POLI 443 Applied Political Research

Size: px
Start display at page:

Download "POLI 443 Applied Political Research"

Transcription

1 POLI 443 Applied Political Research Session 6: Tests of Hypotheses Contingency Analysis Lecturer: Prof. A. Essuman-Johnson, Dept. of Political Science Contact Information: College of Education School of Continuing and Distance Education 2014/ /2017

2 CONTINGENCY ANALYSIS CHI-SQUARE TEST This refers to the idea of applying correlation to qualitative or non quantitative data. Contingency analysis deals with computing the relationship between two qualitative variables. As a test of the significance between two qualitative variables the computations assume that there is no relation between the two variables. On the basis of this assumption, a critical or expected frequencies are computed. Slide 2

3 The difference between the values given (observed values) and the expected values are compared and the greater the difference between the expected and observed frequencies, the stronger the relationship between the two variables. The usual measure of the discrepancy between the observed and expected frequencies is the chi-square test. It is defined as follows: χ 2 = (O F E F ) 2 /E F Slide 3

4 Steps to follow in the χ 2 Test Step 1: Set the Null (H O ) & Alternative (H A ) hypothesis Step 2: Select the test statistic i.e. T = χ 2 = (O F E F ) 2 /E F Step 3: Compute the Expected frequencies (E F ) for the data where E F = (R T )(C T )/N Step 4: Develop working sheet to compute χ 2 from the O F and E F values Step 5: Calculate DF and use it with the given probability level to read χ 2 from table Slide 4

5 Step 6: Set the DR (Decision Rule) as basis for accepting or rejection the Null hypothesis Step 7: Draw conclusion: Compare the Calculated χ 2 (from the working sheet) and χ 2 read from the table and decide whether to accept or reject the H O and H A Illustration A study was conducted about the relationship between region and party vote of 412 voters during one general election in Ghana with the following data: Slide 5

6 Party Vote Ashanti Region Volta NDC NPP Using a 5% level of significance determine if a relationship exist between Region and Party Vote. Slide 6

7 Solution Step 1: Set the Null (H O ) & Alternative (H A ) hypothesis H O: There is no relationship between region and party vote H A : There is a significant relationship between region and party vote Step 2: Select the test statistic i.e. T = χ 2 = (O F E F ) 2 /E F Slide 7

8 Step 3: Compute the Expected frequencies (E F ) for the data where E F = (R T )(C T )/N Computations: 111 = (195)(206)/412 = = (217)(206)/412 = = (217)(206)/412 = = (195)(206)/412 = 97.5 Slide 8

9 Step 4: Developthe working sheet to compute χ 2 from the O F and E F values O F E F O F - E F (O F - E F ) 2 (O F - E F ) 2 /E F Slide 9

10 Step 5: Calculate DF (Degree of freedom) and use it with the given probability level to read χ 2 from table. DF = (#Rows 1)(#Columns 1) for a 2 by 2 table (2-1)(2-1) = 1 x 1 From χ 2 tables at 5% with 1 df, χ 2 = Slide 10

11 Step 6: Set the DR (Decision Rule) as basis for accepting or rejection the Null hypothesis: Accept H o if χ 2 calculated > χ 2 expected (from tables for 5%) Accept H o if χ 2 calculated (7.10) is < χ 2 expected (from tables for 5%) Reject H o otherwise Slide 11

12 Step 7: Draw conclusion: Compare the Calculated χ 2 (from the working sheet) and χ 2 expected (read from the table) and decide whether to accept or reject the H O and H A Conclusion: The calculated χ 2 (7.10) is > χ 2 from tables which means that our calculated χ 2 of 7.1 is significant at 5% level and we reject H o and conclude (with 95% confidence) that there is a relationship between Region and Party vote i.e. region influences how people vote. Slide 12

13 THANK YOU Slide 13

POLI 443 Applied Political Research

POLI 443 Applied Political Research POLI 443 Applied Political Research Session 4 Tests of Hypotheses The Normal Curve Lecturer: Prof. A. Essuman-Johnson, Dept. of Political Science Contact Information: aessuman-johnson@ug.edu.gh College

More information

Lecture 28 Chi-Square Analysis

Lecture 28 Chi-Square Analysis Lecture 28 STAT 225 Introduction to Probability Models April 23, 2014 Whitney Huang Purdue University 28.1 χ 2 test for For a given contingency table, we want to test if two have a relationship or not

More information

STP 226 ELEMENTARY STATISTICS NOTES

STP 226 ELEMENTARY STATISTICS NOTES STP 226 ELEMENTARY STATISTICS NOTES PART 1V INFERENTIAL STATISTICS CHAPTER 12 CHI SQUARE PROCEDURES 12.1 The Chi Square Distribution A variable has a chi square distribution if the shape of its distribution

