Elementary Statistics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Elementary Statistics"

Transcription

1 Elementary Statistics Chapter 1 Dr. Ghamsary Page 1 Elementary Statistics M. Ghamsary, Ph.D. Chap 01 1

2 Elementary Statistics Chapter 1 Dr. Ghamsary Page 2 Statistics: Statistics is the science of collecting, organizing, summarizing, analyzing data, and Draw conclusions. Objective: The primary objective of statistics is inference. The applications of statistics can be divided into two broad areas: 1. Descriptive Statistics 2. Inferential Statistics Variable: is a characteristic of an individual population unit. Data are the values (measurements or observations) that the variables can assume. Variables whose values are determined by chance are called random variables. For example: 12, 13, 69, 98, 78, 87, 36, 54, 68, 36, 63, 85, 79, 75, 32, 16, 57, 58, 34, 91, 74, 83, 92. Each value in the data set is called a data value or a datum. 1. Descriptive statistics: consists numerical and graphical techniques to summarize and present the information in the data set. 2. Inferential statistics consists of estimation, prediction, or generalizing from samples to populations. Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. 2

3 Elementary Statistics Chapter 1 Dr. Ghamsary Page 3 For example, gender (male or female) Race (White, Black, Hispanic, etc) Religion Quantitative variables: are numerical in nature and can be ordered or ranked. For example, Age is numerical and the values can be ranked. Height Scores on a test of Stat class Discrete variables Assumes a finite number of possible values that can be counted. For example: Numbers of telephone calls is made at the switch board of our school every day. {0, 1, 2, 3, 4, } Number of accidents in FWY 5 Number of babies delivered at LLU hospital Continuous variables can assume infinitely many values between any two specific values such that there would be no gaps. Height of boys born at UCLA hospital on July 4 th Amount of rain falls in California in the year # of car accidents in FWY 10 from 5 to 7PM daily # of babies delivered at LLU hospital daiy 3

4 Elementary Statistics Chapter 1 Dr. Ghamsary Page 4 Levels of Measurement When we observe and record a variable, it has characteristics that influence the type of statistical analysis that we can perform on it. These characteristics are referred to as the level of measurement of the variable. The first step in any statistical analysis is to determine the level of measurement; it tells us what statistical tests can and cannot be performed. There are four levels of measurement: 1. Nominal 2. Ordinal 3. Interval 4. Ratio 1. The nominal level of measurement: Refers to data consist of names and/or categories so that the data cannot be arranged in any specific ordering scheme. The nominal level of measurement occurs when the observations do not have a meaningful numeric value. For example: Sex ( Male, Female) Race (White, Black, Hispanic, Asian, Persian, etc) Colors of car in the street Area Code Zip code The values of nominal variables cannot be meaningfully: compared to see if one is larger than another added or subtracted multiplied or divided calculate the mean (what most people call the average) 4

5 Elementary Statistics Chapter 1 Dr. Ghamsary Page 5 2. The ordinal level of measurement classifies data into categories that can be ranked; but differences between the ranks cannot be determined. The Ordinal variables are used to represent observations that can be categorized and rank ordered For example: Letter Grades such as A, superior; B, good; C, average; D, poor; F, Fail Size of cars in the street: Small, Medium, and Large. Scoring in games: 1 st, 2 nd, 3 rd,. Class rank, Order of finishing a horse race, How much you prefer various vegetables The values of ordinal variables can be: compared to see if they are equal or not compared to see if one is larger or smaller than another The values of ordinal variables cannot be meaningfully: added or subtracted multiplied or divided calculate the mean 3. The interval level of measurement is like ordinal, with additional property that differences between units of data can be defined, but there is no meaningful zero. The Interval variables represent observations that can be categorized, rank ordered, and have an unit of measure. An unit of measure implies that the difference between any two successive values is identical With an interval scaled variable, the value 0 does not represent the complete absence of the variable. 5

