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Statistics, Probability, and Decision Making

Statistics, Probability, and Decision Making. Statistics, Probability and Decision Making. Which trial represents the length? Most feel the mean is the best estimate. How Precise is the Estimate?. You decide that the length is 25.43. But look at the measurements.

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Statistics, Probability, and Decision Making

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  1. Statistics, Probability, and Decision Making Statistics, Probability and Decision Making Statistics, Probability and Decision Making

  2. Which trial represents the length? Most feel the mean is the best estimate. Statistics, Probability and Decision Making

  3. How Precise is the Estimate? You decide that the length is 25.43. But look at the measurements. Is 25.50 a misfit? Statistics, Probability and Decision Making Statistics, Probability and Decision Making

  4. What about an unexpected value? • Get rid of it… • No, you need a statistical reason ! • Only if it was a mistake. Statistics, Probability and Decision Making

  5. An outlier: A single observation "far away" from the rest. Is it a mistake? Q: How far away is “far away”? A: It depends on whether the value differs from the rest within a “reasonable” range. Statistics, Probability and Decision Making

  6. Decisions, decisions… Statistics, Probability and Decision Making

  7. Rejecting Data in a Small Data Set Run the “Q-test.” To test 25.50, calculate Q. Q = (The suspect - the value closest to it) Range Q = 0.05 ÷ 0.12 = ≈ 0.42 Statistics, Probability and Decision Making

  8. Compare Qcalculated with Qcritical • If Qcalc > Qcritical, reject. • If Qcalc < Qcritical, keep . Statistics, Probability and Decision Making

  9. From the previous example… Qcalc = 0.42 N = 5, Qcritical = 0.64 • IfQcalc > Qcritical • IfQcalc < Qcritical Statistics, Probability and Decision Making Statistics, Probability and Decision Making

  10. Rejecting data in a large set • Find the confidence interval µ ± 3 σ • Does measurement falls outside the confidence interval? Use a Normal Distribution 95% of the data falls within two standard deviations of the mean. Statistics, Probability and Decision Making

  11. Q: Why worry about them? A: Values may not be properly distributed. Q: Where do they come from? A: Possible sources: Recording and measurement errors Incorrect distribution Unknown data structure Outliers… Note: Outliers are in red Statistics, Probability and Decision Making

  12. Calculate the mean and the standard deviation. Find the ±3 standard deviation range for imposing limits on the data. Identify outliers (greater ± 3 standard deviations). Get rid of them!!! Managing Outliers If the data is a normal distribution: Statistics, Probability and Decision Making

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