More information

Rama Nada. -Ensherah Mokheemer. 1 P a g e

Rama Nada. -Ensherah Mokheemer. 1 P a g e - 9 - Rama Nada -Ensherah Mokheemer - 1 P a g e Quick revision: Remember from the last lecture that chi square is an example of nonparametric test, other examples include Kruskal Wallis, Mann Whitney and

More information

Quantitative Analysis and Empirical Methods

Quantitative Analysis and Empirical Methods Hypothesis testing Sciences Po, Paris, CEE / LIEPP Introduction Hypotheses Procedure of hypothesis testing Two-tailed and one-tailed tests Statistical tests with categorical variables A hypothesis A testable

More information

The goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions.

The goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions. The goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions. A common problem of this type is concerned with determining

More information

Chi-Square. Heibatollah Baghi, and Mastee Badii

Chi-Square. Heibatollah Baghi, and Mastee Badii 1 Chi-Square Heibatollah Baghi, and Mastee Badii Different Scales, Different Measures of Association Scale of Both Variables Nominal Scale Measures of Association Pearson Chi-Square: χ 2 Ordinal Scale

More information

MATH 240. Chapter 8 Outlines of Hypothesis Tests

MATH 240. Chapter 8 Outlines of Hypothesis Tests MATH 4 Chapter 8 Outlines of Hypothesis Tests Test for Population Proportion p Specify the null and alternative hypotheses, ie, choose one of the three, where p is some specified number: () H : p H : p

More information

Introduction to Statistical Data Analysis Lecture 7: The Chi-Square Distribution

Introduction to Statistical Data Analysis Lecture 7: The Chi-Square Distribution Introduction to Statistical Data Analysis Lecture 7: The Chi-Square Distribution James V. Lambers Department of Mathematics The University of Southern Mississippi James V. Lambers Statistical Data Analysis

More information

Inferences About Two Proportions

Inferences About Two Proportions Inferences About Two Proportions Quantitative Methods II Plan for Today Sampling two populations Confidence intervals for differences of two proportions Testing the difference of proportions Examples 1

More information

PSYC 331 STATISTICS FOR PSYCHOLOGISTS

PSYC 331 STATISTICS FOR PSYCHOLOGISTS PSYC 331 STATISTICS FOR PSYCHOLOGISTS Session 4 A PARAMETRIC STATISTICAL TEST FOR MORE THAN TWO POPULATIONS Lecturer: Dr. Paul Narh Doku, Dept of Psychology, UG Contact Information: pndoku@ug.edu.gh College

More information

Lecture 41 Sections Mon, Apr 7, 2008

Lecture 41 Sections Mon, Apr 7, 2008 Lecture 41 Sections 14.1-14.3 Hampden-Sydney College Mon, Apr 7, 2008 Outline 1 2 3 4 5 one-proportion test that we just studied allows us to test a hypothesis concerning one proportion, or two categories,

More information

T.I.H.E. IT 233 Statistics and Probability: Sem. 1: 2013 ESTIMATION AND HYPOTHESIS TESTING OF TWO POPULATIONS

T.I.H.E. IT 233 Statistics and Probability: Sem. 1: 2013 ESTIMATION AND HYPOTHESIS TESTING OF TWO POPULATIONS ESTIMATION AND HYPOTHESIS TESTING OF TWO POPULATIONS In our work on hypothesis testing, we used the value of a sample statistic to challenge an accepted value of a population parameter. We focused only

More information

Statistics for Managers Using Microsoft Excel

Statistics for Managers Using Microsoft Excel Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 1 Chi-Square Tests and Nonparametric Tests Statistics for Managers Using Microsoft Excel 7e Copyright 014 Pearson Education, Inc. Chap

More information

Chapter 10. Chapter 10. Multinomial Experiments and. Multinomial Experiments and Contingency Tables. Contingency Tables.