6 Elementary Statistics Chapter 1 Dr. Ghamsary Page 6 The values of interval variables can be: compared to see if they are equal or not compared to see if one is larger or smaller than another added or subtracted The values of interval variables cannot be meaningfully: multiplied or divided (eg. 60 o F is not twice as hot as 30 o F) For example: Temperature, like Fahrenheit as, we know there is no natural 0. The years IQ scores Shoe size 4. The ratio level of measurement is just like the interval measurement, and there exists a natural zero. In addition, true ratios and differences both exist for the same variable. The Ratio variables represent observations that can be categorized, rank ordered, have an unit of measure and have a true zero The true zero implies that a value of zero represents the complete absence of the variable The values of ratio variables can be: compared to see if they are equal or not compared to see if one is larger or smaller than another added or subtracted multiplied or divided 6

7 Elementary Statistics Chapter 1 Dr. Ghamsary Page 7 For example: Weight Height Age Length Distance Most students have trouble differentiating between interval and ratio levels of measurement. Here is a simple test: If one number is twice the other is the quantity being measured also twice the other quantity? For example if you have two weights 120 lbs. and 240 lbs. it should be clear that 240 lbs. is twice as heavy as 120 lbs. So weights are an example of a ratio level of measurement. However say you have two temperatures 30 degrees and 60 degrees, 60 degrees is not twice as hot as 30 degrees, so this is an example of an interval level of measurement. Another test is that in the ratio level of measurement zero means absence of quantity. If you consider weights, 0 lb. means that you have NO weight (so weight is ratio), while with the interval level of measurement, such as temperature 0 degrees Fahrenheit does not mean the absence of heat which is what temperature measures. Population: consists of all units (subjects, objects, etc) that are being studied. Sample is a subset of the units of a population. Parameter: descriptive measure of the population: Usually represented by Greek letters Statistic: descriptive measure of a sample: Usually represented by Roman letters 7

8 Elementary Statistics Chapter 1 Dr. Ghamsary Page 8 Measure Sample (Statistics) Population (Parameters) Mean x µ 2 Variance s 2 σ Standard Deviation s σ Correlation Coefficient r ρ Proportion ˆp p Slope of Simple Regression 1 ˆβ β 1 Size n N Summary of Data Classifications 8

9 Elementary Statistics Chapter 1 Dr. Ghamsary Page 9 Example1: From a sample of students in your statistics class, you collect the following: the student's name, gender, SAT score, age, IQ, birth date (BD), and their grade in a freshman level math class. Use the measurement of Qualitative or Quantitative to answer the following. Which scale of measurement? 1. The variable student's name is measured on 2. The variable student's gender is measured on 3. The variable student's SAT score is measured on 4. The variable student's age is measured on 5. The variable student's IQ is measured on 6. The variable student's BD is measured on Example2: From a sample of students in your statistics class, you collect the following: the student's name, gender, SAT score, age, IQ, birth date, and their grade in a freshman level math class. Use the measurement of Nominal, Ordinal, Interval or Ratio to answer the following. Which scale of measurement? 1. The variable student's name is measured on 2. The variable student's gender is measured on 3. The variable student's SAT score is measured on 4. The variable student's age is measured on 5. The variable student's IQ is measured on 6. The variable student's BD is measured on 9

10 Elementary Statistics Chapter 1 Dr. Ghamsary Page 10 Example3: A researcher is claiming that the average age of women who are graduated from medical school at Loma Linda Medical School is about 27 years. To test his hypothesis, he randomly selected 200 female doctors who have graduated from LLU medical school. 1. Describe the population. 2. Identify the variable of interest. 3. Is the variable quantitative (qualitative)? 4. Is the variable discrete or continuous? 5. Identify the type of the variable. 6. Describe the sample. 7. Describe the inference. Example4: A researcher in LA county is claiming that the men and women have different attitude toward abortion. He randomly selected 500 men and 500 women and ask them to see if they are antiabortion. 1. Describe the population. 2. Identify the variable of interest. 3. Is the variable quantitative(qualitative)? 4. Is the variable discrete or continuous? 5. Identify the type of the variable. 6. Describe the sample. 7. Describe the inference. Example5: Read the following article and answer the following questions A study in California (which also funds abortions for the poor) found that by 1990, among young white women. there was no difference in the rate of breast cancer between rich and poor. 1. Describe the population. 2. Identify the variable of interest. 3. Is the variable quantitative(qualitative)? 4. Is the variable discrete or continuous? 5. Identify the type of the variable. 6. Describe the sample. 7. Describe the inference 10

