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Screening for Outliers: Univariate Analysis of Hadlum vs. Normal Patterns in Pregnancy Duration

This study examines the deviations observed in Hadlum Jr. compared to normal patterns of pregnancy duration, utilizing a dataset of 13,634 samples. By applying univariate analysis and cumulative probability plots, we illustrate how deviations from a normal distribution can indicate potential outliers or non-normal distributions. We also interpret the findings within the context of skull capacity among the Maoris, exploring hypotheses regarding population differences and the influence of outliers on statistical predictions. This comparative analysis emphasizes the necessity of robust regression techniques to handle deviations effectively.

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Screening for Outliers: Univariate Analysis of Hadlum vs. Normal Patterns in Pregnancy Duration

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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

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