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Probability can be hard –from goats to DNA

       2.3.1 The Monty Hall Problem

       2.3.2 Tip: make the numbers extreme

       2.3.3 DNA evidence

       3 Properties of randomness

       3.1 Bias and variability

       3.1.1 Bias

       3.1.2 Bias vs. variability

       3.2 Independence and non-independence

       3.2.1 Independence of measurements

       3.2.2 Independence of factor effects

       3.2.3 Independence of sample composition

       3.3 Play!

       3.3.1 Virtual two-horse races

       3.3.2 More (virtual) coin tossing

       3.3.3 Fair and biased coins

       3.3.4 No longer independent

       4 Characterising the random through probability distributions

       4.1 Types of probability distribution

       4.1.1 Continuous or discrete?

       4.1.2 Finite or unbounded

       4.1.3 UK income distribution –a long tail

       4.1.4 One tail or two?

       4.2 Normal or not?

       4.2.1 Approximations

       4.2.2 The central limit theorem –(nearly) everything is Normal

       4.2.3 Non-Normal –what can go wrong?

       4.2.4 Power law distributions

       4.2.5 Parametric and Nonparametric

       PART II Doing It –If not p then What

       5 Probing the unknown

       5.1 Recall the job of statistics

       5.2 Conditional probability

       5.3 Likelihood

       5.4 Statistical reasoning

       5.5 Types of statistics

       6 Traditional statistics

       6.1 Hypothesis testing

       6.1.1 The significance level –5 percent and all that

       6.1.2 But what does it mean?

       6.1.3 Non-significant results

       6.1.4 In summary—significance

       6.2 Confidence intervals

       6.2.1 The interval

       6.2.2 Important as well as significant?

       6.2.3 Don’t forget

       7 Bayesian methods

       7.1 Detecting the Martian invasion

       7.2 Quantifying prior belief

       7.3 Bayes for intelligent interfaces

       7.3.1 Bayes as a statistical method

       7.4 How do you get the prior?

       7.5 Handling multiple evidence

       7.6 Internecine warfare

       8 Common issues

       8.1 Cherry picking

       8.1.1 Multiple tests

       8.1.2 Multiple statistics

       8.1.3 Outliers

       8.1.4 Post-hoc hypothesis

       8.1.5 The file drawer effect

       8.2 Inter-related factors

       8.2.1 Non-independently controllable factors

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