Elementary Statistics

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

1) Overview 2) Sample or Census 3) The Sampling Design Process i. Define the Target Population ii. Determine the Sampling Frame iii.

1) Overview 2) Sample or Census 3) The Sampling Design Process i. Define the Target Population ii. Determine the Sampling Frame iii. 1) Overview 2) Sample or Census 3) The Sampling Design Process i. Define the Target Population ii. Determine the Sampling Frame iii. Select a Sampling Technique iv. Determine the Sample Size v. Execute

More information

Chapter 1: The Nature of Probability and Statistics

Chapter 1: The Nature of Probability and Statistics Chapter 1: The Nature of Probability and Statistics Learning Objectives Upon successful completion of Chapter 1, you will have applicable knowledge of the following concepts: Statistics: An Overview and

More information

Sampling. Sampling Design and Procedures. Dr. Paurav Shukla. Marketing Research 1. Chapter Outline. Chapter Outline.

Sampling. Sampling Design and Procedures. Dr. Paurav Shukla. Marketing Research 1. Chapter Outline. Chapter Outline. Design and Procedures 1) Overview 2) Sample or Census 3) The Design Process i. Define the Target Population ii. Determine the Frame iii. Select a Technique iv. Determine the Sample Size v. Execute the

More information

Presentation Name 8/18/16

Presentation Name 8/18/16 Common statistical terms Sampling Methods Methods Data Measurements or observations of a variable Variable A characteristic that is observed or manipulated Can take on different values Statistical terms

More information

Lecture 4 Research Design and Sampling

Lecture 4 Research Design and Sampling Lecture 4 Research Design and Sampling Research Design Research design is a master plan specifying the methods and procedures for collecting and analyzing the needed information Research Designs in Terms

More information

Statistical POPULATION : -Collection of data we wish to gather information about - Eg: All students of CFS IIUM

Statistical POPULATION : -Collection of data we wish to gather information about - Eg: All students of CFS IIUM CHAPTER 3: INTODUCTION TO STATISTICS The Statistical Process Statistical POPULATION : -Collection of data we wish to gather information about - Eg: All students of CFS IIUM Make Inferences : Determine

More information

Concepts of Variables. Levels of Measurement. The Four Levels of Measurement. Nominal Scale. Greg C Elvers, Ph.D.

Concepts of Variables. Levels of Measurement. The Four Levels of Measurement. Nominal Scale. Greg C Elvers, Ph.D. Concepts of Variables Greg C Elvers, Ph.D. 1 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

More information

1.1 What is statistics? Data Collection. Important Definitions. What is data? Descriptive Statistics. Inferential Statistics

1.1 What is statistics? Data Collection. Important Definitions. What is data? Descriptive Statistics. Inferential Statistics 1.1 What is statistics? Data Collection Chapter 1 A science (bet you thought it was a math) of Collecting of data (Chap. 1) Organizing data (Chap. 2) Summarizing data (Chap. 2, 3) Analyzing data (Chap.

More information

Lecture - 8. Final Review

Lecture - 8. Final Review Lecture - 8 Final Review Decisions and Conclusions P-value method: Using the significance level α If P-value α, reject H0 If P-value > α, fail to reject H0 Traditional method: If the test statistic falls

More information

Qualitative. Nonnumerical

Qualitative. Nonnumerical ERRATA: CHAPTER 1 INTRODUCTION TO STATISTICS Page 5: (please cancel Types of data ) Variables Variables can be classified as either qualitative or quantitative. Quantitative variables are further classified

More information

MATH Elementary Probability and Statistics. Chapter 1 Introduction to Statistics

MATH Elementary Probability and Statistics. Chapter 1 Introduction to Statistics Elementary Probability and Statistics MATH 1530 Cheryl B. Slayden Associate Professor of Mathematics Some Graphics by Bob Maschak Media Specialist 1 Permission has been granted by Pearson/Addison-Wesley

More information

Chapter 1. Introduction to Statistics

Chapter 1. Introduction to Statistics Chapter 1 Introduction to Statistics Lesson 1-1 Overview What is Statistics? Statistics is the science of: Collecting information Surveys are used to collect data from a small part of a larger group so

