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# Descriptive statistics

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Focus on graphs for describing data, with a quick overview of central tendency and variability

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### Descriptive statistics

1. 1. Descriptive Statistics<br />PSY 330 Research Methods<br />
2. 2. Measurements Choices Determine Analysis Options<br />Choice of measure occurs in research design<br />Measures yield data at a particular scale (level) of measurement (Nominal, Ordinal, Interval, Ratio)<br />Interval or Ratio data can be “recoded” to create groups (e.g., age groups, income ranges)<br />Grouped data cannot be expanded to create Interval or Ratio data <br />Scale (Level) of Measurement determines which techniques are appropriate.<br />
3. 3. Matching Average to Data<br />
4. 4. Matching Variability Measure to Data<br />Range and Interquartile Range (IQR) use only a few scores.<br />Standard deviation and variance use the value of each score in the data set<br />Range and IQR are related to Median<br />Standard Deviation and Variance are related to the Mean.<br />
5. 5. Purpose of a Graph<br />A visual presentation of data<br />Relationships & comparisons are visual<br />Less daunting to some than tables of numbers<br />Allows some artistry and creativity<br />Accuracy is important<br />Characteristics of data <br />Measurement choices in design determine analysis choices later<br />Scale (level) of measurement determines which graphs can be used<br />Nature of the particular data set is also important<br />
6. 6. Graphs for Complex Data<br />The Future of Food. (2008) WiredMagazine 16:11<br />From ChoiceRanker website via JunkCharts blog at http://junkcharts.typepad.com/junk_charts/2008/07/its-raining-colors-here-too.html<br />
7. 7. Basic requirements for graphs<br /><ul><li>Axes drawn and labeled
8. 8. Category values labeled
9. 9. Title for graph
10. 10. Data bars proportional to number of cases in data
11. 11. Balanced
12. 12. Maintains scale
13. 13. No “chart junk”
14. 14. Not complicated
15. 15. Does not convey too much</li></li></ul><li>Graphs for Discrete Data(counts)<br />Data are in categories<br />Nominal <br />Ordinal (if few categories)<br />Types of graph:<br />Pie Chart<br />Bar Chart or Pictograph (Excel: Column chart)<br />Show the Frequency (count) or Percent<br />
16. 16. BAR CHART: the Good<br />Area of bars combined is 100%<br />Area of each bar is proportional to its percent of total<br />Bars do not touchbecause categoriesare discrete.<br />Many variations; this is the most simple.<br />
17. 17. The Bad:design dominatestrends or data<br />
18. 18. PICTOGRAPH: the Good bars constructed of equal size pictures<br />
19. 19. PICTOGRAPH: the Ugly<br />Elements of unequal size<br />Just heads of some kids<br />All children are playing except those from China – subtle racism<br />
20. 20. BAR CHART – problems to consider:area, color – & why is that jogger there?<br />
21. 21. PIE CHART: the Good<br />Area of pie = 100%<br />Wedge is proportional to percentage of cases<br />Labels show count or percent <br />Ten slices is the maximumto remain clear<br />
22. 22. PIE CHART: the Badcharts confuse or obscure the pattern in the data<br />
23. 23. Graphs for Continuous Data (sometimes Ordinal)<br />Graph shows continuity of the construct<br />Histogram: bars that touch at real limits<br />Line graph: covers range (a.k.a. Frequency Polygon)<br />Horizontal axis goes from low to high<br />Intervals shown for Interval or Ratio data<br />Some ordinal data also graphed this way(e.g., strongly agree, agree, slightly agree, etc)<br />
24. 24. HISTOGRAM: the Good<br />Bar width is a rangeof scores or the reallimits of scores.<br />Ranges equal width<br />Labels show mid-point or real limits<br />Low scores on left, high scores on right<br />
25. 25. HISTOGRAM: the Bad<br />Ranges of data<br />Unequal<br />Indeterminate<br />Spacing of “bars” is unequal.<br />Water, sky, umbrellaall detract from graph<br />
26. 26. Line Graphs / Frequency Polygon<br />Same requirements as histogram.<br />If more than one line,legend or labels are needed.<br />More than four or fivelines can be hard tointerpret<br />from SRB Documentary. (2008). Demographic Winter: the Decline of the Human Family at http://www.demographicwinter.com/index.html<br />
27. 27. LINE GRAPH: the Bad<br />Why is the headline “Steady growth” for this graph?<br />Hint: check the axis values<br />If it is growth, is it steady ?<br />Hint: how did each of the three variables change from 1988 to 1989.<br />
28. 28. Interesting trends in graphs:Population Map Area=population, displayed by location. <br />
29. 29. World Mapper ProjectA collection of world maps, where territories are re-sized according to the subject of interest.<br />Internet Users in 2002<br />
30. 30. World Mapper Projecthttp://www.worldmapper.org/<br />Alcohol Consumption 2006<br />
31. 31. Descriptive Statistics<br />PSY 330 Research Methods<br />