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## Week 1: Ch.1: Statistics and Data

1 review
by: Briana Sangiuliano

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6

# Week 1: Ch.1: Statistics and Data STAT 30100

Briana Sangiuliano
IUPUI
GPA 3.39

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## About this Document

Here are my notes for week 1. This covers the basic terminology and methods associated with statistics.
COURSE
Elementary Statistical Methods
PROF.
Jyotirmoy Sarkar
TYPE
Class Notes
PAGES
6
WORDS
CONCEPTS
Stats, iupui, stat 30100
KARMA
25 ?

## 1

1 review
"I was sick all last week and these notes were exactly what I needed to get caught up. Cheers!"
Tate Halvorson MD

## Popular in Statistics

This 6 page Class Notes was uploaded by Briana Sangiuliano on Saturday December 12, 2015. The Class Notes belongs to STAT 30100 at Indiana University Purdue University - Indianapolis taught by Jyotirmoy Sarkar in Fall 2015. Since its upload, it has received 26 views. For similar materials see Elementary Statistical Methods in Statistics at Indiana University Purdue University - Indianapolis.

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## Reviews for Week 1: Ch.1: Statistics and Data

I was sick all last week and these notes were exactly what I needed to get caught up. Cheers!

-Tate Halvorson MD

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Date Created: 12/12/15
STAT 30100 Elementary Statistical Methods th *Notes are based off lecture and 12  edition Statistics Textbook by James McClave and Terry Sincich Chapter 1: Statistics, Data, and Statistical Thinking What is Statistics?  A mathematical science, but not a branch of mathematics.  Science of data o Deals with the study of:  Collecting  Classifying  Summarizing  Organizing  Analyzing  Interpreting, and  Presenting data  Can be descriptive or inferential o Descriptive  Utilizes numerical and graphical methods to organize, summarize, and present data o Inferential   Utilize   sample   data   to   make   reasonable   estimates,   decisions, predictions, or other generalizations about a population or larger set of data. Important Terminology  Experimental, individual, or observational unit o Object being described by a set of data  Examples: person, thing, or event  Population o Set of units we are interested in studying o The entire group of individuals about which we want information  Examples: all adults in a state/region o Size denoted or represented by N  Sample o A subset of units of a population o A representative part of population  Example: adults in region who are employed  o Size denoted or represented by n  Variables o Characteristic or property  of the experimental or observational unit that can be measured  Example: age, ethnicity, eye color, height o Can be qualitative or quantitative  Qualitative Variable o Aka categorical variable  o Record a response as a category  Example: color, yes or no, religion  Quantitative Variable o Aka Numerical Variable o Measured in numbers  Example: weight,  number of items, length o Values can be discrete or continuous  Discrete Variable o Measured in whole numbers of integers  Example: number of students in a classroom, number of people that go to the movies per day  Continuous Variable o Can be within any ranges of values  Example: distance between objects, height range within a group of people Methods of Collecting Data  Published Source o The data set of interest has already been collected and is available to the public.   Examples  The Wall Street Journal –Financial data  The Sporting News –Sports information  Census –Information is obtained from the whole population Collecting Data  Designed Experimental Study o An investigator observes how a response variable behaves when the researcher manipulates one or more explanatory (independent) variables. o The goal of an experiment is to determine the effect of the manipulated factor on the response (dependent) variable. o In a well­designed experiment, the composition of the groups that will be exposed to different experimental conditions is determined by random assignment. o Experimental studies actively produce data.  Observational Study o An investigator observes characteristics of a sample of one or more existing populations. o The goal of an observational study is usually to draw conclusions about the corresponding population or about differences between two or more populations. o Researcher must obtain a sample that is representative of the population of interest.   Best accomplished through some well designed random sampling procedure such as surveying.  o Observational studies passively collect data. Sampling  Information is obtained from a small group (sample) of objects/individuals taken from the population. o The sample should be a representative sample, that is, it should reflect as closely as possible the relevant characteristics of the population under consideration. Simple Random Sampling  Procedure in which each possible sample of a given size is equally likely to be the one obtained.   This procedure can be implemented in two ways: o Mechanical methods  Thoroughly   mix   symmetrical   items   in   a   physical   randomizing device. (example: drawing slips of paper from a hat) o Methods using Random Numbers  Create a list of all the objects or individuals in the population, assign each item a number and a table of random numbers generator can be used to select the sample. Systematic Random Sampling  Divide a population list into as many consecutive segments as you need.  Randomly choose a starting point in the first segment and sample at that same point in each segment. nd o Example: 12 people into 4 segments, pick every 2  person in segment Segment 1                  Segment 2        Segment 3 Segment 4     Stratified Random Sampling  Data is divided into subgroups based specific characteristic or variable o Like age or education level   Use simple random sampling within each subgroup Seniors                 Juniors Sophomores                  Cluster  Random  Freshmaning  Data is divided into clusters and random sampling used to choose clusters  All data used from selected clusters  Clusters usually based on geographic characteristic Convenience Sampling Convenience Sampling  Data are used from population members that are readily available  Not a good sampling technique in general due to likely bias tendencies.  SAMPLING EXAMPLE SUMMARY In a class of 18 students, 6 are chosen for an assignment. Sampling Type Example Random Pull 6names out of a hat Systematic Selecting every 3rdstudent Stratified Divide the class into 2 equal age groups.  Randomly choose 3 from each group Cluster Divide the class into 6 groups of 3 students  each. Randomly choose 2 groups Convenience Take the 6 students closest to the teacher Bias  The tendency for samples to differ from the corresponding population in some  systematic way. o Can occur because of the method used to select a sample (selection  bias). o Or because of the way the data is collected after the sample has been  selected (non­response or measurement bias). Selection Bias  Occurs when the way the sample is selected systematically excludes some part  of the population of interest.  If the members of the population included in the sample differ from the excluded  members on a variable that is important to the study, conclusions based on the  sample data may not be valid for the population of interest. o Example: surveying individuals at a motor convection on removing street  racing laws   Non­Response Bias  Occurs when responses are not obtained from all individuals selected for  sampling.  o Can distort results if those who respond differ in important ways from  those who do not respond  Example: those with anger issues did not fill an anger management survey from their company Measurement Bias (Error)  Refers to inaccuracies in the values of the data recorded.  o Occurs when the method of observation tends to produce values that  systematically differ from the true value in some way.  Example: realizing a tool or instrument was measuring samples  wrong, calculation error Statistical Thinking  Applying rational thought and the science of statistics to critically assess data  and inferences. o Knowing that variances exists in a population of data is fundamental to the thought process

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