11 Elementary Statistics Chapter 1 Dr. Ghamsary Page 11 Methods of Sampling: There are many method of sampling, but we will describe 5 common and basic method of sampling as follows: a. Convenience Sampling b. Simple Random Sampling c. Systematic Sampling d. Stratified Sampling e. Cluster Sampling Convenience sampling: attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time. For example: use of students, and members of social organizations mall intercept interviews without qualifying the respondents department stores using charge account lists people on the street interviews Simple Random Sampling (SRS) Each element in the population has a known and equal probability of selection. Each possible sample of a given size (n) has a known and equal probability of being the sample actually selected. This implies that every element is selected independently of every other element 11

12 Elementary Statistics Chapter 1 Dr. Ghamsary Page 12 Systematic Sampling The sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame. For example, there are 1000 elements in the population and a sample of 100 is desired. In this case the sampling interval is 10. Stratified Sampling A two-step process in which the population is partitioned into subpopulations, or strata. The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted. Next, elements are selected from each stratum by a random procedure, usually SRS. A major objective of stratified sampling is to increase precision without increasing cost The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible. The stratification variables should also be closely related to the characteristic of interest. Finally, the variables should decrease the cost of the stratification process by being easy to measure and apply. In proportionate stratified sampling, the size of the sample drawn from each stratum is proportionate to the relative size of that stratum in the total population. In disproportionate stratified sampling, the size of the sample from each stratum is proportionate to the relative size of that stratum and to the standard deviation of the distribution of the characteristic of interest among all the elements in that stratum. 12

13 Elementary Statistics Chapter 1 Dr. Ghamsary Page 13 Cluster Sampling The target population is first divided into mutually exclusive and collectively exhaustive subpopulations, or clusters. Then a random sample of clusters is selected, based on a probability sampling technique such as SRS. For each selected cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-stage). Elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population. In probability proportionate to size sampling, the clusters are sampled with probability proportional to size. In the second stage, the probability of selecting a sampling unit in a selected cluster varies inversely with the size of the cluster. 13

14 Elementary Statistics Chapter 1 Dr. Ghamsary Page 14 Review of Chapter 01 Determine whether the given values are from a discrete or continuous data set. 1. In a sample data of 100 Pepsi s can we find that the average size of Pepsi s can was 11.98oz 2. Ina survey of 1,011 adults, it is found that 450 of them have smoked at least once in their life. 3. Ina survey of 3,289 adults, it is found that 45% of them have garden in their homes 4. The average American drink 2 cup of coffee per day. Determine whether the given variables are from a Qualitative or Quantitative. 5. Area Codes of for the phone # of students in this class 6. Social Security of students in this class 7. Professor s nationality who are teaching in this school 8. Height of students in this class. Determine which of the four levels of measurement is most appropriate: Nominal, Ordinal, Interval, or Ratio. 9. Area Codes of for the phone # of students in this class 10. Social Security of students in this class 11. Professor s nationality who are teaching in this school 12. Height of students in this class. 13. Ratings of good, average, poor for today lecture. 14. Current temperatures of this class room. 15. Numbers on the Laker s basketball players. 16. The year of student s birth day. 17. Drivers license numbers. 14

15 Elementary Statistics Chapter 1 Dr. Ghamsary Page 15 Identify which of these types of sampling is used: Random (SRS), Systematic, Stratified, Cluster, or Convenience. 18. An Los Angeles Times reporter gets a reaction to a breaking story by poling people as they pass the front of the Times building. 19. Dr. Ghamsary has randomly selected 5 students in his class. 20. The Orange County Commissioner of Jurors obtains a list of 55,014 car owners and constructs a poll of jurors by selecting every 50 th name on the list. 21. In a Harris poll of 1,011 adults, the interview subjects were selected by using a computer to randomly generate telephone numbers that were then called. 22. A Ford Motor Company researcher has partitioned all registered cars into categories of compact, mid-size, and family-size. He is surveying 75 car owners from each category. 23. Motivated by a student who died from binge drinking, Chico State conducts a study of student drinking by randomly selecting 10 different classes and interviewing all of the students in each of those classes. 24. A statistics student obtains height/weight data by interviewing the members of his fraternity. 25. A UCLA researcher surveys all cardiac patients in each of 30 randomly selected hospitals. 15

