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Agenda

Agenda. Descriptive Statistics Looking at data Univariate statistics Choosing appropriate statistics. Coding. Moving from questions posed to respondents to data for analysis Assigning codes (usually numbers) to raw research materials Questionnaires Closed-ended responses

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Agenda

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  1. Agenda Descriptive Statistics • Looking at data • Univariate statistics • Choosing appropriate statistics

  2. Coding • Moving from questions posed to respondents to data for analysis • Assigning codes (usually numbers) to raw research materials • Questionnaires • Closed-ended responses • Open-ended responses • Archival material

  3. Each column is one variable Each row is one case (e.g., respondent)

  4. Coding open-ends • Words into variables • Basic principles: • Theoretically relevant variable • Single classification principle (single dimension) • Mutually exclusive and exhaustive categories

  5. Coding open-ends In general, what do you think about TV? NOT MUCH i don’t watch enough to have an opinion I really enjoy it I try not to think about TV, it makes me sick People these days are just getting rude and ugly I WISH THERE WERE MORE FOOTBALL GAMES FROM THE WEST MY DRUG OF CHOICE, I LOVE IT It’s getting worse. Was great when I was a kid This season, pretty good so far

  6. Coding open-ends • How about these codes? 1= Mentions specific show 2= Confused 3= Gives an opinion • How about these? 1= Positive comment about TV 2= Neutral comment about TV 3= Negative comment about TV 4= Not discernable/ Expresses no view about TV

  7. Looking at data • Frequency distribution • Graphical displays of the distribution • Pie charts • Bar charts/histograms

  8. Statistics • Quantitative summaries • Univariate statistics summarize single variable • Central tendency of a distribution • Amount of variation in a distribution • Shape of a distribution • Bivariate statistics summarize two variables (i.e., a joint distribution) • Covariation or association • Shape of an association

  9. Central tendency • Summaries of the “center” of a distribution • Mode: the most commonly occurring value • Median: the value that lies halfway through an ordered distribution • Mean: the value that is the arithmetic average

  10. Mode , also Median , also Mean = 1.9

  11. Median Mode Mean = 3.3

  12. Variation • Summaries of amount of “dispersion” in a distribution • Range: the difference between the highest to lowest value • Interquartile range: the difference between the 25th percentile and the 75th percentile • Variance: the average of squared deviations from the mean • Standard deviation: the square root of the variance

  13. Variance (average squared deviation) = 6.34 Stand. Dev. = 2.50 (1 - 3.3)2 IQ Range 1-5 Range 0-7

  14. Shape of a distribution • Summaries of the way distributions are shaped • Statistics assess the symmetry and normality of a distribution • Skewness: the degree to which a distribution has an asymmetrical right-hand or left-hand “tail” • Kurtosis: the degree to which a distribution is taller and skinnier (or shorter and fatter) than a random distribution • Both statistics equal 0 for a random (normal) distribution, and take on larger positive and negative values as departures from normality get more extreme

  15. A B Normal Bimodal Positive kurtosis (leptokurtotic) E C D Positively skewed Negative kurtosis (platykurtotic) Median Mean

  16. Which statistics? • Variable: Make of Car Owned • What level of measurement? • How would we represent the distribution graphically? Pie, Bar Chart, or Histogram? • How would we measure the “center” of the distribution? Mean, Median, or Mode? • How would we measure “dispersion” of the distribution? Range(IQ range) or Variance(Standard Deviation)?

  17. Which statistics? • Variable: Years of residence in Philadelphia • What level of measurement? • How would we represent the distribution graphically? Pie, Bar Chart, or Histogram? • How would we measure the “center” of the distribution? Mean, Median, or Mode? • How would we measure “dispersion” of the distribution? Range(IQ range) or Variance(Standard Deviation)?

  18. Transformations • When to alter a distribution? • Natural “cut points” in the distribution • To isolate a particular group for comparison (e.g., people who never watch TV) • To simplify an analysis (e.g., compare high versus low groups)

  19. Transformations (cont.) • Aggregating variables can improve distributions • What is a “good” distribution? • Central tendency that is indeed central (i.e., not badly skewed) • Adequate variation Co-variation between variables requires variation • Many statistical procedures assume normality (at least, rough approximations of normality)

  20. For Tuesday • Bivariate statistics • Measures of association • Readings • Schutt, sections of Ch. 12 • Rosenberg, “The meaning of relationships” • Norusis, Ch. 8,17,19

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