More information

Sampling: Design and Procedures

Sampling: Design and Procedures Chapter Eleven Sampling: Design and Procedures 11-1 Brand name change and re-position Coke to New Coke Legend to Lenovo (2003) Panasonic, National, Technic all to Panasonic Vegemite to isnack 2.0 (social

More information

Data Collection L2 2. Timing and quantity of data collection

Data Collection L2 2. Timing and quantity of data collection presenting Data Collection Data Collection Data The management of data is an important skill to develop. In some situations, the data requirement is clear, and in other is less clear. Mostly you will find

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. 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

9.63 Laboratory in Visual Cognition

9.63 Laboratory in Visual Cognition 9.63 Laboratory in Visual Cognition Why do you need to know about methods if you work in an advertising firm? Fall 2009 Variables & Controls (Chapters 5 & 8) Confounded Experiment in Advertising In the

More information

Basic Statistical Concepts, Research Design, & Notation

Basic Statistical Concepts, Research Design, & Notation , Research Design, & Notation Variables, Scores, & Data A variable is a characteristic or condition that can change or take on different values. Most research begins with a general question about the relationship

More information

Introduction to Statistics

Introduction to Statistics 1 1.1 Introduction Introduction to Statistics Statistics is a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting and drawing

More information

Sampling Designs. 1. Simple random sampling (SRS) Steps: The method is not very different from winning a lottery.

Sampling Designs. 1. Simple random sampling (SRS) Steps: The method is not very different from winning a lottery. Sampling Designs 1. Simple random sampling (SRS) Steps: (1) Assign a single number to each element in the sampling frame. (2) Use random numbers to select elements into the sample until the desired number

More information

Introduction to Statistics Slide 1-1

Introduction to Statistics Slide 1-1 Chapter 1 Introduction to Statistics Slide 1-1 Data collections of observations (such as measurements, genders, survey responses) Slide 1-2 Statistics It is the study of the collection, organization, analysis,

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

Sampling Design. Population SAMPLING. Characteristics of Good Samples. Sampling. Sample -- contacting a portion of the population (e.g.

Sampling Design. Population SAMPLING. Characteristics of Good Samples. Sampling. Sample -- contacting a portion of the population (e.g. Sampling Design The process of obtaining information from a subset (sample) of a larger group (population) The results for the sample are then used to make estimates of the larger group Faster and cheaper

More information

Sampling Design SAMPLING. Sampling. Sample --contacting a portion of the population (e.g., 10% or 25%) Census -- the entire population

Sampling Design SAMPLING. Sampling. Sample --contacting a portion of the population (e.g., 10% or 25%) Census -- the entire population Sampling Design The process of obtaining information from a subset (sample) of a larger group (population) The results for the sample are then used to make estimates of the larger group Faster and cheaper

More information

CTRC Core Curriculum Seminar Series

CTRC Core Curriculum Seminar Series CTRC Core Curriculum Seminar Series Descriptive Statistics: Data Types and Measures, Central Tendency, Variability Chang-Xing Ma, PhD Associate Professor Department of Biostatistics, UB January 4, 2012

More information

Chapter 1 - The Nature of Probability and Statistics

Chapter 1 - The Nature of Probability and Statistics 1. Statistics is the science of conducting studies to A) solve a system of equations. B) hypothesize, experiment, and form conclusions. C) collect, organize, summarize, analyze, and draw conclusions from

More information

UNIT-II SAMPLING DISTRIBUTION AND ESTIMATION

UNIT-II SAMPLING DISTRIBUTION AND ESTIMATION Sampling: Design and Procedures UNIT-II SAMPLING DISTRIBUTION AND ESTIMATION Non Probability Sampling Convenience Judgemental Sampling Techniques Simple Random Quota Snow Ball Systematic Probability Sampling

More information

Handout 1: Basic Definitions, Samples and Populations, and Sampling Methods

Handout 1: Basic Definitions, Samples and Populations, and Sampling Methods Handout 1: Basic Definitions, Samples and Populations, and Sampling Methods Reading Assignment: Sections 1.1, 1.2, Chapter 2 Statistics v. statistics Statistics (capital S ) is a collection of techniques

More information

PROBABILITY SAMPLING: CONCEPTS AND TERMINOLOGY. Selecting individual observations to most efficiently yield knowledge without bias