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 1 Introduction to Statistics 1.1 An Overview of Statistics 1 Distinguish Between a Population and a Sample Identify the population and the sample. survey of 1353 American households found that 18%

More information

Northumberland Knowledge

Northumberland Knowledge Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about

More information

Basic Concepts in Research and Data Analysis

Basic Concepts in Research and Data Analysis Basic Concepts in Research and Data Analysis Introduction: A Common Language for Researchers...2 Steps to Follow When Conducting Research...3 The Research Question... 3 The Hypothesis... 4 Defining the

More information

Determine whether the data are qualitative or quantitative. 8) the colors of automobiles on a used car lot Answer: qualitative

Determine whether the data are qualitative or quantitative. 8) the colors of automobiles on a used car lot Answer: qualitative Name Score: Math 227 Review Exam 1 Chapter 2& Fall 2011 ********************************************************************************************************************** SHORT ANSWER. Show work on

More information

Statistics Review PSY379

Statistics Review PSY379 Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

More information

There are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month

More information

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

More information

Business Statistics: Intorduction

Business Statistics: Intorduction Business Statistics: Intorduction Donglei Du (ddu@unb.edu) Faculty of Business Administration, University of New Brunswick, NB Canada Fredericton E3B 9Y2 September 23, 2015 Donglei Du (UNB) AlgoTrading

More information

Topic #1: Introduction to measurement and statistics

Topic #1: Introduction to measurement and statistics Topic #1: Introduction to measurement and statistics "Statistics can be fun or at least they don't need to be feared." Many folks have trouble believing this premise. Often, individuals walk into their

More information

The SURVEYFREQ Procedure in SAS 9.2: Avoiding FREQuent Mistakes When Analyzing Survey Data ABSTRACT INTRODUCTION SURVEY DESIGN 101 WHY STRATIFY?

The SURVEYFREQ Procedure in SAS 9.2: Avoiding FREQuent Mistakes When Analyzing Survey Data ABSTRACT INTRODUCTION SURVEY DESIGN 101 WHY STRATIFY? The SURVEYFREQ Procedure in SAS 9.2: Avoiding FREQuent Mistakes When Analyzing Survey Data Kathryn Martin, Maternal, Child and Adolescent Health Program, California Department of Public Health, ABSTRACT

More information

Descriptive Inferential. The First Measured Century. Statistics. Statistics. We will focus on two types of statistical applications

Descriptive Inferential. The First Measured Century. Statistics. Statistics. We will focus on two types of statistical applications Introduction: Statistics, Data and Statistical Thinking The First Measured Century FREC 408 Dr. Tom Ilvento 213 Townsend Hall ilvento@udel.edu http://www.udel.edu/frec/ilvento http://www.pbs.org/fmc/index.htm

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

More information

Mind on Statistics. Chapter 10

Mind on Statistics. Chapter 10 Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine

More information

Levels of measurement in psychological research:

Levels of measurement in psychological research: Research Skills: Levels of Measurement. Graham Hole, February 2011 Page 1 Levels of measurement in psychological research: Psychology is a science. As such it generally involves objective measurement of

More information

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

More information

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1) Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

More information

Measurement & Data Analysis. On the importance of math & measurement. Steps Involved in Doing Scientific Research. Measurement

Measurement & Data Analysis. On the importance of math & measurement. Steps Involved in Doing Scientific Research. Measurement Measurement & Data Analysis Overview of Measurement. Variability & Measurement Error.. Descriptive vs. Inferential Statistics. Descriptive Statistics. Distributions. Standardized Scores. Graphing Data.