Chapter 10. Chapter 10. Multinomial Experiments and. Multinomial Experiments and Contingency Tables. Contingency Tables. Chapter 10 Multinomial Experiments and Contingency Tables 1 Chapter 10 Multinomial Experiments and Contingency Tables 10-1 1 Overview 10-2 2 Multinomial Experiments: of-fitfit 10-3 3 Contingency Tables:

More information

16.3 One-Way ANOVA: The Procedure

16.3 One-Way ANOVA: The Procedure 16.3 One-Way ANOVA: The Procedure Tom Lewis Fall Term 2009 Tom Lewis () 16.3 One-Way ANOVA: The Procedure Fall Term 2009 1 / 10 Outline 1 The background 2 Computing formulas 3 The ANOVA Identity 4 Tom

More information

Study Ch. 9.3, #47 53 (45 51), 55 61, (55 59)

Study Ch. 9.3, #47 53 (45 51), 55 61, (55 59) GOALS: 1. Understand that 2 approaches of hypothesis testing exist: classical or critical value, and p value. We will use the p value approach. 2. Understand the critical value for the classical approach

More information

Example. χ 2 = Continued on the next page. All cells

Example. χ 2 = Continued on the next page. All cells Section 11.1 Chi Square Statistic k Categories 1 st 2 nd 3 rd k th Total Observed Frequencies O 1 O 2 O 3 O k n Expected Frequencies E 1 E 2 E 3 E k n O 1 + O 2 + O 3 + + O k = n E 1 + E 2 + E 3 + + E

More information

Class 24. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700

Class 24. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700 Class 4 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 013 by D.B. Rowe 1 Agenda: Recap Chapter 9. and 9.3 Lecture Chapter 10.1-10.3 Review Exam 6 Problem Solving

More information

Class 19. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700

Class 19. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700 Class 19 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 2017 by D.B. Rowe 1 Agenda: Recap Chapter 8.3-8.4 Lecture Chapter 8.5 Go over Exam. Problem Solving

More information

(x t. x t +1. TIME SERIES (Chapter 8 of Wilks)

(x t. x t +1. TIME SERIES (Chapter 8 of Wilks) 45 TIME SERIES (Chapter 8 of Wilks) In meteorology, the order of a time series matters! We will assume stationarity of the statistics of the time series. If there is non-stationarity (e.g., there is a

More information

Hint: The following equation converts Celsius to Fahrenheit: F = C where C = degrees Celsius F = degrees Fahrenheit

Hint: The following equation converts Celsius to Fahrenheit: F = C where C = degrees Celsius F = degrees Fahrenheit Amherst College Department of Economics Economics 360 Fall 2014 Exam 1: Solutions 1. (10 points) The following table in reports the summary statistics for high and low temperatures in Key West, FL from

More information

HYPOTHESIS TESTING: THE CHI-SQUARE STATISTIC

HYPOTHESIS TESTING: THE CHI-SQUARE STATISTIC 1 HYPOTHESIS TESTING: THE CHI-SQUARE STATISTIC 7 steps of Hypothesis Testing 1. State the hypotheses 2. Identify level of significant 3. Identify the critical values 4. Calculate test statistics 5. Compare

More information

Hypothesis Tests and Estimation for Population Variances. Copyright 2014 Pearson Education, Inc.

Hypothesis Tests and Estimation for Population Variances. Copyright 2014 Pearson Education, Inc. Hypothesis Tests and Estimation for Population Variances 11-1 Learning Outcomes Outcome 1. Formulate and carry out hypothesis tests for a single population variance. Outcome 2. Develop and interpret confidence

More information

13.1 Categorical Data and the Multinomial Experiment

13.1 Categorical Data and the Multinomial Experiment Chapter 13 Categorical Data Analysis 13.1 Categorical Data and the Multinomial Experiment Recall Variable: (numerical) variable (i.e. # of students, temperature, height,). (non-numerical, categorical)

More information

Psych 230. Psychological Measurement and Statistics

Psych 230. Psychological Measurement and Statistics Psych 230 Psychological Measurement and Statistics Pedro Wolf December 9, 2009 This Time. Non-Parametric statistics Chi-Square test One-way Two-way Statistical Testing 1. Decide which test to use 2. State

More information

Econ 325: Introduction to Empirical Economics

Econ 325: Introduction to Empirical Economics Econ 325: Introduction to Empirical Economics Lecture 6 Sampling and Sampling Distributions Ch. 6-1 Populations and Samples A Population is the set of all items or individuals of interest Examples: All

More information

UC Berkeley Math 10B, Spring 2015: Midterm 2 Prof. Sturmfels, April 9, SOLUTIONS

UC Berkeley Math 10B, Spring 2015: Midterm 2 Prof. Sturmfels, April 9, SOLUTIONS UC Berkeley Math 10B, Spring 2015: Midterm 2 Prof. Sturmfels, April 9, SOLUTIONS 1. (5 points) You are a pollster for the 2016 presidential elections. You ask 0 random people whether they would vote for

