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Chapter 4

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Transcript

  • 1. Chapter 4 Statistical Concepts: Making Meaning Out of Scores
  • 2. Raw Scores
    • Jeremiah scores a 47 on one test and Elise scores a 95 on a different test. Who did better?
      • Depends on:
        • How many items there are on the tests (47 or 950?)
        • Average score of everyone who took the tests.
        • Is higher or lower a better score?
  • 3. Rule #1: Raw Scores are Meaningless !
    • Raw scores tell us little, if anything, about how an individual did on a test
    • Must take those raw scores and do something to make meaning of them
  • 4. Making Raw Scores Meaningful: Norm Group Comparisons
    • However, norm group comparisons are helpful:
      • They tell us the relative position, within the norm group, of a person’s score
      • They allow us to compare the results among test-takers who took the same
      • They allow us to compare test results on two or more different tests taken by the same individual
  • 5. Frequency Distributions
    • Using a frequency distribution helps to make sense out of a set of scores
    • A frequency distribution orders a set of scores from high to low and lists the corresponding frequency of each score
    • See Table 4.1, p. 69
  • 6. Frequency Distributions (cont’d)
    • Make a frequency distribution:
    • 1 2 4 6 12 16 14 4
    • 7 21 4 3 11 4 10
    • 12 7 9 3 2 1 3
    • 6 1 3 6 5 10 3
  • 7. Histograms and Frequency Polygons
    • Use a graph to make sense out your frequency distribution
    • Two types of graphs:
      • Histograms (bar graph)
      • Frequency Polygons
    • Must determine class intervals to draw a histogram or frequency polygon
      • Class intervals tell you how many people scored within a grouping of scores
  • 8. Class Intervals
    • Making Class Intervals (Numbers from Table 4.1, p. 69)
    • Subtract lowest number in series of scores from highest number: 66 - 32 = 34
    • Divide number by number of class intervals you want (e.g., 7). 34/7 = 4.86
    • Round off number obtained: 4.86 becomes 5
    • Starting with lowest number, use number obtained (e.g., 5) for number of scores in each interval:
    • 32–36, 37–41,42–46, 47–51, 52–56, 57–61, 62–66
    • See Table 4.2, p. 70; then Fig 4.1 and 4.2, p. 71
  • 9. Creating Class Intervals
    • Make a distribution that has class intervals of 3 from the same set of scores:
    • 1 2 4 6 12 16 14 4
    • 7 21 4 3 11 4 10
    • 12 7 9 3 2 1 3
    • 6 1 3 6 5 10 3
  • 10. Making a Frequency Polygon and a Histogram
    • From your frequency distribution of class intervals (done on last slide), place each interval on a graph.
    • Then, make a frequency polygon and then a histogram using your answers.
  • 11. Another Frequency Distribution
    • Make a frequency distribution from the following scores:
    • 15, 18, 25, 34, 42, 17, 19,
    • 20, 15, 33, 32, 28, 15, 19,
    • 30, 20, 24, 31, 16, 25, 26
  • 12. Make a Class Interval
    • Make a distribution that has class Intervals of 4 from the same set of scores:
    • 15, 18, 25, 34, 42, 17, 19, 20, 15, 33, 32, 28, 15, 19,
    • 30, 20, 24, 31, 16, 25, 26
  • 13. Create A Frequency Polygon and Histogram
    • From your frequency distribution of class intervals (done on last slide), place each interval on a graph
    • Then, make a frequency polygon and then a histogram using your answers
  • 14. Cumulative Distributions
    • Also called Ogive curve
    • Gives information about the percentile rank
    • Convert frequency of each class interval into a percentage and add it to previous cumulative percentage (see Table 4.3, p. 72)
    • Graph class intervals with their cumulative percentages (see Figure 4.3, p. 73)
    • Helps to determine percentage on any point in the distribution
  • 15. Normal and Skewed Curves
    • The Normal Curve
      • Follows Natural Laws of the Universe
      • Quincunx (see Fig. 4.4, p. 73):
      • www.stattucino.com/berrie/dsl/Galton.html
    • Rule Number 2:
      • God does not play dice with the universe.” (Einstein)
      • Contrast with Skewed Curves (See Fig. 4.5, p. 74)
  • 16. Measures of Central Tendency
    • Helps to put more meaning to scores
    • Tells you something about the “center” of a series of scores
    • Mean, Median, Mode
    • Compare means, medians, and modes on skewed and normal curves (see page 76, Figure 4.6)
  • 17. Measures of Central Tendency
    • Median: Middle Score
      • odd number of scores—exact middle
      • even number: average of two middle scores.
    • Mode: Most frequent score
    • Median: Add scores and divide by number of scores
    • See Table 4.4, p. 75
  • 18. Measures of Variability
    • Tells you even more about a series of scores
    • Three types:
      • Range: Highest score - Lowest score +1
      • Standard Deviation
      • Interquartile Range
  • 19. Interquartile Range
    • (middle 50% of scores--around median)
    • see Figure 4.7, p. 77
    • Using numbers from previous example:
      • (3/4)N - (1/4)N (where N = number of scores)
      • 2 then, round off and find
      • that specific score
    • See Table 4.5, p. 78
  • 20. Standard Deviation
    • Can apply S.D. to the normal curve (see Fig. 4.9, p. 80)
    • Many human traits approximate the normal curve
    • Finding Standard Deviation (see Table 4.6, p. 80)
    • Find another SD (next two slides)
  • 21. Figuring Out SD
        • X X - M (X - M) 2
        • 12 12-8 4 2 = 16
        • 11 11-8 3 2 = 9
        • 10 10-8 2 2 = 4
        • 10 10-8 2 2 = 4
        • 10 10-8 2 2 = 4
        • 8 8-8 0 2 = 0
        • 7 7-8 1 2 = 1
        • 5 5-8 3 2 = 9
        • 4 4-8 4 2 = 16
        • 3 3-8 5 2 = 25
        • 80 88
  • 22. Figuring Out SD (Cont’d)
    • SD = 88/10 =
    •  8.8 = 2.96
  • 23. Remembering the Person
    • Understanding measures of central tendency and variability helps us understand where a person falls relative to his or her peer group, but….
    • Don’t forget, that how a person FEELS about where he or she falls in his or her peer group is always critical