More information

Fundamentals of Probability

Fundamentals of Probability Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible

More information

DATA ANALYSIS. QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University

DATA ANALYSIS. QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University DATA ANALYSIS QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University Quantitative Research What is Statistics? Statistics (as a subject) is the science

More information

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre-

More information

INTRODUCTION TO SURVEY DATA ANALYSIS THROUGH STATISTICAL PACKAGES

INTRODUCTION TO SURVEY DATA ANALYSIS THROUGH STATISTICAL PACKAGES INTRODUCTION TO SURVEY DATA ANALYSIS THROUGH STATISTICAL PACKAGES Hukum Chandra Indian Agricultural Statistics Research Institute, New Delhi-110012 1. INTRODUCTION A sample survey is a process for collecting

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

More information

Probability and Statistics Vocabulary List (Definitions for Middle School Teachers)

Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence

More information

Mind on Statistics. Chapter 4

Mind on Statistics. Chapter 4 Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender

More information

STAT 350 Practice Final Exam Solution (Spring 2015)

STAT 350 Practice Final Exam Solution (Spring 2015) PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

More information

List of Examples. Examples 319

List of Examples. Examples 319 Examples 319 List of Examples DiMaggio and Mantle. 6 Weed seeds. 6, 23, 37, 38 Vole reproduction. 7, 24, 37 Wooly bear caterpillar cocoons. 7 Homophone confusion and Alzheimer s disease. 8 Gear tooth strength.

More information

STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

More information

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph. MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

More information

Statistics E100 Fall 2013 Practice Midterm I - A Solutions

Statistics E100 Fall 2013 Practice Midterm I - A Solutions STATISTICS E100 FALL 2013 PRACTICE MIDTERM I - A SOLUTIONS PAGE 1 OF 5 Statistics E100 Fall 2013 Practice Midterm I - A Solutions 1. (16 points total) Below is the histogram for the number of medals won

More information

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm

More information

COMMON CORE STATE STANDARDS FOR

COMMON CORE STATE STANDARDS FOR COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in

More information

Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.)

Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Unit 12 Logistic Regression Supplementary Chapter 14 in IPS On CD (Chap 16, 5th ed.) Logistic regression generalizes methods for 2-way tables Adds capability studying several predictors, but Limited to

More information

Practice#1(chapter1,2) Name

Practice#1(chapter1,2) Name Practice#1(chapter1,2) Name Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) inferential statistics

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96 1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

More information

6.2 Normal distribution. Standard Normal Distribution:

6.2 Normal distribution. Standard Normal Distribution: 6.2 Normal distribution Slide Heights of Adult Men and Women Slide 2 Area= Mean = µ Standard Deviation = σ Donation: X ~ N(µ,σ 2 ) Standard Normal Distribution: Slide 3 Slide 4 a normal probability distribution

More information

4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"

4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: What do the data look like? Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses

More information

Elementary Statistics

Elementary Statistics lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chi-square Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page

More information

Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name: Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

More information

STATISTICAL ANALYSIS AND INTERPRETATION OF DATA COMMONLY USED IN EMPLOYMENT LAW LITIGATION

STATISTICAL ANALYSIS AND INTERPRETATION OF DATA COMMONLY USED IN EMPLOYMENT LAW LITIGATION STATISTICAL ANALYSIS AND INTERPRETATION OF DATA COMMONLY USED IN EMPLOYMENT LAW LITIGATION C. Paul Wazzan Kenneth D. Sulzer ABSTRACT In employment law litigation, statistical analysis of data from surveys,

More information

DRIVER ATTRIBUTES AND REAR-END CRASH INVOLVEMENT PROPENSITY

DRIVER ATTRIBUTES AND REAR-END CRASH INVOLVEMENT PROPENSITY U.S. Department of Transportation National Highway Traffic Safety Administration DOT HS 809 540 March 2003 Technical Report DRIVER ATTRIBUTES AND REAR-END CRASH INVOLVEMENT PROPENSITY Published By: National

More information

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009 Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level

More information

The Chi-Square Test. STAT E-50 Introduction to Statistics

The Chi-Square Test. STAT E-50 Introduction to Statistics STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

More information

IAM 530 ELEMENTS OF PROBABILITY AND STATISTICS INTRODUCTION

IAM 530 ELEMENTS OF PROBABILITY AND STATISTICS INTRODUCTION IAM 530 ELEMENTS OF PROBABILITY AND STATISTICS INTRODUCTION 1 WHAT IS STATISTICS? Statistics is a science of collecting data, organizing and describing it and drawing conclusions from it. That is, statistics

