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Psychology 10

Psychology 10. Analysis of Psychological Data February 3, 2014. The Plan for Today. Wrap up measures of central tendency One more example of interpolation Choosing a measure of central tendency Reporting measures of central tendency In text In graphs

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Psychology 10

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  1. Psychology 10 Analysis of Psychological Data February 3, 2014

  2. The Plan for Today • Wrap up measures of central tendency • One more example of interpolation • Choosing a measure of central tendency • Reporting measures of central tendency • In text • In graphs • Geometric interpretations of central tendency • Central tendency and symmetry

  3. What is the median of this distribution? Score Frequency 0 – 9 5 10 – 19 18 20 – 29 24 30 – 39 2 40 – 49 1

  4. What is the median of this distribution? Cumu. Score Frequency Frequency 0 – 9 5 5 10 – 19 18 23 20 – 29 24 47 30 – 39 2 49 40 – 49 1 50

  5. What is the median of this distribution? Cumu. Cumu. Score Frequency Percent 0 – 9 5 10 10 – 19 23 46 20 – 29 47 94 30 – 39 49 98 40 – 49 50 100

  6. Some people like a single formula • Formula:

  7. Choosing a measure of central tendency • In general, start by assuming that you will use the mean. • Why? Because the mean uses the most information from the data. That makes procedures have more oomph when we get into inferential statistics. • Use another measure of central tendency if there is a compelling reason to do so.

  8. What are compelling reasons? • If the data are not interval or ratio level, do not use the mean. • If the nature of your question demands another measure of central tendency, use the other measure. • If you are concerned that extreme observations might make the mean not a good representation of typical value, consider using the median.

  9. Compelling reasons, cont. • If the data are discrete and there are only a few values possible, consider using the mode. • If the data are ordinal, you should probably be using the median. • If the data are open ended, consider using the median.

  10. What’s this about the nature of the question? • Three different reasons for interest in number of kids in a typical family. • First reason: redesigning a breakfast cereal box. • Second reason: building houses. • Third reason: planning for a tax.

  11. Breakfast cereal

  12. Reporting measures of central tendency • APA style reserves the symbol “M ” to denote the mean. • Example: “The response time for the reinforced group was shorter (M = 744 ms).” • APA style allows the use of “Mdn” to denote the median, but it is more common to spell the word out fully. • Example: “The median response time for the reinforced group was 655 ms.”

  13. Reporting measures of central tendency using graphics. • If the independent variable is interval or ratio level, line graphs or histograms may be used to present measures of central tendency. • If the independent variable is nominal or ordinal, use a bar graph. • Note: this rule is frequently violated with no major consequences. • Note: the criterion is not whether the independent variable is continuous or discrete.

  14. Principles of good graphing • Aspect ratio: ideally the height of the graph should be about 2/3 the width. This matches the human visual field well. • Normally, the vertical axis of the graph should start at zero. • If that is impractical, the fact that the axis does not start at zero should be highlighted in the graph by breaking the vertical axis below the lowest value.

  15. What is a line graph? • List the independent variable on the X axis. • Place a dot at the appropriate height for each mean. • Connect the dots.

  16. What is a histogram of means? • The same information can be presented using a histogram. • Create the X axis the same way as in a line plot. • Add a histobar that extends to the height of each mean. • Note that the histobars should touch one another, just as in an ordinary histogram.

  17. What is a bar plot of means? • If the independent variable is nominal or ordinal, a bar plot is appropriate for presenting means. • List the values of the independent variable on the X axis. • Draw a bar to the height of each mean; the bars should not touch.

  18. Why must the Y axis begin at zero? • Not starting the Y axis at zero has the potential to create severely distorted impressions of the truth.

  19. Geometric interpretations of measures of central tendency • The mean is the point where the distribution would balance if we drew the histogram on plywood, cut it out, and placed it on a fulcrum. • The median is the value that divides the histogram into two parts with equal areas. • It is often possible to make very good guesses at the values of these statistics using that knowledge.

  20. Central tendency and symmetry • Because of the mean’s tendency to be more influenced by extreme observations, a skewed distribution will often pull the mean in the direction of the long tail. • Hence, the order of the mean and median may contain information about skew. • Mean < median indicates negative skew. • Mean > median indicates positive skew.

  21. Actual values: • M = 7.6 • Mdn= 4.4

  22. Next time • Measures of variability. • Activity

  23. Peabody Picture Vocabulary Test 57 61 64 65 65 67 69 69 71 72 76 76 77 79 80 81 81 81 83 84 84 84 85 86 86 87 89 89 90 90 91 91 92 92 93 94 95 95 96 100

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