1. 1 Chapter 4 Statistical Concepts: Making Meaning Out of Scores

2. 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 test (95 or 950?)  Average score of everyone who took the test.  How close a score of 47 is to a score of 95. (If the highest score possible was a 950, and Jeremiah and Elise scored the two lowest scores, there scores might not be that different).  Is higher or lower a better score?

3. 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. 4 Making Raw Scores Meaningful Obtain person’s score and compare that person’s score to a norm or peer group.  Allows individuals to compare themselves to their norm(peer) group.  Allows test takers who took the same test but are in different norm groups to compare their results.  Allows an individual to compare scores on two different tests.

5. 5 Making Scores Meaningful Using a frequency distributions 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. 67

6. 6 Making Scores Meaningful Use a graph to make sense out of scores 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. See Table 4.2, p. 68; then Figures 3.1 and 4.2

7. 7 Making Meaning From Scores Make a frequency distribution: 1 2 4 6 12 16 14 4 7 21 4 3 11 4 10 12 7 9 3 21 3 6 1 3 6 5 10 3

8. 8 Making Meaning From Scores 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

9. 9 Making Meaning From Scores 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.

10. 10 Making Scores Meaningful 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

11. 11 Making Meaning From Scores 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

12. 12 Making Meaning From Scores 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.

13. 13 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 73, Figure 4.5)

14. 14 Measures of Variability Tells you even more about a series of scores Three types: Range: Highest score - Lowest score +1 Standard Deviation Semi-Interquartile Range

15. 15 Standard Deviation The Normal Curve and Standard Deviation Natural Laws of the Universe Quincunx (see Fig. 4.3, p. 70): www.stattucino.com/berrie/dsl/Galton.html Rule Number 2: God does not play dice with the universe.” (Einstein)

16. 16 Standard Deviation Standard Deviation Formula: x 2 x 2 = (X-M) 2 N Can apply S.D. to the normal curve Most human traits approximate the normal curve

17. 17 Figuring Out SD  X X - M (X - M) 5  12 12-8 4 5 = 16  11 11-8 3 5 = 9  10 10-8 2 5 = 4  8 8-8 0 5 = 0  7 7-8 1 5 = 1  5 5-8 3 5 = 9  4 4-8 4 5 = 16  3 3-8 5 5 = 25  80 88

18. 18 Figuring Out SD (Cont’d) SD = 88/10 = 8.8 = 2.96

19. 19 Semi-Interquartile Range (middle 50% of scores--around median) Using numbers from previous example: (3/4)N - (1/4)N 2 8th score - 3rd score = 2 (10 - 5)/2 = 2.5 9 (median) +/- 2.5 = 6.5  11.5

20. 20 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.