![]() ![]() Moreover we start with the full probability of 1 at the single entry point on the extreme left, so we need at the right hand side to account for all of this (i.e., the same ‘total’) probability. Trees show that - no matter whether the events are independent or dependent - the probability of a particular sequence is always a fraction of a fraction of a fraction. Tip: try to order letters so it is \(A\rightarrow B\), rather than \(B\rightarrow A.\) Probability trees make it easy to see the direction in which one is preceeding, or looking, where simply (and often arbitrarily chosen) algebraic symbols like A and B can not trees make it easier to distinguish 'forward' from 'reverse' probabilities. It is surprising how few textbooks use 'trees' (such as shown above) to explain conditional probabilities. Canada will use $US before the year 2010ġ1.4 Conditional probabilities, and (in)dependence."How Medical Professionals Evaluate Expressions of Probability" NEJM 315: 740-744, 1986 Kong A, Barnett O, Mosteller F, and Youtz C.50 year old with ve haemoccult test has colon ca.To convert a LOGIT back to an odds, ODDS = anti-log(LOGIT) = exp(LOGIT), and to convert an odds back to a probability, P = ODDS/(1 ODDS). The probit scale transforms P into a Z score: thus P = 0.025 becomes Z = -1.96, and P = 0.975 becomes Z = 1.96 to reverse direction, if Z = qnorm(P), then P = pnorm(Z). Gauss' Law of Errorsįigure 11.2: The probability scale, along with 3 equivalent scales derived from it. Elementary Statistical Principles if necessary, by breaking complex outcomes into simpler onesĪdvanced Statistical Theory, e.g.Intuition, Informal calculation, consensus Empirically Experience (actuarial.Measure how far data are from some hypothesized model Communicate one's (un)certainty about the value of a parameter.In practice, most of our probability values come from some pDistribution function, and we will encounter some of the 'off the shelf' ones in the next chapter.īe warned against calculating the wrong probability.īeware of intuition, especially with 'after the fact' calculations for non-standard situations. See the basic rules for calculating probabilities in a few examples, but appreciate that calculating non-standard probabilities should be left to experts. Understand the meanings, uses and ways of arriving at, numerical values for probabilities.Īppreciate the context for a probability, and that context (the conditioning, the information relied on) matters. 18.3 Other Exercises (under construction).18.2.10 Correcting length-biased sampling.18.2.6 Height differences of random M-F pairs.18.2.4 Variable-length (parallel) parking spaces.17.3 Other Exercises (under construction).16.5.2 Statistical Concepts and Principles.15.7.2 Statistical Concepts and Principles.15.4 The p and q functions: an orientation.14.2 Powers, Logarithms and Anti–logarithms.13.3.10 weights of offspring (pups/twins).13.3.8 CI for proportion when observe 0/n or n/n. ![]() 13.3.6 It's the 3rd week of the course: it must be Binomial.13.3.5 Can one influence the sex of a baby?.13.3.4 Binomial or Opportunistic? (Capitalization on chance.13.3.3 Automated Chemistries (from Ingelfinger et al).12.8 Linear combinations of RVs (regression slopes).12.6 Variance and SD of a FUNCTION of a random variable.12.5.4 Example of Variance-calculation using one-pass formula.12.5.2 Some (good) reasons for using variance, which averages the squares of the deviations from the mean.12.5 Variance (and thus, SD) of a random variable. ![]() 12.4 Expected value of a FUNCTION of a random variable.12.3 Expectation (mean) of a Random Variable.11.5 Changing the Conditioning: the direction matters.11.4 Conditional probabilities, and (in)dependence.11.3 Basic rules for probability calculations.5.2 Fitting these to data / Estimating them from data.3.2.2 Ingredients and methods of procedure in a statistical test.3.2.1 (Frequentist) Test of a Null Hypothesis.3.1.3 Examples: parameter is a personal number or population mean.3.1.2 Example: parameter is a proportion.3.1.1 Example: parameter is 2-valued: yes or no.2.2.2 Parameter relations in symbols, and with the help of an index-category indicator.2.2.1 Parameter relations in numbers and words. ![]()
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