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

More information

Mathematics. Probability and Statistics Curriculum Guide. Revised 2010

Mathematics. Probability and Statistics Curriculum Guide. Revised 2010 Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction

More information

11. Analysis of Case-control Studies Logistic Regression

11. Analysis of Case-control Studies Logistic Regression Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

More information

Survey Data Analysis in Stata

Survey Data Analysis in Stata Survey Data Analysis in Stata Jeff Pitblado Associate Director, Statistical Software StataCorp LP Stata Conference DC 2009 J. Pitblado (StataCorp) Survey Data Analysis DC 2009 1 / 44 Outline 1 Types of

More information

Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 13 Introduction to Linear Regression and Correlation Analysis Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

More information

Section 2: Ten Tools for Applying Sociology

Section 2: Ten Tools for Applying Sociology Section 2: Ten Tools for Applying Sociology CHAPTER 2.6: DATA COLLECTION METHODS QUICK START: In this chapter, you will learn The basics of data collection methods. To know when to use quantitative and/or

More information

Introduction to Statistics and Quantitative Research Methods

Introduction to Statistics and Quantitative Research Methods Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.

More information

Chapter 11 Introduction to Survey Sampling and Analysis Procedures

Chapter 11 Introduction to Survey Sampling and Analysis Procedures Chapter 11 Introduction to Survey Sampling and Analysis Procedures Chapter Table of Contents OVERVIEW...149 SurveySampling...150 SurveyDataAnalysis...151 DESIGN INFORMATION FOR SURVEY PROCEDURES...152

More information

2013 State of Colorado Distracted Driver Study

2013 State of Colorado Distracted Driver Study 2013 State of Colorado Distracted Driver Study Colorado Department of Transportation SEAT BE L STUDY T INSTITUTE OF TRANSPORTATION MANAGEMENT EXECUTIVE SUMMARY The Institute of Transportation Management

More information

STAT 121 Hybrid SUMMER 2014 Introduction to Statistics for the Social Sciences Session I: May 27 th July 3 rd

STAT 121 Hybrid SUMMER 2014 Introduction to Statistics for the Social Sciences Session I: May 27 th July 3 rd STAT 121 Hybrid SUMMER 2014 Introduction to Statistics for the Social Sciences Session I: May 27 th July 3 rd Instructor: Ms. Bonnie Kegan EMAIL: bkegan1@umbc.edu Contact Numbers: Mobile Phone: 410 507

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 10 Chi SquareTests and the F-Distribution 10.1 Goodness of Fit 1 Find Expected Frequencies Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees.

More information

Example Research Scenarios

Example Research Scenarios Example Research Scenarios In this document, I've collected many of the scenario problems that we discussed in class throughout the semester. For each problem you should: a) Identify the most appropriate

More information

Big Ideas in Mathematics

Big Ideas in Mathematics Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

More information

Best Practices in Data Visualizations. Vihao Pham January 29, 2014

Best Practices in Data Visualizations. Vihao Pham January 29, 2014 Best Practices in Data Visualizations Vihao Pham January 29, 2014 Agenda Best Practices in Data Visualizations Why We Visualize Understanding Data Visualizations Enhancing Visualizations Visualization

More information

Best Practices in Data Visualizations. Vihao Pham 2014

Best Practices in Data Visualizations. Vihao Pham 2014 Best Practices in Data Visualizations Vihao Pham 2014 Agenda Best Practices in Data Visualizations Why We Visualize Understanding Data Visualizations Enhancing Visualizations Visualization Considerations

More information

Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

More information

Foundation of Quantitative Data Analysis

Foundation of Quantitative Data Analysis Foundation of Quantitative Data Analysis Part 1: Data manipulation and descriptive statistics with SPSS/Excel HSRS #10 - October 17, 2013 Reference : A. Aczel, Complete Business Statistics. Chapters 1

More information

Statistics Class Level Test Mu Alpha Theta State 2008

Statistics Class Level Test Mu Alpha Theta State 2008 Statistics Class Level Test Mu Alpha Theta State 2008 1. Which of the following are true statements? I. The histogram of a binomial distribution with p = 0.5 is always symmetric no matter what n, the number