PROBABILITY SAMPLING: CONCEPTS AND TERMINOLOGY. Selecting individual observations to most efficiently yield knowledge without bias PROBABILITY SAMPLING: CONCEPTS AND TERMINOLOGY Selecting individual observations to most efficiently yield knowledge without bias What is sampling? If all members of a population were identical, the population

More information

DATA COLLECTION AND ANALYSIS

DATA COLLECTION AND ANALYSIS DATA COLLECTION AND ANALYSIS Quality Education for Minorities (QEM) Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. August 23, 2013 Objectives of the Discussion 2 Discuss

More information

Chapter 1 (Definitions)

Chapter 1 (Definitions) FINAL EXAM REVIEW Chapter 1 (Definitions) Qualitative: Nominal: Ordinal: Quantitative: Ordinal: Interval: Ratio: Observational Study: Designed Experiment: Sampling: Cluster: Stratified: Systematic: Convenience:

More information

6. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey):

6. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey): MATH 1040 REVIEW (EXAM I) Chapter 1 1. For the studies described, identify the population, sample, population parameters, and sample statistics: a) The Gallup Organization conducted a poll of 1003 Americans

More information

Data. Statistics. Chapter 1 5/27/2014. Data are collections of observations (such as measurements, genders, survey responses)

Data. Statistics. Chapter 1 5/27/2014. Data are collections of observations (such as measurements, genders, survey responses) Chapter 1 Data Data are collections of observations (such as measurements, genders, survey responses) Statistics Statistics is the science of planning studies and experiments, obtaining data, and then

More information

Instructor: Darryl Alien Assignment: Homework I Date: Course: Elementary Statistics Book: Triola: Elementary Statistics, 11 th ed

Instructor: Darryl Alien Assignment: Homework I Date: Course: Elementary Statistics Book: Triola: Elementary Statistics, 11 th ed Student: Instructor: Darryl Alien Assignment: Homework I Date: Course: Elementary Statistics 60157 Time: Book: Triola: Elementary Statistics, 11 th ed 1. What is a voluntary response sample? Choose the

More information

Math 240 Practice Exam 1 Note: Show all work whenever possible for full credit. You may leave your answers in terms of fractions.

Math 240 Practice Exam 1 Note: Show all work whenever possible for full credit. You may leave your answers in terms of fractions. Name: (Solution on last page)... Math 240 Practice Exam 1 Note: Show all work whenever possible for full credit. You may leave your answers in terms of fractions. Formulas: 2 2 x x n x x s x x n f x f

More information

Review: Stratified Sampling

Review: Stratified Sampling STA 291 Lecture 5 Chap 4 Graphical and Tabular Techniques for categorical data Graphical Techniques for numerical data STA 291 - Lecture 5 1 Review: Stratified Sampling Suppose the population can be divided

More information

STA 291 Lecture 5 Chap 4

STA 291 Lecture 5 Chap 4 STA 291 Lecture 5 Chap 4 Graphical and Tabular Techniques for categorical data Graphical Techniques for numerical data STA 291 - Lecture 5 1 Review: Stratified Sampling Suppose the population can be divided

More information

Unit 1: Research Design, Sampling & Measurement

Unit 1: Research Design, Sampling & Measurement Unit 1: Research Design, Sampling & Measurement irat You have 10 minutes to do it Mark your answer on both answer sheet and question sheet Turn in the answer sheet GOG502/PLN504 Youqin Huang 1 GOG502/PLN504

More information

unit of analysis = type of case you are collecting data on and to whom you want to generalize

unit of analysis = type of case you are collecting data on and to whom you want to generalize SAMPLING Introduction sample = subset of a population population = all cases that apply to your RQ element = single member of the population Sampling Frame = list of all population elements stratum= sub

More information

Directions: Answer the questions by bubbling in the best choice on your answer sheet.

Directions: Answer the questions by bubbling in the best choice on your answer sheet. FGCU INVITATIONAL MATH COMPETITION INDIVIDUAL STATISTIC TEST Directions: Answer the questions by bubbling in the best choice on your answer sheet. (1) A coin is tossed 1,000 times and 650 heads are observed.

