CS4220: Knowledge Discovery Methods for Bioinformatics Unit 1: Essence of Biostatistics Wong Limsoon 2 Outline • Basics of biostatistics • Statistical estimation • Hypothesis testing – Measurement data: z-test, t-test – Categorical data: 2-test, Fisher’s exact test – Non-parametric methods • Ranking and rating • Summary Copyright 2013 © Limsoon Wong, 3 Why need biostatistics? Intrinsic & extrinsic noise Measurement errors Nat Rev Genet, 9:583-593, 2008 J Comput Biol, 8(6):557-569, 2001 Copyright 2013 © Limsoon Wong, 4 Why need to learn biostatistics? • Essential for scientific method of investigation – Formulate hypothesis – Design study to objectively test hypothesis – Collect reliable and unbiased data – Process and evaluate data rigorously – Interpret and draw appropriate conclusions • Essential for understanding, appraisal and critique of scientific literature Copyright 2013 © Limsoon Wong, 5 Type of statistical variables • Descriptive (categorical) variables – Nominal variables (no order between values): gender, eye color, race group, … – Ordinal variables (inherent order among values): response to treatment: none, slow, moderate, fast • Measurement variables – Continuous measurement variable: height, weight, blood pressure … – Discrete measurement variable (values are integers): number of siblings, the number of times a person has been admitted to a hospital … Copyright 2013 © Limsoon Wong, 6 Statistical variables • It is important to be able to distinguish different types of statistical variables and the data they generate as the kind of statistical indices and charts and the type of statistical tests used depend on knowledge of these basics Copyright 2013 © Limsoon Wong, 7 Types of statistical methods • Descriptive statistical methods – Provide summary indices for a given data, e.g. arithmetic mean, median, standard deviation, coefficient of variation, etc. • Inductive (inferential) statistical methods – Produce statistical inferences about a population based on information from a sample derived from the population, need to take variation into account sample Population 7 Estimating population values from sample values Copyright 2013 © Limsoon Wong, 8 Summarizing data • Statistic is “making sense of data” • Raw data have to be processed and summarized before one can make sense of data • Summary can take the form of – Summary index: using a single value to summarize data from a study variable – Tables – Diagrams 8 Copyright 2013 © Limsoon Wong, 9 Summarizing categorical data • A Proportion is a type of fraction in which the numerator is a subset of the denominator – proportion dead = 35/86 = 0.41 • Odds are fractions where the numerator is not part of the denominator – Odds in favor of death = 35/51 = 0.69 • A Ratio is a comparison of two numbers – ratio of dead: alive = 35: 51 • Odds ratio: commonly used in case-control study – Odds in favor of death for females = 12/25 = 0.48 – Odds in favor of death for males = 23/26 = 0.88 – Odds ratio = 0.88/0.48 = 1.84 Copyright 2013 © Limsoon Wong, 10 Summarizing measurement data • Distribution patterns – Symmetrical (bell-shaped) distribution, e.g. normal distribution – Skewed distribution – Bimodal and multimodal distribution • Indices of central tendency – Mean, median • Indices of dispersion – Variance, standard deviation, coefficient of variance Copyright 2013 © Limsoon Wong,