BIOS601 Resources: Models/ Inference / Planning [proportion]

ONE PROPORTION

(jh) Lecture Notes

• Proportion

(jh) Binomial Distribution

• How shapes varies with n and p) ( excel )
• Random 0's and 1's: Excel
• Binomial Probabilities: Excel

Computing

• CI for a Proportion (Excel spreadsheet, based on exact Binomial model)
• 95%CI for a Proportion (java applet, based on exact Binomial model)
• Illustration of Power and sample size for test of single proportion (Excel)
• Sample Size requirements for inference re: a single proportion (Excel)
• Bayesian Inference for a Proportion (Excel)
• Links to software for sample size/precision/statistical power
  PS: Power and Sample Size     Epi Info

Tables Graphs Figures Historical/Biographical Material etc.

• Which is more probable:
  ... at least one 6 in 4 dice?
  ... at least one 12 in 24 pairs of dice?
  
  R Code
  
  Links to material on Chevalier de Meré and his paradox: 1     2     3     4     5
  
  
• 95%CI for a Proportion (Table, based on exact Binomial model)
• Wanted: Boys (newspaper article)
• George Gallup, Twentieth-Century Pioneer bio Gallup Ogranization Website
• George Gallup and the Scientific Opinion Poll
• Social Science in America's Bedroom Alfred Kinsey Measures Sexual Behavior

Book Chapters etc.

• Chapter 4.4 (Inferences from Proportions) from Statistical Methods for Medical Research
  Armitage, Berry and Matthews (4th edition). Section 4.4
• Mid-P values [from Armitage and Berry]
• Bayesian Inference for a Proportion (e.g. from Bayesian statistics textbook)

Articles

• Pearson's classic 1900 paper introducing his Goodness-of-Fit Chi-Squared Statistic
  
  The paper, published in Philosophical Magazine Series 5,50:302,157 - 175, was entitled
  "On the criterion that a given system of deviations from the probable
  in the case of a correlated system of variables is such that it can be
  reasonably supposed to hove arisen from random sampling."
   
  Getting the degrees of freedom right ...
  
      Greenwood and Yule, 1915.
      They "directed attention to the discrepancy between the results given by the ChiSq
      method, as ordinarily applied to the fourfold table for estimating the probability
      that any given divergence from independence might have arisen by random sampling,
      and the results given by the more elementary test afforded by comparing
      p1 - p2 with its probable error."
  
      Yule 1922:
      On the Application of the ChiSq Method to Association and Contingency Tables, with Experimental Illustrations
  
      R A Fisher:
      On the Interpretation of ChiSq from Contingency Tables, and the Calculation of P.
  
      S Stigler
      Karl Pearson's Theoretical Errors and the Advances They Inspired
  
      The chi-square controversy: what if Pearson had R?
  
  
• Wilson. Gaussian-based, but asymmetric, CI for proportion. JASA 1927
• Mathematical Distributions used in Common Tests, RA Fisher, 1935
• Course 607  [see 1-Phenylalanine mustard (L-PAM) in management of primary breast cancer]
• The only formula a clinician-trialist is ever likely to need (or understand!)
• If Nothing Goes Wrong, Is Everything All Right? Interpreting Zero Numerators
• A defence of the small clinical trial
• A Close Look at Therapeutic Touch: JAMA article

Data / Miscellaneous

• M:F Births, Canada and Provinces 1931-90: ( excel )
• M:F Births, Canada and Provinces 1931-90: ( .csv )
• M:F Births, Canada and Provinces 1931-90: ( .R code )
   
  
• The sampling makes Independent observations: Time Spent Inside

TWO (OR MORE) PROPORTIONS

(jh) Lecture Notes

• 2 Proportions
• Analysis of Proportions via Chi-Squared tests

Computing

• Fisher's Exact Test (Excel spreadsheet, based on Hypergeometric model)