More information

1. A population is a collection of all individuals, objects, or measurements of

1. A population is a collection of all individuals, objects, or measurements of Chapter 01 What Is Statistics? True / False Questions 1. A population is a collection of all individuals, objects, or measurements of interest. True False 2. Statistics are used as a basis for making decisions.

More information

MATH 10: Elementary Statistics and Probability Chapter 1: Sampling and Data

MATH 10: Elementary Statistics and Probability Chapter 1: Sampling and Data MATH 10: Elementary Statistics and Probability Chapter 1: Sampling and Data Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 What is Statistics? Statistics The collection of methods

More information

What Is Statistics. Chapter 1

What Is Statistics. Chapter 1 What Is Statistics Chapter 1 Learning Objectives Explain why we study statistics. Explain what is meant by descriptive statistics and inferential statistics. Distinguish between a quantitative variable

More information

Conceptualization. 1. Definition 2. Dimensions 3. Indicators 4. Comparison of Concept, Dimension, and Indicator 5. Example

Conceptualization. 1. Definition 2. Dimensions 3. Indicators 4. Comparison of Concept, Dimension, and Indicator 5. Example Conceptualization 1. Definition 2. Dimensions 3. Indicators 4. Comparison of Concept, Dimension, and Indicator 5. Example Definition Conceptualization is the process of development and clarification of

More information

II. DISTRIBUTIONS distribution normal distribution. standard scores

II. DISTRIBUTIONS distribution normal distribution. standard scores Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

More information

Sampling in Marketing Research

Sampling in Marketing Research Sampling in Marketing Research 1 Basics of sampling I A sample is a part of a whole to show what the rest is like. Sampling helps to determine the corresponding value of the population and plays a vital

More information

Choosing the Correct Statistical Test

Choosing the Correct Statistical Test Choosing the Correct Statistical Test Chi-Square Analysis February 20, 2006 Choosing the Correct Statistical Test Knowing which statistical test to use in order to test the relationship between your independent

More information

Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.

More information

Lecture 1: Chapters 1, 2 Introduction, Sampling

Lecture 1: Chapters 1, 2 Introduction, Sampling Lecture 1: Chapters 1, 2 Introduction, Sampling Variable Types and Roles Summarizing Variables 4 Processes of Statistics Data Production; Sampling Cengage Learning Elementary Statistics: Looking at the

More information

Chapter 7 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 7 Multiple Choice Questions (The answers are provided after the last question.) Chapter 7 Multiple Choice Questions (The answers are provided after the last question.) 1. When each member of a population has an equally likely chance of being selected, this is called: a. A nonrandom

More information

Sample Design and Sampling Error. Professor Ron Fricker Naval Postgraduate School Monterey, California

Sample Design and Sampling Error. Professor Ron Fricker Naval Postgraduate School Monterey, California Sample Design and Sampling Error Professor Ron Fricker Naval Postgraduate School Monterey, California 1 Goals for this Lecture Introduction to sampling Convenience vs. random sampling Types of random sampling:

More information

What is statistics? Why do engineers need statistics?

What is statistics? Why do engineers need statistics? ENGINEERING STATISTICS What is statistics? Why do engineers need statistics? Engineers build, design, operate, and/or improve physical systems and products. When theory fails, the engineer may need to

More information

Descriptive Statistics and Measurement Scales

Descriptive Statistics and Measurement Scales Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample

More information

STAT 100, Section 4 Sample Mid-term Examination I Fall 2015

STAT 100, Section 4 Sample Mid-term Examination I Fall 2015 STAT 100, Section 4 Sample Mid-term Examination I Fall 2015 The following 60 questions are similar to the types of questions you will see on the midterm exam. The actual midterm will be 50 to 60 multiple-choice

More information

Research Design Concepts. Independent and dependent variables Data types Sampling Validity and reliability

Research Design Concepts. Independent and dependent variables Data types Sampling Validity and reliability Research Design Concepts Independent and dependent variables Data types Sampling Validity and reliability Research Design Action plan for carrying out research How the research will be conducted to investigate

More information

Why Sample? Because heterogeneity or variability in population requires sampling --homogenous populations require only a single sample

Why Sample? Because heterogeneity or variability in population requires sampling --homogenous populations require only a single sample Sampling Why Sample? Because heterogeneity or variability in population requires sampling --homogenous populations require only a single sample A sample is said to be representative if the aggregate characteristics

