ch. 10: summarizing the data

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Ch. 10: Summarizing the Data

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Ch. 10: Summarizing the Data. 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. Frequency Distribution Example. - PowerPoint PPT Presentation

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Page 1: Ch. 10: Summarizing the Data

Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall

Ch. 10: Summarizing the Data

Page 2: 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.

Page 3: Ch. 10: Summarizing the Data

Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall

Frequency Distribution Example

Page 4: Ch. 10: Summarizing the Data

Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall

Bar Graphs Example

Page 5: Ch. 10: Summarizing the Data

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

Page 6: Ch. 10: Summarizing the Data

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

Page 7: Ch. 10: Summarizing the Data

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

Page 8: Ch. 10: Summarizing the Data

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

Page 9: Ch. 10: Summarizing the Data

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

Page 10: Ch. 10: Summarizing the Data

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)

Page 11: Ch. 10: Summarizing the Data

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

Page 12: Ch. 10: Summarizing the Data

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

Page 13: Ch. 10: Summarizing the Data

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

Page 14: Ch. 10: Summarizing the Data

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

Page 15: Ch. 10: Summarizing the Data

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

Page 16: Ch. 10: Summarizing the Data

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”

Page 17: Ch. 10: Summarizing the Data

Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall

Confidence Interval for a Mean

n

St )05(.LimitLower

n

St )05(.LimitUpper

Page 18: Ch. 10: Summarizing the Data

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

Page 19: Ch. 10: Summarizing the Data

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

Page 20: Ch. 10: Summarizing the Data

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

Page 21: Ch. 10: Summarizing the Data

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