# chap1 - 1 Stat 211 Prof Parzen CHAPTER 1 STATISTICAL DATA...

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1 Stat 211 Prof Parzen CHAPTER 1 STATISTICAL DATA ANALYSIS Statistical methods seek to learn patterns from a data set by computing, comparing, and interpreting statistical summaries, including mean, median, quartiles, mid- quartile, inter-quartile range, standard deviation, box plot, QQ quantile plot, scatter diagram. 1.1 DATA, VARIABLES, QUANTITATIVE, CATEGORICAL, FREQUENCY By data or a sample we mean a set of n observations or measurements , denoted by capital letters X or Y with subscripts (for example 1 , , n Y Y or X_1,…,X_n). We assume data to be observations on a variable (denoted by capital letters , , Y X etc.) which represents a population which was sampled to collect the data. HISTORY: A fascinating story can be told about the first published example of a statistical data analysis by John Graunt around 1660 DESIGN OF DATA COLLECTION: Statisticians distinguish between (1) random samples which are representative of a population, and (2) samples from volunteers (called convenience samples) which may not yield conclusions valid about a population because the sample is not representative of the population. EXAMPLE: To collect data on opinions of workers in a factory one could (1) randomly select a sample of workers to interview from a complete list of workers, (2) use as a sample workers who sign up on a list osted on a bulletin board requesting volunteers for the survey. EXAMPLE: A grocery store company asks a consultant to estimate how much money is lost by an average grocery store due to shoplifting by choosing (by statistical random methods) a representative sample rather than conveniently choosing a few local grocery stores who are asked to report their losses due to shoplifting. Statisticians distinguish between (1) data from experiments, and (2) data from observational studies. One often observes two groups: (1) control group, (2) treatment group. An experiment is called (1) blind if subjects do not know which group they are in, (2) double blind if both subjects and investigators do not know whether a subject is in the treatment or control (placebo) group. EXAMPLE: Does earting dark cholate lower blood pressure in men? Two large groups of men are entrolled in an experiment for many months. Control group eats

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2 milk cholate; control group eats dark chocolate. Why do we want that the kind of chocolate a man is eating be a secret from everybody, including the man? Often observe bivariate data (X,Y) which means we are observing variables X and Y on the same subject. The data is recorded as a table of (x,y) values or a plot in the (x,y) called a scatter-diagram. EXAMPLE 1.1: United States Senators. A list of the names of the 100 senators in the Senate of the United Statistics in alphabetical order can be obtained from the internet. By randomly choosing a number from 1 to 100 randomly choose a senator on the list. Define variables X and Y as follows: X is the gender (woman or man) of the senator chosen; Y is the party affiliation (Republican or Democratic/
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## This note was uploaded on 03/27/2008 for the course STAT 211 taught by Professor Parzen during the Fall '07 term at Texas A&M.

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chap1 - 1 Stat 211 Prof Parzen CHAPTER 1 STATISTICAL DATA...

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