Social Science Reasoning Using Statistics

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Social Science Reasoning Using Statistics

• Psychology 138
• Spring 2004

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Homework help

• Getting the datafile from your textbook CD-ROM

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Rolling the dice

• Lets collect set of data
• Ill pass out some pairs of dice
• Collect n36 data points

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Rolling the dice

• Distribution
• The distribution of a variable is a summary of
  all the different values of a variable
• both type (each value) and token (each instance)
• The set of all of the outcomes of rolling the
  dice
• Un-organized, the overall pattern and properties
  of the distribution are difficult to see
• Descriptive statistics
• Statistical tools/procedures to help organize,
  summarize, and simplify large sets of data
  (distributions)

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Distributions

• Properties of a distribution
• Shape
• Symmetric v. asymmetric (skew)
• Unimodal v. multimodal
• Center
• Where most of the data in the distribution are
• Spread (variability)
• How similar/dissimilar are the scores in the
  distribution?

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Distributions

• A picture of the distribution is usually helpful
• Gives a good sense of the properties of the
  distribution
• Many different ways to display distribution
• Table
• Frequency distribution table
• Stem and leaf plot
• Graphs

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Frequency distribution
p f/N
Ntotal
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Cumulative percent
What got this score or worse?
10
9
Cumulative percent
What got this score or worse?
25
10
10
Cumulative percent
What got this score or worse?
35
25
10
11
Cumulative percent
What got this score or worse?
70
35
25
10
12
Cumulative percent
What got this score or worse?
90
70
35
25
10
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Cumulative percent
What got this score or worse?
100
90
70
35
25
10
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Frequency distribution
Whats the most frequent score?
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Frequency distribution
Whats the most frequent score?
Where do most of the scores lie?
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Frequency distribution
Whats the most frequent score?
Where do most of the scores lie?
What was the range of scores?
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Stem and Leaf Plots

• Distribution of exam scores (section 01)
• 67, 90, 92, 58, 76, 75, 84, 92, 78, 93, 89, 74,
  62, 98, 75, 73, 75, 89, 89, 76, 65, 49

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2
0
2
8
4
9
9
9
5
6
4
8
5
3
5
6
7
2
5
8
9
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Stem and Leaf Plots

• Distribution of exam scores (section 01)
• 67, 90, 92, 58, 76, 75, 84, 92, 78, 93, 89, 74,
  62, 98, 75, 73, 75, 89, 89, 76, 65, 49

• Distribution of exam scores (section 03)
• 72, 90, 83, 58, 66, 65, 84, 95, 72, 93, 89, 70,
  42, 100, 71, 73, 75, 62, 62, 74, 65

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Graphing distributions

• Graphs types
• Continuous variable
• histogram, line graph (frequency polygons)
• Categorical (discrete) variable
• pie chart, bar chart

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Graphs for continuous variables

• Histogram

• Line graph

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Graphs for categorical variables

• Bar chart

• Pie chart

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Descriptive statistics

• In addition to pictures of the distribution,
  numerical summaries are also presented.
• Numeric Descriptive Statistics
• Shape
• Skew (symmetry) Kurtosis (flatness)
• Number of modes
• Measures of Center
• Next lecture
• Measures of Variability (Spread)
• Lecture in a week

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Shape

• Symmetric

• Asymmetric

Positive Skew
Negative Skew
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Shape

• Unimodal (one mode)

• Multimodal
• Bimodal examples