More information

RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY

RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY I. INTRODUCTION According to the Common Core Standards (2010), Decisions or predictions are often based on data numbers

More information

DATA INTERPRETATION AND STATISTICS

DATA INTERPRETATION AND STATISTICS PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE

More information

Introduction to Regression and Data Analysis

Introduction to Regression and Data Analysis Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

More information

Tutorial Segmentation and Classification

Tutorial Segmentation and Classification MARKETING ENGINEERING FOR EXCEL TUTORIAL VERSION 1.0.8 Tutorial Segmentation and Classification Marketing Engineering for Excel is a Microsoft Excel add-in. The software runs from within Microsoft Excel

More information

Introduction to Linear Regression

Introduction to Linear Regression 14. Regression A. Introduction to Simple Linear Regression B. Partitioning Sums of Squares C. Standard Error of the Estimate D. Inferential Statistics for b and r E. Influential Observations F. Regression

More information

The Importance of Community College Honors Programs

The Importance of Community College Honors Programs 6 This chapter examines relationships between the presence of honors programs at community colleges and institutional, curricular, and student body characteristics. Furthermore, the author relates his

More information

Social Media Mining. Data Mining Essentials

Social Media Mining. Data Mining Essentials Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers

More information

Exercise 1.12 (Pg. 22-23)

Exercise 1.12 (Pg. 22-23) Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

More information

Elements of statistics (MATH0487-1)

Elements of statistics (MATH0487-1) Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -

More information

Lecture 6 - Data Mining Processes

Lecture 6 - Data Mining Processes Lecture 6 - Data Mining Processes Dr. Songsri Tangsripairoj Dr.Benjarath Pupacdi Faculty of ICT, Mahidol University 1 Cross-Industry Standard Process for Data Mining (CRISP-DM) Example Application: Telephone

More information

Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012

Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012 Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization GENOME 560, Spring 2012 Data are interesting because they help us understand the world Genomics: Massive Amounts

More information

Illustration (and the use of HLM)

Illustration (and the use of HLM) Illustration (and the use of HLM) Chapter 4 1 Measurement Incorporated HLM Workshop The Illustration Data Now we cover the example. In doing so we does the use of the software HLM. In addition, we will

More information

UNIVERSITY of MASSACHUSETTS DARTMOUTH Charlton College of Business Decision and Information Sciences Fall 2010

UNIVERSITY of MASSACHUSETTS DARTMOUTH Charlton College of Business Decision and Information Sciences Fall 2010 UNIVERSITY of MASSACHUSETTS DARTMOUTH Charlton College of Business Decision and Information Sciences Fall 2010 COURSE: POM 500 Statistical Analysis, ONLINE EDITION, Fall 2010 Prerequisite: Finite Math

More information

Need for Sampling. Very large populations Destructive testing Continuous production process

Need for Sampling. Very large populations Destructive testing Continuous production process Chapter 4 Sampling and Estimation Need for Sampling Very large populations Destructive testing Continuous production process The objective of sampling is to draw a valid inference about a population. 4-

More information

Data Analysis and Interpretation. Eleanor Howell, MS Manager, Data Dissemination Unit State Center for Health Statistics

Data Analysis and Interpretation. Eleanor Howell, MS Manager, Data Dissemination Unit State Center for Health Statistics Data Analysis and Interpretation Eleanor Howell, MS Manager, Data Dissemination Unit State Center for Health Statistics Why do we need data? To show evidence or support for an idea To track progress over

More information

Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

More information

Math and Science Bridge Program. Session 1 WHAT IS STATISTICS? 2/22/13. Research Paperwork. Agenda. Professional Development Website

Math and Science Bridge Program. Session 1 WHAT IS STATISTICS? 2/22/13. Research Paperwork. Agenda. Professional Development Website Math and Science Bridge Program Year 1: Statistics and Probability Dr. Tamara Pearson Assistant Professor of Mathematics Research Paperwork Informed Consent Pre-Survey After you complete the survey please

More information

The Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)

The Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175) Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,

