Slide 1

Thank you Prof. Gooch. 1POL 242Introduction to Research MethodsAssignment One TutorialDescriptive Statistics

June 2, 2011Anthony Sealey anthony.sealey@utoronto.cahttp://individual.utoronto.ca/sealey

2Agenda

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

3Introduction

4Please be sure to sign the attendance form.

5

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Review of Types of Variables

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Review of Principal Descriptives

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1. Measures of Central Tendency

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Pick a number

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close counts.

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1, 2, 3, 4, 5, 6, 7, 8, 9, 10

nwhere n denotes the number of elements S xi _______ n

Mean (x) =(1+2+3+4+5+6+7+8+9+10) 10Mean =Mean = 5.5i = 1_http://cs-www.bu.edu/~reyzin/pptips.html

microsoft equation??? 12

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1, 2, 3, 4, 5, 6, 7, 8, 9, 100

13

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

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close doesnt count.

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1, 2, 2, 3, 4, 5, 6, 7, 8, 9

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

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2. Measures of Dispersion

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1, 2, 3, 4, 5

nwhere x denotes the Mean S (xi x)2 _________________ n 1

(1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2 5 1 Mean =Mean = 2.5i = 1Variance (s2) =_ _http://cs-www.bu.edu/~reyzin/pptips.html20where s2 denotes the VarianceVariance(s) =StandardDeviation (s2) 2.5Variance (s) =1.58114Variance (s) http://cs-www.bu.edu/~reyzin/pptips.html21

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Descriptive StatisticsMeasures of Central TendencyMeasures of DispersionMeanMedianModeVarianceStandard (m)(s2) Deviation (s)NominalData TypeOrdinalIntervalRatioWhen to use key descriptive statistics:

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Review of Webstats

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. 24 In todays tutorial well use the 2006 CES to consider three variables: (1) A citizens province. (2) Citizens preferences for or against income redistribution. (3) Citizens evaluations of the competence of political leaders. 25

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I strongly recommend going to my site, downloading the code file and following along:

http://individual.utoronto.ca/sealey

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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 .

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Step Two: Run a Frequency

Lets 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).

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Moving on to the next variable

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The question wording for cps_f6 in the 2006 iteration of the Canadian Elections Study:

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Step Two: Run a Frequency

Since weve already selected the dataset, we dont need to repeat step one. To run a frequency, use this code: fre VAR = cps_f6.

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Step Three: Refine the Variable

Notice the dont know and refused responses. These responses take on the values of 8 and 9 respectively. Well want to code them as missing, and then rerun the frequency: missing values cps_f6 (8,9). fre VAR = cps_f6.

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And finally

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The cps_h2b0 and cps_h2d0 variables in the 2006 iteration of the Canadian Elections Study asks about respondents perceptions of levels of political leaders competence. In todays tutorial, well focus on the two most successful political leaders in the 2011 election.

Smiling Jack

Smiling Stephen

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Step Two: Run a Frequency

Since weve already selected the dataset, we dont need to repeat step one. To run frequencies, use this code: fre VAR = cps_h2b0. fre VAR = cps_h2d0.

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Step Three: Refine the Variables

Notice the dont 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.

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Descriptives in Webstats

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Once weve 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.

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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.

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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.

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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.

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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.

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We can use the means and standard deviations of similar variables to compare them. For example, if we want to compare perceptions of Jacks and Stephens 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.

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

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Exercise in Webstats

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Exercise Choose a public opiniondataset that you are interested in. Find a variable for each of the nominal, ordinal and (interval or ratio) levels ofmeasurement. Run frequency distributions, refine the variables by declaring missing values and performing necessary recodes and calculate appropriatedescriptive statistics for each of the identified variables.Whats the story of your analysis? What have you learned?