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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Unit 1: Background to Inferential Statistics
Lesson 5: Measures of Distribution
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Measures of DistributionNormal Distribution
Characteristics:•Mean = Median = Mode•Skewness = 0•Kurtosis = 0
34.13% 34.13%
13.59%13.59%
2.14%2.14%
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Skewness“Distributional Shape and the Blind Date”
n
ZSkewness i
3Sum of all of the Z-scores cubed
Number of people in the study
Skewness = 0, distribution is symmetrical < 0, negatively skewed > 0, positively skewed
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Skewness
Positively Skewed
Negatively Skewed
No Skewness
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Many Forms of Skewness
X
ii SD
XXZ
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Kurtosis and the Blind DateHeight Small Medium LargeMen
5’9” 142-151 148-160 155-1765’10” 144-154 151-163 158-1805’11” 146-157 154-166 161-1846’ 149-160 157-170 164-1886’1” 152-164 160-174 168-1926’2” 155-168 164-178 172-1976’3” 158-172 167-182 176-202Women
5’4” 114-127 124-138 134-1515’5” 117-130 127-141 137-1555’6” 120-133 130-144 140-1595’7” 123-136 133-147 143-1635’8” 126-139 136-150 146-1675’9” 129-142 139-153 149-1705’10” 132-145 142-156 152-173
Kurtosis is the ratio of height to width relative to the normal curve
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Kurtosis
34
n
ZKurtosis i
Sum of all of the Z-scores to the fourth power
Number of people in the study
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Kurtosis
Kurtosis = 0
Kurtosis > 0, Leptokurtic
Kurtosis < 0, Platykurtic
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Infinite Number of Normal Distributions
-4.24276 -0.24276 3.75724 7.75724 11.7572415.7572419.7572423.75724
x
0.00
0.05
0.10
0.15
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Unit 1: Background to Inferential Statistics
Lesson 5: Measures of Distribution
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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