Statistics

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

2. 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

3. Overview • Class structure • 8 sessions • 1.5 hours per session • Several homework assignments • Class website • http://www.medsci.udel.edu/open/StatClass/March2009 Nemours Biomedical Research

4. 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

5. 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, SubjID,…) • Operations (e.g., ‘+’ ‘-’ ‘*’ ‘/’ ‘^’ ‘>’ ‘<‘ ‘==‘ ‘<-’) • Functions (e.g., sum(c(1,2,3)), mean(c(1,2,3))…) Nemours Biomedical Research

6. 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 5th element of ‘a’. Nemours Biomedical Research

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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