More information

Data Collection. MATH 130, Elements of Statistics I. J. Robert Buchanan. Fall Department of Mathematics

Data Collection. MATH 130, Elements of Statistics I. J. Robert Buchanan. Fall Department of Mathematics Data Collection MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Big Definition Definition Statistics is the science of collecting, organizing, summarizing, and

More information

INTRODUCTION TO SURVEY SAMPLING

INTRODUCTION TO SURVEY SAMPLING INTRODUCTION TO SURVEY SAMPLING February 26, 2003 Karen Foote Retzer Survey Research Laboratory University of Illinois at Chicago www.srl.uic.edu Census or Sample? Census: Gathering information about every

More information

Chapter 1 What is Statistics?

Chapter 1 What is Statistics? Chapter 1 What is Statistics? True/False 1. A population is a collection of all individuals, objects, or measurements of interest. 2. A sample is a portion or part of the population of interest. 3. To

More information

Organizing and Graphing Data

Organizing and Graphing Data Department of Econometrics FVL UO Brno office 69a, tel. 973 442029 email:jiri.neubauer@unob.cz Statistics as a subject provides a body of principles and methodology for designing the process of data collection,

More information

Provide an appropriate response. 1) Define the terms population, sample, parameter and statistic. How does a census compare to a sample?

Provide an appropriate response. 1) Define the terms population, sample, parameter and statistic. How does a census compare to a sample? Math 227 Ch 1 Study Guide Name Provide an appropriate response. 1) Define the terms population, sample, parameter and statistic. How does a census compare to a sample? 2) Distinguish between categorical

More information

Introduction. Marc H. Mehlman University of New Haven

Introduction. Marc H. Mehlman University of New Haven Introduction Marc H. Mehlman marcmehlman@yahoo.com University of New Haven To understand God s thoughts, we must study statistics, for these are the measure of his purpose. Florence Nightingale Statistics:

More information

Statistical POPULATION: -Collection of data we wish to gather information about -Eg: All students of CFS IIUM

Statistical POPULATION: -Collection of data we wish to gather information about -Eg: All students of CFS IIUM CHAPTER 3: INTODUCTION TO STATISTICS The Statistical Process Statistical POPULATION: -Collection of data we wish to gather information about -Eg: All students of CFS IIUM Make Inferences : Determine what

More information

Andria Christodoulou BSc, MSc, ACCA. Sampling

Andria Christodoulou BSc, MSc, ACCA. Sampling Sampling Types of Statistics Descriptive Statistics Collecting, summarizing, and describing data Inferential Statistics Drawing conclusions and/or making decisions concerning a population based only on

More information

2.1 Data: Types of Data and Levels of Measurement

2.1 Data: Types of Data and Levels of Measurement 2.1 Data: Types of Data and Levels of Measurement 1 Quantitative or Qualitative?! Quantitative data consist of values representing counts or measurements " Variable: Year in school! Qualitative (or non-numeric)

More information

Introduction to Statistics

Introduction to Statistics 1 Introduction to Statistics LEARNING OBJECTIVES After reading this chapter, you should be able to: 1. Distinguish between descriptive and inferential statistics. 2. Explain how samples and populations,

More information

AP Statistics A Summary of Sampling and Sampling Methods

AP Statistics A Summary of Sampling and Sampling Methods Introduction Surveying an entire population is generally expensive in terms of both time and money. We live in a country of over 300 million people, spread over 50 states and almost four million square

More information

Statistics for Managers Using Microsoft Excel 5th Edition

Statistics for Managers Using Microsoft Excel 5th Edition Statistics for Managers Using Microsoft Excel 5th Edition Module 1: Reduction Statistics for Managers Using Microsoft Excel, 5e 2008 Pearson Prentice-Hall, Inc. Chap 1-1 Course structure - Modules Module

More information

Dallastown Area School District Mathematics Curriculum Map Probability and Statistics

Dallastown Area School District Mathematics Curriculum Map Probability and Statistics Mathematics Curriculum Map Probability and What is? How do we define and interpret the different types of data (variables) used in statistics? 1.1-1.2 2 days Define the basic terms needed for statistics

More information

Chapter 1 Introduction to Statistics

Chapter 1 Introduction to Statistics Chapter 1 Introduction to Statistics 1-1 Review and Preview 1-2 Statistical and Critical Thinking 1-3 Types of Data 1-4 Collecting Sample Data Preview Polls, studies, surveys and other data collecting

More information

Statistics: Introduction:

Statistics: Introduction: Statistics: Introduction: STAT- 114 Notes Definitions Statistics Collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and

More information

Quantitative or Qualitative?

