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Distribution and Outliers

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Distribution and Outliers

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  1. Distribution and Outliers

  2. Screening (Significant Effects)

  3. Hadlum vs Hadlum A univariate example that illustrates deviation from a normal pattern.

  4. Normal duration Percentage (n=13634) Duration of Pregnancy Bannet (1978) Appl. Statist. 27, 242-250

  5. Comparison of Hadlum Jr. to normal pattern Normal duration Percentage (n=13634) Hadlum Jr.

  6. Deviation = observed value - predicted value residual measurement Model  ^ y y Model validation

  7. Normally distributed population P(yi)

  8. Normal Population - Cumulative plots Traditional Graphical paper Normal distribution paper

  9. Normal plot 1) Sort the observations in increasing order 2) Let each observation present a percent interval that equals of the normal distribution If the observations are normally distributed, they plot like a straight line in the normal plot! Deviation from straight line implies outlying observations or non-normal distribution

  10. Scull capacity of the Maoris

  11. Sculls from a cemetery maximum Karl Pearson (1931) Tables for Statisticans and Biometricans, Biometric Lab., London

  12. Is the largest scull from a Maori? Hypothesis: The Maoris have less scull capacity than the whites - the largest scull is a contaminant shipwrecked sailor or missionary?

  13. Probability plot Scull Capacity

  14. What to do with the damned point destroying the curve?

  15. The easy way: Erase it!

  16. Example P. Garrigues R. De Sury M. L. Angelin J. Bellocq J. L. Oudin M. Ewald Geochemica et Cosmochimica Acta, 52, (1988) 375-384

  17. Data ? ?

  18. Robust regression? Two outliers Useful tool to avoid thinking? Sloppy data analyst can find relief in robust regression

  19. Result of “pooled” regression r=0.995

  20. Observation r=0.865 Two phenomena influencing the ratio (predictor) No prediction possible!

  21. Parallel displacement - perfect result for the one who wants to be “straight-lined”

  22. Let the computer restore harmony and beauty