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Unit 5: Distributional ShapeLesson 2:Kurtosis : 

Unit 5: Distributional ShapeLesson 2:Kurtosis EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Many “odd-shaped” distributions can be symmetrical. : 

Many “odd-shaped” distributions can be symmetrical. So, we need another statistic for shape! Dr. Robin K. Henson © 2002 University of North Texas Next Slide

What is a “normal” body shape? : 

What is a “normal” body shape? Dr.’s Weight Chart Dr. Robin K. Henson © 2002 University of North Texas Frame Size Next Slide

Normality(Coefficient of Kurtosis) : 

Normality(Coefficient of Kurtosis) Does the distribution have an appropriate height relative to its width? Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Normal – appropriate height to width : 

Normal – appropriate height to width Leptokurtic – tall, thin Platykurtic – short, wide Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Coefficient of Kurtosis : 

Coefficient of Kurtosis Leptokurtic Platykurtic Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Slide 7: 

Z -1.16 -.39 .39 1.16 1.81 .02 .02 1.81 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Infinitely many different normal distributions. : 

Infinitely many different normal distributions. Dr. Robin K. Henson © 2002 University of North Texas Next Slide

What’s the kurtosis? : 

What’s the kurtosis? 1, 2, 3, 4, 5 Negative 1, 2, 2, 2, 2, 2, 3 Positive 3, 3, 3, 3, 3 Can’t Compute! Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Slide 10: 

Dr. Robin K. Henson © 2002 University of North Texas Q: If a distribution has a coefficient of skewness = 0, which of the following must be true? a. The distribution is normal (K=0). b. The distribution is leptokurtic (K>0). c. The distribution is platykurtic (K<0). d. The distribution is skewed. e. None of the above. Go to next slide for answer. Click mouse to continue

Answer : 

Answer a. No, the coefficient of skewness only tells you the distribution is symmetrical. We noted earlier that there are many different symmetrical distributions that are not normal, such as a symmetrical but bimodal distribution. A normal distribution must be symmetrical, but that is a necessary but insufficient condition for the distribution to be normal. b. No, given skewness, we can tell nothing about kurtosis. See (a) discussion. c. No, given skewness, we can tell nothing about kurtosis. See (a) discussion. d. No, a skewness of 0 indicates the distribution is perfectly symmetrical. e. Yes, because none of the above are true. See (a) discussion.

Slide 12: 

Dr. Robin K. Henson © 2002 University of North Texas Next Slide

Unit 5: Distributional ShapeLesson 2:Kurtosis : 

Unit 5: Distributional ShapeLesson 2:Kurtosis EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 End

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