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Quantitative Data Analysis Definitions Examples of a data set Creating a data set Displaying and presenting data – frequency distributions Grouping and recoding Visual presentations Summary statistics, central tendency, variability

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What do we analyze? Variable – characteristic that varies Data – information on variables (values) Data set – lists variables, cases, values Qualitative variable – discrete values, categories. –Frequencies, percentages, proportions Quantitative variable- range of numerical values –Mean, median, range, standard deviation, etc.

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Creating a data set Enter into a statistical package (program) Program does calculations and displays results Examples: census datacensus data Data on CD (GSS 2004) http://www.d.umn.edu/~sjanssen/Intro%20to %20SPSS%20exercise.htm http://www.d.umn.edu/~sjanssen/Intro%20to %20SPSS%20exercise.htm

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Creating a data set May involve coding and data entry Coding = assigning numerical value to each value of a variable –Gender: 1= male, 2 = female –Year in school: 1= freshman, 2= sophomore, etc. –May need codes for missing data (no response, not applicable) –Large data sets come with codebooks

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Displaying and Presenting Data Frequency distribution – list of all possible values of a variable and the # of times each occurs –May require grouping into categories –May include percentages, cumulative frequencies, cumulative percentages

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Ungrouped frequency distribution –Usually qualitative variables Grouped frequency distribution –Values are combined (grouped) into categories –Use for quantitative variables –Many separate values Displaying and Presenting Data

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Grouping into categories May use meaningful groupings May use equal intervals (more common) –Equal width –Mutually exclusive –Exhaustive Class interval = category, range of values Midpoint = exact middle of interval Limits = halfway to next interval

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Summary statistics Percent = relative frequencies; standardized units. Cumulative frequency or percent = frequency at or below a given category (at least ordinal data required)

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Visual Presentation of Data Bar graph (column chart, histogram): best with fewer categories Pie chart: good for displaying percentages; easily understood by general audience Line graph: good for numerical variables with many values or for trend data

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Summary statistics: central tendency “Where is the center of the distribution?” Mode = category with highest frequency Median = middle category or score Mean = average score

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Summary Statistics: Variability “Where are the ends of the distribution? How are cases distributed around the middle?” Range = difference between highest and lowest scores Standard deviation = measure of variability; involves deviations of scores from mean; most scores fall within one standard deviation above or below mean.

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