Statistical Concepts:

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 persons score and compare that persons
  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
• 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

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
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)
  www.stattucino.com/berrie/dsl/Galton.html
• Rule Number 2
• God does not play dice with the universe.
  (Einstein)

16
Standard Deviation

• Standard Deviation Formula
• x2 x2 (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
• 12 12-8
  45 16
• 11 11-8
  35 9
• 10 10-8
  25 4
• 10 10-8
  25 4
• 10 10-8
  25 4
• 8 8-8
  05 0
• 7 7-8
  15 1
• 5 5-8
  35 9
• 4 4-8
  45 16
• 3 3-8
  55 25
• 80
  88

18
Figuring Out SD (Contd)

• 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 2.5
• 9 (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.
• Dont forget, that how a person FEELS about where
  he or she falls in his or her peer group is
  always critical.