Chapter 4: Characterising randomness through probability distributions

Contents

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?
4.3  Power law distributions
4.4  Parametric and non-parametric
4.4.1  Transforming data
4.4.2  Contingency table
4.4.3  Order statistics

Glossary items referenced in this chapter

ANOVA (Analysis of Variance), applied mathematics, approximate distribution, approximately Normal, arithmetical data, asymmetric distribution, bias, bimodal distribution, binary data, Binomial distribution, bounded below, bounded data, categorical data, Central Limit Theorem, chi squared, citation data, coin tossing, contingency table, continuous data, continuous distribution, count data, discrete data, empirical distribution, error rate, fair coin, false negative, feedback effects, finite data, finite variance, income distribution, independence, independence condition, Kruskal-Wallis test, Likert scale, linear regression, linearity condition, Log-Normal distribution, long-tail distribution, mathematics, mean (μ), negative binomial, network data, non-independence, nonlinearity, nonparametric statistics, Normal approximation, Normal distribution, one-tailed test, order statistics, ordinal data, parametric statistics, Pearson correlation coefficient, Poisson distribution, positive feedback, power-law distribution, probability distribution, quartile, residuals, sample size, scale free distribution, social network data, Spearman's rank correlation coefficient, standard deviation (s.d., σ), statistical analysis, statistical power, Student's t-test, survey data, tail, tail heavy, task completion time, theoretical distribution, threshold effect, transforming data, two-tailed test, UK income distribution, unbounded data, unbounded tail, usability evaluation, user experience studies, user studies, variability, variance, Wilcoxon rank sum test