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Skew or kurtosis
The document discusses skew and kurtosis, which are statistical measures that help describe the shape of a distribution. Skew measures the symmetry of a distribution and indicates if the mean is pulled towards higher or lower values. Kurtosis measures the "peakedness" or "flatness" of a distribution compared to a normal distribution. Both skew and kurtosis provide additional information about a distribution beyond measures of central tendency and dispersion.
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Skew or kurtosis
- 1. Skew and Kurtosis Skewand Kurtosis
- 2. We have illustratedthe central tendency of a distribution and the dispersion of scores within a distribution. There are two other categories of statistics that help tell the story of a distribution: • Skew • Kurtosis Skew and Kurtosis
- 3. Skew Distributions (aggregations ofobservations) can be spread evenly around both sides of the central tendency, like so: Skew and Kurtosis
- 4. Skew Distributions (aggregations ofobservations) can be spread evenly around both sides of the central tendency, like so: 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Skew and Kurtosis
- 5. Skew Such distributions areconsidered symmetrical with no skew. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Skew and Kurtosis
- 6. Skew In symmetrical distributionsthe mean and the median are identical. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 5 5 Mean = Median = Skew and Kurtosis
- 7. Skew As scores areweighted and distribute unevenly around the median, the mean is “pulled” toward the extreme outlier and it diverges away from the median. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 5 5 Mean = Median = Skew and Kurtosis
- 8. Skew As scores areweighted and distribute unevenly around the median, the mean is “pulled” toward the extreme outlier and it diverges away from the median. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 7 5 Mean = Median = 2120 Skew and Kurtosis
- 9. Skew When the outlyingscores are on the higher end of the scale the distribution becomes positively skewed. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 2120 + Skew and Kurtosis
- 10. Skew When the outlyingscores are on the lower end of the scale the distribution becomes negatively skewed. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 2120 _ Skew and Kurtosis
- 11. Skew Review Skew andKurtosis
- 12. Skew Review Mean =3 Median = 5 Negatively Skewed Distribution Mostly higher scores Skew and Kurtosis
- 13. Skew Review Mean =5 Median = 5 Mean = 3 Median = 5 Normal Distribution Negatively Skewed Distribution Mostly higher scores Scores Evenly Distributed Skew and Kurtosis
- 14. Skew Review Mean =5 Median = 5 Mean = 7 Median = 5 Mean = 3 Median = 5 Normal Distribution Positively Skewed Distribution Negatively Skewed Distribution Mostly higher scores Scores Evenly Distributed Mostly lower scores Skew and Kurtosis
- 15. Skew Review A simpleway to screen for the direction of the skew is to subtract the median from the mean. Mean = 5 Median = 5 Mean = 7 Median = 5 Mean = 3 Median = 5 Normal Distribution Positively Skewed Distribution Negatively Skewed Distribution Mostly higher scores Scores Evenly Distributed Mostly lower scores Skew and Kurtosis
- 16. Skew Review If mean– median results in a positive number then the skew is positive. Mean = 5 Median = 5 Mean = 7 Median = 5 Mean = 3 Median = 5 Positively Skewed Distribution Negatively Skewed Distribution Mostly higher scores Scores Evenly Distributed Mostly lower scores = +2 Normal Distribution Skew and Kurtosis
- 17. Skew Review If mean– median results in a negative number then the skew is negative. Mean = 5 Median = 5 Mean = 7 Median = 5 Mean = 3 Median = 5 Positively Skewed Distribution Negatively Skewed Distribution Mostly higher scores Scores Evenly Distributed Mostly lower scores = -2 Normal Distribution Skew and Kurtosis
- 18. Skew Review If mean– median results in zero then the skew is zero. Mean = 5 Median = 5 Mean = 7 Median = 5 Mean = 3 Median = 5 Positively Skewed Distribution Negatively Skewed Distribution Mostly higher scores Mostly lower scores = 0 Normal Distribution Scores Evenly Distributed Skew and Kurtosis
- 19. Skew and theMean In practice almost no distributions are perfectly symmetrical. Most are skewed to some degree. At some point they become so extremely skewed that we have to make adjustments to the scales or use alternative inferential techniques in our analyses. Skew and Kurtosis
- 20. Kurtosis Kurtosis represents theattribute of flatness Scores are fairly evenly spread out. Skew and Kurtosis
- 21. Kurtosis Kurtosis represents theattribute of flatness Or peakedness of a distribution Scores are fairly evenly spread out. Scores cluster around a particular point Skew and Kurtosis
- 22. Kurtosis Distributions with thesame range of scores and central tendency may nonetheless be shaped differently. Skew and Kurtosis
- 23. Kurtosis Distributions with thesame range of scores and central tendency may nonetheless be shaped differently. Skew and Kurtosis
- 24. Kurtosis Distributions with thesame range of scores and central tendency may nonetheless be shaped differently. Skew and Kurtosis
- 25. Kurtosis Distributions with thesame range of scores and central tendency may nonetheless be shaped differently. 1 9 1 9 Mean = 5 Median = 5 Mode = 5 Mean = 5 Median = 5 Mode = 5 Skew and Kurtosis
- 26. Kurtosis Distributions with thesame range of scores and central tendency may nonetheless be shaped differently. 1 9 1 9 Same Range Mean = 5 Median = 5 Mode = 5 Mean = 5 Median = 5 Mode = 5 Skew and Kurtosis
- 27. Kurtosis Distributions with thesame range of scores and central tendency may nonetheless be shaped differently. 1 9 1 9 Same Mean and Median and Mode Mean = 5 Median = 5 Mode = 5 Mean = 5 Median = 5 Mode = 5 Skew and Kurtosis
- 28. Is your questiondealing with SKEW? or KURTOSIS? Skew and Kurtosis