Working with Probability
Chapter 3 was a coherent presentation of material on descriptive statistics and probability distributions, which are viewed as theoretical populations. Chapter 4 follows with seven sections that are grouped into three themes. The first four sections treat inferential statistics, beginning with an introductory section that introduces the central question of whether a test population is the same as or different from a general population. This is followed by a section that presents the Cramer–von Mises test for consistency of a data set with a normal distribution. This test serves as a convenient analytical tool for observing the convergence as n → ∞ of distributions of means of samples of size n to a normal distribution, regardless of the underlying distribution from which the samples are drawn. Section 4.3 presents the central limit theorem, which is then used in Section 4.4 to address statistical inference. Section 4.5 serves as a brief introduction to maximum likelihood, and the chapter closes with two sections on conditional probability. Many of the problems use real data sets that were introduced in Chapterer 3.
KeywordsConditional Probability Likelihood Function Success Probability Sequence Rule Bernoulli Trial
- 1.Durbin J, M Knott, and CC Taylor. Components of Cramer-von Mises statistics. J. Royal Stat. Soc., B, 37: 216–237 (1975)Google Scholar
- 2.Hand DJ, F Daly, K McConway, D Lunn, and E Ostrowski. Handbook of Small Data Sets. CRC Press, Boca Raton, FL (1993)Google Scholar
- 3.Labby Z. Weldon’s dice, automated. Chance, 22: 6–13 (2009). Available online at http://galton.uchicago.edu/about/docs/labby09dice.pdf. Google Scholar
- 4.Masjuan J, JC Alvarez-Cemeño, N Garcia-Barragán, M Diaz-Sánchez, M Espiño, MC Sádaba, P González-Porqué, J Martinez San Millán, LM Villar. Clinically isolated syndromes: a new oligoclonal band test accurately predicts conversion to MS. Neurology, 66: 576–578 (2006)Google Scholar
- 5.National Park Service. The Bean Counters: Mark-Recapture. Available on line at http://www.nps.gov/akso/parkwise/teachers/nature/wear_hoofinit/activities/MarkRecapture.htm.CitedJan2013.
- 9.Sprott DA. Statistical Inference in Science Springer (2000)Google Scholar
- 10.Stephens MA. Tests based on EDF statistics. In Goodness-of-Fit Techniques, eds. RB D’Agostino and MA Stephens. Marcel Dekker (1986)Google Scholar
- 11.Thode Jr HC. Testing for Normality. Marcel Dekker (2002)Google Scholar
- 12.Tietjen GL. The analysis and detection of outliers. In Goodness-of-Fit Techniques, eds. RB D’Agostino and MA Stephens. Marcel Dekker (1986)Google Scholar