Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Ch. 10: Summarizing the Data
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Criteria for Good Visual Displays Clarity
Data is represented in a way closely integrated with their numerical meaning.
Precision Data is not exaggerated.
Efficiency Data is presented in a reasonably
compact space.
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Frequency Distribution Example
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Bar Graphs Example
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Stem-and-Leaf Chart
Stems Leaves
8 2 7
7 0 4 9
6 2 6 6 9
5 1 2 6
4 1 7
3 7
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Back-to-Back Stem-and-Leaf Chart
Depression Stems Hypomania
2 5 8
1 6
5 5 4 3 1 1 0 0 1 2 4
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Measures of Central Tendency: Determining The Median
Arrange scores in order Determine the position of the
midmost score: (N+1)*.50 Count up (or down) the number of
scores to reach the midmost position
The median is the score in this (N+1)*.50 position
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Measures of Central Tendency: The Arithmetic Mean
The balancing point in the distribution
Sum of the scores divided by the number of scores, or
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Measures of Central Tendency: The Mode
The most frequently occurring score
Problem: May not be one unique mode
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Symmetry and Asymmetry
Symmetrical (b) Asymmetrical or Skewed
Positively Skewed (a) Negatively Skewed (c)
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Comparing the Measures of Central Tendency
If symmetrical: M = Mdn = Mo If negatively skewed: M < Mdn
Mo If positively skewed: M > Mdn
Mo
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Measures of Spread:Types of Ranges
Crude Range: High score minus Low score
Extended Range: (High score plus ½ unit) minus (Low score plus ½ unit)
Interquartile Range: Range of midmost 50% of scores
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Measures of Spread: Variance and Standard Deviation
Variance: Mean of the squared deviations of the scores from its mean
2
2
Standard Deviation: Square root of the variance
2
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Summary Data for Computing the Variance and Standard Deviation
Raw scores X - M (X – M)2
2 -3 9
4 -1 1
4 -1 1
5 0 0
7 2 4
8 3 9
X = 30 (X – M) = 0 (X – M)2 = 24
M = 5
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Descriptive vs. Inferential Formulas Use descriptive formula when:
One is describing a complete population of scores or events
Symbolized with Greek letters Use inferential formula when:
Want to generalize from a sample of known scores to a population of unknown scores
Symbolized with Roman letters
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Variance: Descriptive vs. Inferential Formulas
2
2
Descriptive FormulaDescriptive Formula
1
2
2
S
Inferential FormulaInferential Formula
Called the “unbiased estimator of the
population value”
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Confidence Interval for a Mean
n
St )05(.LimitLower
n
St )05(.LimitUpper
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Values of x (for df =5) for Five Different Confidence Intervals
CI x t(x) (for df = 5)
99.9% .001 6.87
99% .01 4.03
95% .05 2.57
90% .10 2.02
80% .20 1.48
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
The Normal Distribution
Standard Normal Distribution: Mean is set equal to 0, Standard deviation is set equal to 1
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Standard Scores or z-scores Raw score is transformed to a standard
score corresponding to a location on the abscissa (x-axis) of a standard normal curve
Allows for comparison of scores from different data sets.
scorez
Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall
Raw Scores (X) and Standard Scores (z) on Two Exams
Student ID and gender
Exam 1 Exam 2 Average of z1 and
z2 scoresX1 score z1 score X2 score z2 score
1 (M) 42 +1.78 90 +1.21 +1.50
2 (M) 9 -1.04 40 -1.65 -1.34
3 (F) 28 +0.58 92 +1.33 +0.96
4 (M) 11 -0.87 50 -1.08 -0.98
5 (M) 8 -1.13 49 -1.13 -1.13
6 (F) 15 -0.53 63 -0.33 -0.43
7 (M) 14 -0.62 68 -0.05 -0.34
8 (F) 25 +0.33 75 +0.35 +0.34
9 (F) 40 +1.61 89 +1.16 +1.38
10 (F) 20 -0.10 72 +0.18 +0.04
Sum () 212 0 688 0 0
Mean (M) 21.2 0 68.8 0 0
SD () 11.69 1.0 17.47 1.0 0.98