Sealey [email protected] http://individual.utoronto.ca/sealey Agenda (1) Introduction • (2) Review (i) Types of Variables (ii) Principal Descriptives (iii) Webstats (3) Descriptives in Webstats (4) Exercise in Webstats Introduction Please be sure to sign the attendance form. Review of Types of Variables Research Questions Review of Principal Descriptives Research Questions 1. Measures of Central Tendency Research Questions “Pick a number …” Research Questions “… close counts.” Research Questions 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Research Questions n S xi where ‘n’ denotes the Mean (x) = _______ i=1 _ number of elements Mean = n (1+2+3+4+5+6+7+8+9+10) Mean = 5.5 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 100 Research Questions Median: After arranging the data from highest to lowest, Research Questions the median is the value in the middle. “… close doesn’t count.” Research Questions 1, 2, 2, 3, 4, 5, 6, 7, 8, 9 Research Questions Mode: The value that occurs with the highest frequency Research (i.e. theQuestions value that appears most often). 2. Measures of Dispersion Research Questions 1, 2, 3, 4, 5 Research Questions _ n S (xi – = _________________ i=1 _ Variance (s2) x)2 n–1 Mean = where ‘x’ denotes the Mean (1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2 Mean = 2.5 5–1 Standard Variance(s) = Deviation Variance (s) = (s2) 2.5 Variance (s) ≈ 1.58114 where ‘s2’ denotes the Variance When to use key descriptive statistics: Descriptive Statistics Research Questions Measures of Central Tendency Mean Median Mode (m) Variance Standard (s2) Deviation (s) Nominal Ordinal Data Type Measures of Dispersion Interval Ratio Review of Webstats Research Questions • 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. • 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. I strongly recommend going to my site, downloading the ‘code’ file Research Questions and following along: http://individual.utoronto.ca/sealey Step One: Select the dataset • Go to the course website located at: http://groups.chass.utoronto.ca/pol242/ Research Questions • Go to: Webstats > Start Webstats. • In section 1, select ‘CES 2006’. • In section 3, select ‘Syntax Method’. • Hit <PROCEED>. Step Two: Run a Frequency • Let’s begin with the ‘province’ variable. • To run a frequency, use this code: fre VAR = province. Research Questions • 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’). Moving on to the next variable … Research Questions The question wording for ‘cps_f6’ in the 2006 iteration of the Canadian Elections Study: Research Questions Step Two: Run a Frequency • Since we’ve already selected the dataset, Research Questions we don’t need to repeat step one. • To run a frequency, use this code: fre VAR = cps_f6. Step Three: Refine the Variable • Notice the ‘don’t know’ and ‘refused’ responses. These responses take on the valuesResearch of ‘8’ and Questions ‘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. And finally … 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 Research Questions political leaders’ competence. In today’s tutorial, we’ll focus on the two most successful political leaders in the 2011 election. Smiling Jack Smiling Stephen Step Two: Run a Frequency • Since we’ve already selected the dataset, Research Questions we don’t need to repeat step one. • To run frequencies, use this code: fre VAR = cps_h2b0. fre VAR = cps_h2d0. Step Three: Refine the Variables • Notice the ‘don’t knows’ are coded as ‘98’. To code them as missing, use this code: Research Questions missing values cps_h2b0 (98). fre VAR = cps_h2b0. missing values cps_h2d0 (98). fre VAR = cps_h2d0. Descriptives in Webstats Research Questions Once we’ve refined our variables, the final step is to perform the analysis.Research To obtainQuestions descriptive statistics, we do this by simply adding some extra code at the end of our frequency command. Step Four: Perform the Analysis • Suppose we want to find the mode of the ‘province’ variable; in order to do Research Questions this, we simply add ‘/statistics=mode’ at the end of our frequency command: fre VAR = province/statistics=mode. • 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 Questions median,Research mean, variance and standard devation, simply add ‘/statistics=median mean variance stddev’ at the end of our frequency command. Use appropriate descriptives for each level of measurement. • For nominal variables, find the mode: fre VAR = province/statistics=mode. Research Questions • For ordinal variables, find the mode and median: missing values cps_f6 (8,9). fre VAR = cps_f6/statistics=mode median. • For interval/ratio variables, find the mode, median, mean, variance and Research Questions standard deviation: missing values cps_h2b0 (98). fre VAR = cps_h2b0/statistics = mode median mean variance stddev. We can use the means and standard deviations of similar variables to compare them. • For example, if we want to compare Research Questions 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. Once we’ve completed our analysis, we’ll be prepared to ‘tell the story’. In other words, what have we learned from our analysis? Research QuestionsWhen doing this, use the information we’ve gathered from the frequency distribution as well as from the appropriate descriptive statistics. Exercise in Webstats 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 Research Questions 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?