More information

General Certificate of Education Advanced Level Examination June 2014

General Certificate of Education Advanced Level Examination June 2014 General Certificate of Education Advanced Level Examination June 2014 Biology BIO6T/Q14/task Unit 6T A2 Investigative Skills Assignment Task Sheet Introduction Investigating populations You will use leaves

More information

2 and F Distributions. Barrow, Statistics for Economics, Accounting and Business Studies, 4 th edition Pearson Education Limited 2006

2 and F Distributions. Barrow, Statistics for Economics, Accounting and Business Studies, 4 th edition Pearson Education Limited 2006 and F Distributions Lecture 9 Distribution The distribution is used to: construct confidence intervals for a variance compare a set of actual frequencies with expected frequencies test for association

More information

Parametric versus Nonparametric Statistics-when to use them and which is more powerful? Dr Mahmoud Alhussami

Parametric versus Nonparametric Statistics-when to use them and which is more powerful? Dr Mahmoud Alhussami Parametric versus Nonparametric Statistics-when to use them and which is more powerful? Dr Mahmoud Alhussami Parametric Assumptions The observations must be independent. Dependent variable should be continuous

More information

11-2 Multinomial Experiment

11-2 Multinomial Experiment Chapter 11 Multinomial Experiments and Contingency Tables 1 Chapter 11 Multinomial Experiments and Contingency Tables 11-11 Overview 11-2 Multinomial Experiments: Goodness-of-fitfit 11-3 Contingency Tables:

More information

Review: General Approach to Hypothesis Testing. 1. Define the research question and formulate the appropriate null and alternative hypotheses.

Review: General Approach to Hypothesis Testing. 1. Define the research question and formulate the appropriate null and alternative hypotheses. 1 Review: Let X 1, X,..., X n denote n independent random variables sampled from some distribution might not be normal!) with mean µ) and standard deviation σ). Then X µ σ n In other words, X is approximately

More information

7.2 One-Sample Correlation ( = a) Introduction. Correlation analysis measures the strength and direction of association between

7.2 One-Sample Correlation ( = a) Introduction. Correlation analysis measures the strength and direction of association between 7.2 One-Sample Correlation ( = a) Introduction Correlation analysis measures the strength and direction of association between variables. In this chapter we will test whether the population correlation

More information

Tables Table A Table B Table C Table D Table E 675

Tables Table A Table B Table C Table D Table E 675 BMTables.indd Page 675 11/15/11 4:25:16 PM user-s163 Tables Table A Standard Normal Probabilities Table B Random Digits Table C t Distribution Critical Values Table D Chi-square Distribution Critical Values

More information

Module 10: Analysis of Categorical Data Statistics (OA3102)

Module 10: Analysis of Categorical Data Statistics (OA3102) Module 10: Analysis of Categorical Data Statistics (OA3102) Professor Ron Fricker Naval Postgraduate School Monterey, California Reading assignment: WM&S chapter 14.1-14.7 Revision: 3-12 1 Goals for this

More information

Chapter 5: HYPOTHESIS TESTING

Chapter 5: HYPOTHESIS TESTING MATH411: Applied Statistics Dr. YU, Chi Wai Chapter 5: HYPOTHESIS TESTING 1 WHAT IS HYPOTHESIS TESTING? As its name indicates, it is about a test of hypothesis. To be more precise, we would first translate

More information

Section 9.4. Notation. Requirements. Definition. Inferences About Two Means (Matched Pairs) Examples

Section 9.4. Notation. Requirements. Definition. Inferences About Two Means (Matched Pairs) Examples Objective Section 9.4 Inferences About Two Means (Matched Pairs) Compare of two matched-paired means using two samples from each population. Hypothesis Tests and Confidence Intervals of two dependent means

More information

CHAPTER 17 CHI-SQUARE AND OTHER NONPARAMETRIC TESTS FROM: PAGANO, R. R. (2007)

CHAPTER 17 CHI-SQUARE AND OTHER NONPARAMETRIC TESTS FROM: PAGANO, R. R. (2007) FROM: PAGANO, R. R. (007) I. INTRODUCTION: DISTINCTION BETWEEN PARAMETRIC AND NON-PARAMETRIC TESTS Statistical inference tests are often classified as to whether they are parametric or nonparametric Parameter

More information

Sociology 6Z03 Review II

Sociology 6Z03 Review II Sociology 6Z03 Review II John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review II Fall 2016 1 / 35 Outline: Review II Probability Part I Sampling Distributions Probability

More information

The Chi-Square Distributions

The Chi-Square Distributions MATH 183 The Chi-Square Distributions Dr. Neal, WKU The chi-square distributions can be used in statistics to analyze the standard deviation σ of a normally distributed measurement and to test the goodness

