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 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 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 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 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 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 Making Meaning From Scores Make a frequency distribution:

8 Making Meaning From Scores Make a distribution that has class intervals of 3 from the same set of scores:

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 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 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 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 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 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 Standard Deviation The Normal Curve and Standard Deviation Natural Laws of the Universe Quincunx (see Fig. 4.3, p. 70): Rule Number 2: God does not play dice with the universe.” (Einstein)

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 Figuring Out SD  X X - M (X - M) 5  = 16  = 9  = 4  = 0  = 1  = 9  = 16  = 25  80 88

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

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 = (median) +/- 2.5 = 6.5  11.5

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.