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So, if there is one 'master' formula to pay attention to and to 'own', it is the one for the variance of a linear combination of random variables. The latter is central, not just to simple contrasts involving just 2 sample means or proportions, but also in the much wider world of regression, since the variance (sampling variability) of any regression slope can be viewed as the variance of a linear combination of random 'errors', or random deviations, or random variables. It gives the laws governing the variance of a sum of 2, or (especially) \(n\) random variables - and even more importantly - the laws governing the variance of a difference of two random variables. This central chapter addresses a fundamental concept, namely the variance of a random variable. 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).
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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.0.5 Let's switch to "y-bar", and drop "x-bar".