More information

Econ 325: Introduction to Empirical Economics

Econ 325: Introduction to Empirical Economics Econ 325: Introduction to Empirical Economics Chapter 9 Hypothesis Testing: Single Population Ch. 9-1 9.1 What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population

More information

AMS7: WEEK 7. CLASS 1. More on Hypothesis Testing Monday May 11th, 2015

AMS7: WEEK 7. CLASS 1. More on Hypothesis Testing Monday May 11th, 2015 AMS7: WEEK 7. CLASS 1 More on Hypothesis Testing Monday May 11th, 2015 Testing a Claim about a Standard Deviation or a Variance We want to test claims about or 2 Example: Newborn babies from mothers taking

More information

Statistics for Business and Economics

Statistics for Business and Economics Statistics for Business and Economics Chapter 6 Sampling and Sampling Distributions Ch. 6-1 6.1 Tools of Business Statistics n Descriptive statistics n Collecting, presenting, and describing data n Inferential

More information

Chi Square Analysis M&M Statistics. Name Period Date

Chi Square Analysis M&M Statistics. Name Period Date Chi Square Analysis M&M Statistics Name Period Date Have you ever wondered why the package of M&Ms you just bought never seems to have enough of your favorite color? Or, why is it that you always seem

More information

Sampling Distributions: Central Limit Theorem

Sampling Distributions: Central Limit Theorem Review for Exam 2 Sampling Distributions: Central Limit Theorem Conceptually, we can break up the theorem into three parts: 1. The mean (µ M ) of a population of sample means (M) is equal to the mean (µ)

More information

CBA4 is live in practice mode this week exam mode from Saturday!

CBA4 is live in practice mode this week exam mode from Saturday! Announcements CBA4 is live in practice mode this week exam mode from Saturday! Material covered: Confidence intervals (both cases) 1 sample hypothesis tests (both cases) Hypothesis tests for 2 means as

More information

10.4 Hypothesis Testing: Two Independent Samples Proportion

10.4 Hypothesis Testing: Two Independent Samples Proportion 10.4 Hypothesis Testing: Two Independent Samples Proportion Example 3: Smoking cigarettes has been known to cause cancer and other ailments. One politician believes that a higher tax should be imposed

More information

Inferences About Two Population Proportions

Inferences About Two Population Proportions Inferences About Two Population Proportions MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Background Recall: for a single population the sampling proportion

More information

10.2 Hypothesis Testing with Two-Way Tables

10.2 Hypothesis Testing with Two-Way Tables 10.2 Hypothesis Testing with Two-Way Tables Part 2: more examples 3x3 Two way table 2x3 Two-way table (worksheet) 1 Example 2: n Is there an association between the type of school area and the students'

More information

Lecture 9 Two-Sample Test. Fall 2013 Prof. Yao Xie, H. Milton Stewart School of Industrial Systems & Engineering Georgia Tech

Lecture 9 Two-Sample Test. Fall 2013 Prof. Yao Xie, H. Milton Stewart School of Industrial Systems & Engineering Georgia Tech Lecture 9 Two-Sample Test Fall 2013 Prof. Yao Xie, yao.xie@isye.gatech.edu H. Milton Stewart School of Industrial Systems & Engineering Georgia Tech Computer exam 1 18 Histogram 14 Frequency 9 5 0 75 83.33333333

More information

We know from STAT.1030 that the relevant test statistic for equality of proportions is:

We know from STAT.1030 that the relevant test statistic for equality of proportions is: 2. Chi 2 -tests for equality of proportions Introduction: Two Samples Consider comparing the sample proportions p 1 and p 2 in independent random samples of size n 1 and n 2 out of two populations which

More information

9.5 t test: one μ, σ unknown

9.5 t test: one μ, σ unknown GOALS: 1. Recognize the assumptions for a 1 mean t test (srs, nd or large sample size, population stdev. NOT known). 2. Understand that the actual p value (area in the tail past the test statistic) is

More information

Institute of Actuaries of India

Institute of Actuaries of India Institute of Actuaries of India Subject CT3 Probability & Mathematical Statistics May 2011 Examinations INDICATIVE SOLUTION Introduction The indicative solution has been written by the Examiners with the

More information

General Certificate of Education Advanced Level Examination June 2013

General Certificate of Education Advanced Level Examination June 2013 General Certificate of Education Advanced Level Examination June 2013 Human Biology HBI6T/P13/task Unit 6T A2 Investigative Skills Assignment Task Sheet Investigation into whether reaction time is different

More information

Statistical Analysis for QBIC Genetics Adapted by Ellen G. Dow 2017

Statistical Analysis for QBIC Genetics Adapted by Ellen G. Dow 2017 Statistical Analysis for QBIC Genetics Adapted by Ellen G. Dow 2017 I. χ 2 or chi-square test Objectives: Compare how close an experimentally derived value agrees with an expected value. One method to

More information

Question. Hypothesis testing. Example. Answer: hypothesis. Test: true or not? Question. Average is not the mean! μ average. Random deviation or not?

