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Paired Data

Paired Data. Statistical control of variability. Dr. Tom’s Elixir to Improve Performance(of whatever). Select victims (oops, subjects) Collect baseline data on IQ Give Snake Oil supplement (subject to rigorous QC and QA standards) After six weeks retest subjects

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Paired Data

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  1. Paired Data Statistical control of variability

  2. Dr. Tom’s Elixir to Improve Performance(of whatever) • Select victims (oops, subjects) • Collect baseline data on IQ • Give Snake Oil supplement (subject to rigorous QC and QA standards) • After six weeks retest subjects • Test for “significant” improvement in IQ

  3. Raw Data

  4. Graph the data first!

  5. Is there an improvement? • A lot of “noise” is in the data • Pre vs. Post seems to show a slight improvement • All subjects showed some degree of improvement • Need significant p-value for Marketing!

  6. Some dependency appears in data due to repeated measurements on each subject

  7. What would a two-sample t-test show? • A two sample t-test gives a p-value of .8458 • Therefore this difference is likely due to chance  • But everyone improved!! • Call a Statistician!

  8. Statistical consultant notes: • The design was correct • The analysis did not take into account that the data was paired • One should analyze the differences instead of individual values • We take all major credit cards

  9. New improved analysis:

  10. Practical vs. Statistical Significance • A study can always be designed to pick up “small” differences. • Practical Significance is typically evaluated by looking at the ES or Effect Size. • The ES is the Mean Improvement divided by the Standard Deviation (of the population, not differences). • If the Standard Deviation of a typical IQ instrument is about 10, then the ES that was observed is about .0889, which would be considered very small in the Psychometric literature.

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