Statistics March 2009 Tim Bunnell Ph D Jobayer

Statistics March 2009 Tim Bunnell, Ph. D. & Jobayer Hossain, Ph. D. Nemours Bioinformatics Core Facility Nemours Biomedical Research

Overview • Class goals – Master basic statistical concepts – Learn analytic techniques & when to apply them – Learn how to interpret analysis results – Develop familiarity with R and related tools – Gain understanding that will transfer to a broad range of other statistics tool Nemours Biomedical Research

Overview • Class structure – 8 sessions – 1. 5 hours per session – Several homework assignments • Class website – http: //www. medsci. udel. edu/open/Stat. Class/March 2009 Nemours Biomedical Research

R • Installing – Download from Class website • Pick right (Mac versus Windows) version – Run installer program • Go with all the defaults • Running R – Live Demonstration Nemours Biomedical Research

R Concepts • Command line similar to – Windows Command Shell – Mac Terminal – Unix/Linux Shell • Uses ‘>’ as prompt • Accepts – – Constants (e. g. , 2 3 156 -99. 0, etc. ) Variables (e. g. , Height, Weight, Subj. ID, …) Operations (e. g. , ‘+’ ‘-’ ‘*’ ‘/’ ‘^’ ‘>’ ‘<‘ ‘==‘ ‘<-’) Functions (e. g. , sum(c(1, 2, 3)), mean(c(1, 2, 3))…) Nemours Biomedical Research

R Concepts • Variable types – – Scalar (a = 128) Vector (a = c(3, 2, 9, 5)) Matrix (dim(a) = c(2, 2)) Data Frame - collection of vectors. • • Similar to spread sheet ‘rows’ are indexed ‘cols’ named and indexed E. g. , df$a is the column of data frame df named ‘a’ and df$a[5] is the 5 th element of ‘a’. Nemours Biomedical Research

Statistics • Science of data collection, summarization, analysis and interpretation. • Descriptive versus Inferential Statistics: – Descriptive Statistic: Data description (summarization) such as center, variability and shape for quantitative variable (e. g. age) and number (frequency) and percentage for categorical variable (e. g. gender, race etc). – Inferential Statistic : Drawing conclusion beyond the sample studied, allowing for prediction. Nemours Biomedical Research

Statistical Description of Data • Statistics describes a numeric set of data by its • Center (mean, median, mode etc) • Variability (standard deviation, range etc) • Shape (skewness, kurtosis etc) • Statistics describes a categorical set of data by • Frequency, percentage or proportion of each category Nemours Biomedical Research

Statistical Inference sample population • Statistical inference is the process by which we acquire information about populations from samples. • Two types of estimates for making inferences: –Point estimation. –Interval estimate. Nemours Biomedical Research

Population and Sample • Population: The entire collection of individuals or measurements about which information is desired. • Sample: A subset of the population selected for study. – Primary objective is to create a subset of population whose center, spread and shape are as close as that of population. Nemours Biomedical Research

Parameter v. s. Statistic • Parameter: – Any statistical characteristic of a population. – Population mean, population median, population standard deviation are examples of parameters. – Parameter describes the distribution of a population – Parameters are fixed and usually unknown Nemours Biomedical Research

Parameter v. s. Statistic • Statistic: – Any statistical characteristic of a sample. – Sample mean, sample median, sample standard deviation are some examples of statistics. – Statistic describes the distribution of population – Value of a statistic is known and is varies for different samples – Are used for making inference on parameter Nemours Biomedical Research

Parameter v. s. Statistic • Statistical Issue – Estimate a population parameter using a sample statistic. – E. g. , the sample mean is an estimate of the population mean. Nemours Biomedical Research