Question. Hypothesis testing. Example. Answer: hypothesis. Test: true or not? Question. Average is not the mean! μ average. Random deviation or not? Hypothesis testing Question Very frequently: what is the possible value of μ? Sample: we know only the average! μ average. Random deviation or not? Standard error: the measure of the random deviation.

More information

Chapter Seven: Multi-Sample Methods 1/52

Chapter Seven: Multi-Sample Methods 1/52 Chapter Seven: Multi-Sample Methods 1/52 7.1 Introduction 2/52 Introduction The independent samples t test and the independent samples Z test for a difference between proportions are designed to analyze

More information

Difference between means - t-test /25

Difference between means - t-test /25 Difference between means - t-test 1 Discussion Question p492 Ex 9-4 p492 1-3, 6-8, 12 Assume all variances are not equal. Ignore the test for variance. 2 Students will perform hypothesis tests for two

More information

8.1-4 Test of Hypotheses Based on a Single Sample

8.1-4 Test of Hypotheses Based on a Single Sample 8.1-4 Test of Hypotheses Based on a Single Sample Example 1 (Example 8.6, p. 312) A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation

More information

15: CHI SQUARED TESTS

15: CHI SQUARED TESTS 15: CHI SQUARED ESS MULIPLE CHOICE QUESIONS In the following multiple choice questions, please circle the correct answer. 1. Which statistical technique is appropriate when we describe a single population

More information

Inferential statistics

Inferential statistics Inferential statistics Inference involves making a Generalization about a larger group of individuals on the basis of a subset or sample. Ahmed-Refat-ZU Null and alternative hypotheses In hypotheses testing,

More information

STAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and Q-Q plots. March 8, 2015

STAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and Q-Q plots. March 8, 2015 STAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and Q-Q plots March 8, 2015 The duality between CI and hypothesis testing The duality between CI and hypothesis

More information

Chapter Eight: Assessment of Relationships 1/42

Chapter Eight: Assessment of Relationships 1/42 Chapter Eight: Assessment of Relationships 1/42 8.1 Introduction 2/42 Background This chapter deals, primarily, with two topics. The Pearson product-moment correlation coefficient. The chi-square test

More information

χ L = χ R =

χ L = χ R = Chapter 7 3C: Examples of Constructing a Confidence Interval for the true value of the Population Standard Deviation σ for a Normal Population. Example 1 Construct a 95% confidence interval for the true

More information

Unit 27 One-Way Analysis of Variance

Unit 27 One-Way Analysis of Variance Unit 27 One-Way Analysis of Variance Objectives: To perform the hypothesis test in a one-way analysis of variance for comparing more than two population means Recall that a two sample t test is applied

More information

STP 226 EXAMPLE EXAM #3 INSTRUCTOR:

STP 226 EXAMPLE EXAM #3 INSTRUCTOR: STP 226 EXAMPLE EXAM #3 INSTRUCTOR: Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned. Signed Date PRINTED

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. describes the. Practice Test 3 Math 1342 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The term z α/2 σn describes the. 1) A) maximum error of estimate

More information

CIVL /8904 T R A F F I C F L O W T H E O R Y L E C T U R E - 8

CIVL /8904 T R A F F I C F L O W T H E O R Y L E C T U R E - 8 CIVL - 7904/8904 T R A F F I C F L O W T H E O R Y L E C T U R E - 8 Chi-square Test How to determine the interval from a continuous distribution I = Range 1 + 3.322(logN) I-> Range of the class interval

More information

Statistical Inference for Means

Statistical Inference for Means Statistical Inference for Means Jamie Monogan University of Georgia February 18, 2011 Jamie Monogan (UGA) Statistical Inference for Means February 18, 2011 1 / 19 Objectives By the end of this meeting,

More information

Section 9.5. Testing the Difference Between Two Variances. Bluman, Chapter 9 1

Section 9.5. Testing the Difference Between Two Variances. Bluman, Chapter 9 1 Section 9.5 Testing the Difference Between Two Variances Bluman, Chapter 9 1 This the last day the class meets before spring break starts. Please make sure to be present for the test or make appropriate