More information

Rates for Vehicle Loans: Race and Loan Source

Rates for Vehicle Loans: Race and Loan Source Rates for Vehicle Loans: Race and Loan Source Kerwin Kofi Charles Harris School University of Chicago 1155 East 60th Street Chicago, IL 60637 Voice: (773) 834-8922 Fax: (773) 702-0926 e-mail: kcharles@gmail.com

More information

3. Data Analysis, Statistics, and Probability

3. Data Analysis, Statistics, and Probability 3. Data Analysis, Statistics, and Probability Data and probability sense provides students with tools to understand information and uncertainty. Students ask questions and gather and use data to answer

More information

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

More information

AP * Statistics Review. Designing a Study

AP * Statistics Review. Designing a Study AP * Statistics Review Designing a Study Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

More information

Lecture 14. Chapter 7: Probability. Rule 1: Rule 2: Rule 3: Nancy Pfenning Stats 1000

Lecture 14. Chapter 7: Probability. Rule 1: Rule 2: Rule 3: Nancy Pfenning Stats 1000 Lecture 4 Nancy Pfenning Stats 000 Chapter 7: Probability Last time we established some basic definitions and rules of probability: Rule : P (A C ) = P (A). Rule 2: In general, the probability of one event

More information

DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS

DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi - 110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics

More information

Geostatistics Exploratory Analysis

Geostatistics Exploratory Analysis Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt

More information

Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

More information

Algebra 1 Course Information

Algebra 1 Course Information Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

More information

Name: Date: Use the following to answer questions 2-4:

Name: Date: Use the following to answer questions 2-4: Name: Date: 1. A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. What does this proportion represent? A) The probability

More information

Sample design for educational survey research

Sample design for educational survey research Quantitative research methods in educational planning Series editor: Kenneth N.Ross Module Kenneth N. Ross 3 Sample design for educational survey research UNESCO International Institute for Educational

More information

CITY OF MILWAUKEE POLICE SATISFACTION SURVEY

CITY OF MILWAUKEE POLICE SATISFACTION SURVEY RESEARCH BRIEF Joseph Cera, PhD Survey Center Director UW-Milwaukee Atiera Coleman, MA Project Assistant UW-Milwaukee CITY OF MILWAUKEE POLICE SATISFACTION SURVEY At the request of and in cooperation with

More information

Los Angeles County 2010

Los Angeles County 2010 Indicators of Alcohol and Other Drug Risk and Consequences for California Counties County 2010 Indicators of Alcohol and Other Drug Risk and Consequences for California Counties County 2010 TABLE OF CONTENTS

More information

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

More information

Glossary of Terms Ability Accommodation Adjusted validity/reliability coefficient Alternate forms Analysis of work Assessment Battery Bias

Glossary of Terms Ability Accommodation Adjusted validity/reliability coefficient Alternate forms Analysis of work Assessment Battery Bias Glossary of Terms Ability A defined domain of cognitive, perceptual, psychomotor, or physical functioning. Accommodation A change in the content, format, and/or administration of a selection procedure

More information

Sacramento County 2010

Sacramento County 2010 Indicators of Alcohol and Other Drug Risk and Consequences for California Counties County 21 Indicators of Alcohol and Other Drug Risk and Consequences for California Counties County 21 TABLE OF CONTENTS

More information

Lecture 13. Understanding Probability and Long-Term Expectations

Lecture 13. Understanding Probability and Long-Term Expectations Lecture 13 Understanding Probability and Long-Term Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).

More information

Organizing Your Approach to a Data Analysis

Organizing Your Approach to a Data Analysis Biost/Stat 578 B: Data Analysis Emerson, September 29, 2003 Handout #1 Organizing Your Approach to a Data Analysis The general theme should be to maximize thinking about the data analysis and to minimize

More information

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

More information

E3: PROBABILITY AND STATISTICS lecture notes

E3: PROBABILITY AND STATISTICS lecture notes E3: PROBABILITY AND STATISTICS lecture notes 2 Contents 1 PROBABILITY THEORY 7 1.1 Experiments and random events............................ 7 1.2 Certain event. Impossible event............................

More information

" Y. Notation and Equations for Regression Lecture 11/4. Notation:

 Y. Notation and Equations for Regression Lecture 11/4. Notation: Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

More information