Quantitative or Qualitative? 2.1 Data: and Levels of Measurement 1 Quantitative or Qualitative?! Quantitative data consist of values representing counts or measurements " Variable: Year in school! Qualitative (or non-numeric) data

More information

A variable is the mathematical model for a characteristic observed or measured in an experiment, survey, or observational study.

A variable is the mathematical model for a characteristic observed or measured in an experiment, survey, or observational study. Types of Variables This material is covered partially by Sall, Lehman and Creighton (2001) Chapters 1 and 2, by Milton (1992) Chapters 1 and 4, by Sokal and Rohlf (1995) Chapters 1 and 2, by Koopmans (1987),

More information

4) A researcher randomly selects and interviews fifty male and fifty female teachers. 4)

4) A researcher randomly selects and interviews fifty male and fifty female teachers. 4) THT # 4 STAT 2023 SPR'11 Due Wed. April 6 NO EXCEPTIONS Name SHOW ALL WORK ATTACHED Use the given data to construct a frequency distribution. 1) Kevin asked some of his friends how many hours they had

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. Exam Name 1) Statistics is the science of conducting studies to 1) A) solve a system of equations. B) collect, organize, summarize, analyze, and draw conclusions from data. C) hypothesize, experiment,

More information

DEFINITIONS AND SCALING

DEFINITIONS AND SCALING CHAPTER 2 DEFINITIONS AND SCALING OBJECTIVES After completing this chapter, you should be able to define terms important for statistics, such as variable (independent and dependent), population and parameter,

More information

Basic Research Progress

Basic Research Progress Mgt 540 Research Methods Sampling Issues 1 Basic Research Progress Explorative - Descriptive (Qualitative) 1. Framework / Domain extant knowledge for reference 2. Research Design 3. Data collection / presentation

More information

SAMPLING METHODS. Chapter 5

SAMPLING METHODS. Chapter 5 SAMPLING METHODS Chapter 5 1 LEARNING OBJECTIVES Reasons for sampling Different sampling methods Probability & non probability sampling Advantages & disadvantages of each sampling method 2 SAMPLING A sample

More information

1.1 What is Statistics?

1.1 What is Statistics? 1.1 What is Statistics? Statistics is the science that deals with the collection, analysis, and interpretation of numerical information. This science can be divided into two areas: descriptive statistics

More information

Sampling. Typically a sample is just a small portion of the population. Census: inspection of the entire population

Sampling. Typically a sample is just a small portion of the population. Census: inspection of the entire population Sampling In most statistical applications, one should select a sample from a population. The idea is to infer, or make educated guesses about, the population from information in the sample. Typically a

More information

Descriptive Statistics. Applied Statistics Advanced Data Analysis. Variable Types. Descriptive Statistics DS - 1

Descriptive Statistics. Applied Statistics Advanced Data Analysis. Variable Types. Descriptive Statistics DS - 1 Applied Statistics Advanced Data Analysis Andy Chang Youngstown State University Statistics in Broader Sense Statistics is a field of study concerned with the 1) data collection, [Producing data] 2) organization,

More information

Outline. Planning a statistically sound research project. Types of research studies. Sample Surveys

Outline. Planning a statistically sound research project. Types of research studies. Sample Surveys Outline Planning a statistically sound research project. Rick White October 28, 2015 Types of research studies Planning your research study Sample size calculations Experimental design Types of analysis

More information

Data. Observations, Measurements or Responses that are collected. There are Two Types of Data

Data. Observations, Measurements or Responses that are collected. There are Two Types of Data Section : Types of Data Descriptive Statistics is the act of collecting, organizing, displaying and summarizing information about populations or samples of populations. Inferential statistics involves

More information

Chapter 7 Sampling and Sampling Distributions. Learning objectives

Chapter 7 Sampling and Sampling Distributions. Learning objectives Chapter 7 Sampling and Sampling Distributions Slide 1 Learning objectives 1. Understand Simple Random Sampling 2. Understand Point Estimation and be able to compute point estimates 3. Understand Sampling

More information

Sample Size Matters What type of cook (researcher) are you?