More information

AMS 7 Correlation and Regression Lecture 8

AMS 7 Correlation and Regression Lecture 8 AMS 7 Correlation and Regression Lecture 8 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Suumer 2014 1 / 18 Correlation pairs of continuous observations. Correlation

More information

CHAPTER 9, 10. Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities:

CHAPTER 9, 10. Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities: CHAPTER 9, 10 Hypothesis Testing Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities: The person is guilty. The person is innocent. To

More information

Test 3 Practice Test A. NOTE: Ignore Q10 (not covered)

Test 3 Practice Test A. NOTE: Ignore Q10 (not covered) Test 3 Practice Test A NOTE: Ignore Q10 (not covered) MA 180/418 Midterm Test 3, Version A Fall 2010 Student Name (PRINT):............................................. Student Signature:...................................................

More information

LAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2

LAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2 LAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2 Data Analysis: The mean egg masses (g) of the two different types of eggs may be exactly the same, in which case you may be tempted to accept

More information

Confidence Interval Estimation

Confidence Interval Estimation Department of Psychology and Human Development Vanderbilt University 1 Introduction 2 3 4 5 Relationship to the 2-Tailed Hypothesis Test Relationship to the 1-Tailed Hypothesis Test 6 7 Introduction In

More information

LECTURE 5. Introduction to Econometrics. Hypothesis testing

LECTURE 5. Introduction to Econometrics. Hypothesis testing LECTURE 5 Introduction to Econometrics Hypothesis testing October 18, 2016 1 / 26 ON TODAY S LECTURE We are going to discuss how hypotheses about coefficients can be tested in regression models We will

More information

Topic 21 Goodness of Fit

Topic 21 Goodness of Fit Topic 21 Goodness of Fit Contingency Tables 1 / 11 Introduction Two-way Table Smoking Habits The Hypothesis The Test Statistic Degrees of Freedom Outline 2 / 11 Introduction Contingency tables, also known

More information

Quantitative Introduction ro Risk and Uncertainty in Business Module 5: Hypothesis Testing

Quantitative Introduction ro Risk and Uncertainty in Business Module 5: Hypothesis Testing Quantitative Introduction ro Risk and Uncertainty in Business Module 5: Hypothesis Testing M. Vidyasagar Cecil & Ida Green Chair The University of Texas at Dallas Email: M.Vidyasagar@utdallas.edu October

More information

Political Science 236 Hypothesis Testing: Review and Bootstrapping

Political Science 236 Hypothesis Testing: Review and Bootstrapping Political Science 236 Hypothesis Testing: Review and Bootstrapping Rocío Titiunik Fall 2007 1 Hypothesis Testing Definition 1.1 Hypothesis. A hypothesis is a statement about a population parameter The

More information

Part III: Unstructured Data

Part III: Unstructured Data Inf1-DA 2010 2011 III: 51 / 89 Part III Unstructured Data Data Retrieval: III.1 Unstructured data and data retrieval Statistical Analysis of Data: III.2 Data scales and summary statistics III.3 Hypothesis

More information

Statistical Inference

Statistical Inference Statistical Inference Classical and Bayesian Methods Revision Class for Midterm Exam AMS-UCSC Th Feb 9, 2012 Winter 2012. Session 1 (Revision Class) AMS-132/206 Th Feb 9, 2012 1 / 23 Topics Topics We will

More information

Summary of Chapter 7 (Sections ) and Chapter 8 (Section 8.1)

Summary of Chapter 7 (Sections ) and Chapter 8 (Section 8.1) Summary of Chapter 7 (Sections 7.2-7.5) and Chapter 8 (Section 8.1) Chapter 7. Tests of Statistical Hypotheses 7.2. Tests about One Mean (1) Test about One Mean Case 1: σ is known. Assume that X N(µ, σ

More information

10.2: The Chi Square Test for Goodness of Fit

10.2: The Chi Square Test for Goodness of Fit 10.2: The Chi Square Test for Goodness of Fit We can perform a hypothesis test to determine whether the distribution of a single categorical variable is following a proposed distribution. We call this

More information

INTERVAL ESTIMATION AND HYPOTHESES TESTING

INTERVAL ESTIMATION AND HYPOTHESES TESTING INTERVAL ESTIMATION AND HYPOTHESES TESTING 1. IDEA An interval rather than a point estimate is often of interest. Confidence intervals are thus important in empirical work. To construct interval estimates,

More information

Chi square test of independence

Chi square test of independence Chi square test of independence Eyeball differences between percentages: large enough to be important Better: Are they statistically significant? Statistical significance: are observed differences significantly

More information

χ test statistics of 2.5? χ we see that: χ indicate agreement between the two sets of frequencies.

χ test statistics of 2.5? χ we see that: χ indicate agreement between the two sets of frequencies. I. T or F. (1 points each) 1. The χ -distribution is symmetric. F. The χ may be negative, zero, or positive F 3. The chi-square distribution is skewed to the right. T 4. The observed frequency of a cell

More information

Inference for Regression

Inference for Regression Inference for Regression Section 9.4 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 13b - 3339 Cathy Poliak, Ph.D. cathy@math.uh.edu

More information

Hypothesis testing: Steps

Hypothesis testing: Steps Review for Exam 2 Hypothesis testing: Steps Repeated-Measures ANOVA 1. Determine appropriate test and hypotheses 2. Use distribution table to find critical statistic value(s) representing rejection region

More information

STAT Chapter 13: Categorical Data. Recall we have studied binomial data, in which each trial falls into one of 2 categories (success/failure).

STAT Chapter 13: Categorical Data. Recall we have studied binomial data, in which each trial falls into one of 2 categories (success/failure). STAT 515 -- Chapter 13: Categorical Data Recall we have studied binomial data, in which each trial falls into one of 2 categories (success/failure). Many studies allow for more than 2 categories. Example

More information

Chapter 8. Inferences Based on a Two Samples Confidence Intervals and Tests of Hypothesis

Chapter 8. Inferences Based on a Two Samples Confidence Intervals and Tests of Hypothesis Chapter 8 Inferences Based on a Two Samples Confidence Intervals and Tests of Hypothesis Copyright 2018, 2014, and 2011 Pearson Education, Inc. Slide - 1 Content 1. Identifying the Target Parameter 2.

More information

The t-statistic. Student s t Test

The t-statistic. Student s t Test The t-statistic 1 Student s t Test When the population standard deviation is not known, you cannot use a z score hypothesis test Use Student s t test instead Student s t, or t test is, conceptually, very

More information

Lecture 17: Small-Sample Inferences for Normal Populations. Confidence intervals for µ when σ is unknown

Lecture 17: Small-Sample Inferences for Normal Populations. Confidence intervals for µ when σ is unknown Lecture 17: Small-Sample Inferences for Normal Populations Confidence intervals for µ when σ is unknown If the population distribution is normal, then X µ σ/ n has a standard normal distribution. If σ

More information

Lecture 22. December 19, Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Johns Hopkins University.

Lecture 22. December 19, Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Johns Hopkins University. Lecture 22 Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Johns Hopkins University December 19, 2007 1 2 3 4 5 6 7 8 9 1 tests for equivalence of two binomial 2 tests for,

More information

Chi square test of independence

Chi square test of independence Chi square test of independence We can eyeball differences between percentages to determine whether they seem large enough to be important Better: Are differences in percentages statistically significant?

More information

:the actual population proportion are equal to the hypothesized sample proportions 2. H a

:the actual population proportion are equal to the hypothesized sample proportions 2. H a AP Statistics Chapter 14 Chi- Square Distribution Procedures I. Chi- Square Distribution ( χ 2 ) The chi- square test is used when comparing categorical data or multiple proportions. a. Family of only

More information

Hypothesis testing. Data to decisions

Hypothesis testing. Data to decisions Hypothesis testing Data to decisions The idea Null hypothesis: H 0 : the DGP/population has property P Under the null, a sample statistic has a known distribution If, under that that distribution, the

More information

10/4/2013. Hypothesis Testing & z-test. Hypothesis Testing. Hypothesis Testing

10/4/2013. Hypothesis Testing & z-test. Hypothesis Testing. Hypothesis Testing & z-test Lecture Set 11 We have a coin and are trying to determine if it is biased or unbiased What should we assume? Why? Flip coin n = 100 times E(Heads) = 50 Why? Assume we count 53 Heads... What could

More information

Hypothesis Testing. Week 04. Presented by : W. Rofianto

Hypothesis Testing. Week 04. Presented by : W. Rofianto Hypothesis Testing Week 04 Presented by : W. Rofianto Tests about a Population Mean: σ unknown Test Statistic t x 0 s / n This test statistic has a t distribution with n - 1 degrees of freedom. Example:

More information

COGS 14B: INTRODUCTION TO STATISTICAL ANALYSIS

COGS 14B: INTRODUCTION TO STATISTICAL ANALYSIS COGS 14B: INTRODUCTION TO STATISTICAL ANALYSIS TA: Sai Chowdary Gullapally scgullap@eng.ucsd.edu Office Hours: Thursday (Mandeville) 3:30PM - 4:30PM (or by appointment) Slides: I am using the amazing slides

More information