Sample Size Matters What type of cook (researcher) are you? Sample Size Matters What type of cook (researcher) are you? Excerpted from: Dissertation and Scholarly Research: Recipes for Success, 2012 Edition (Simon & Goes, 2012) Find this and many other dissertation

More information

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo Readings: Ha and Ha Textbook - Chapters 1 8 Appendix D & E (online) Plous - Chapters 10, 11, 12 and 14 Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability

More information

STA2023 FINAL EXAM REVIEW

STA2023 FINAL EXAM REVIEW STA2023 FINAL EXAM REVIEW 1. Data that can be classified according to color are measured on what scale? (a) Nominal (b) Ordinal (c) Interval (d) Ratio 2. The difference between a sample result and 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

Biostatistics 621: Statistical Methods I. Fall Semester 2007

Biostatistics 621: Statistical Methods I. Fall Semester 2007 Biostatistics 621: Statistical Methods I Fall Semester 2007 Course Information Instructor: T. Mark Beasley, PhD Associate Professor of Biostatistics Office: Ryals Room 309E Phone: (205) 975-4957 Email:

More information

Sampling Methods Using STATA

Sampling Methods Using STATA Sampling Methods Using STATA Department of Internal Medicine Division of Epidemiology, Biostatistics, & Preventive Medicine University of New Mexico Health Sciences Center September 14, 2015 Sampling (Department

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

Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign

Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign Key Points 1. Data 2. Variable 3. Types of data 4. Define

More information

An Introduction to Complex Survey Sampling

An Introduction to Complex Survey Sampling An Introduction to Complex Survey Sampling Trent D. Buskirk, Ph.D. Vice President Statistics and Methodology Marketing Systems Group May 7, 2014 5/7/2014 1 Warm-Up Three men are in a hot-air balloon. Soon,

More information

Sampling method refers to the way that observations are selected from a population to be in the sample for a sample survey.

Sampling method refers to the way that observations are selected from a population to be in the sample for a sample survey. Session 02 Survey Sampling Methods Why Is This Important? Who is in our study and how we sample them are critical aspects of psychological research. The sample that we draw for our study determines the

More information

Methods Supplementary Lecture 1: Survey Sampling and Design

Methods Supplementary Lecture 1: Survey Sampling and Design Methods Supplementary Lecture 1: Survey Sampling and Design Department of Government London School of Economics and Political Science 1 Populations Representativeness Sampling Frames Sampling without a

More information

Section 1: Glossary of Terms Used in STEPS

Section 1: Glossary of Terms Used in STEPS Introduction This section provides an alphabetical list of all the terms used in a STEPS surveillance with definitions that are appropriate for STEPS. Term Agestandardisation Archive Average Bias Cluster

More information

ADMS Sampling Technique and Survey Studies

ADMS Sampling Technique and Survey Studies Survey sampling Many of our behaviours and action are based on samples (could be of size one), for incidence, our like or dislike of a foreign dish. Would such a sample be representative of the whole population?

More information

Experimental design and inferential statistics: An introduction. Dr. Alissa Melinger School of Psychology University of Dundee

Experimental design and inferential statistics: An introduction. Dr. Alissa Melinger School of Psychology University of Dundee Experimental design and inferential statistics: An introduction Dr. Alissa Melinger School of Psychology University of Dundee Structure of Tutorial Block 1: Background and fundamental underpinnings to

More information

Chapter 1 Introduction

Chapter 1 Introduction Chapter 1 Introduction Statistics is the science of data. Data are the numerical values containing some information. Statistical tools can be used on a data set to draw statistical inferences. These statistical

More information

Module 1: Introduction to Statistics. The Applied Research Center

Module 1: Introduction to Statistics. The Applied Research Center Module 1: Introduction to Statistics The Applied Research Center Module 1 Overview } The Role of Statistics } The Research Process } Threats to Validity } Statistical Terminology } Scales of Measurement

More information