Contingency Tables and the Chi Square Statistic. Interpreting Computer Printouts and Constructing Tables

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Contingency Tables and the Chi Square Statistic. Interpreting Computer Printouts and Constructing Tables"

Transcription

1 Contingency Tables and the Chi Square Statistic Interpreting Computer Printouts and Constructing Tables

2 Contingency Tables/Chi Square Statistics What are they? A contingency table is a table that shows the relationship between two categorical variables. The Chi-square statistic reflects the strength of this relationship. All else equal, the greater the chi-square statistic, the stronger the relationship. The chi square statistic is usually reported at the bottom of a contingency table. The probability associated with the chi-square statistic indicates the probability that you would be incorrect if you were to assert that there is a relationship between these same two variables in the population from which you drew your sample.

3 Contingency Tables/Chi Square Statistics Why should you be able to interpret a contingency table and chi-square statistic? If you are submitting an article for publication in a peer reviewed journal you may use a contingency table. You want to interpret it accurately. Before you implement a program, you want to review the literature and read about the same or similar programs. These articles may contain contingency tables. You want to be a wise consumer of information. If you are evaluating your own program, it is likely that you will use contingency tables. Contingency tables can not only help you discern if your program is working, but how effective it is and/or if the effectiveness varies by such factors as gender, race, etc. Before you make recommendations or engage in political advocacy, you want empirical evidence to substantiate your claims. Contingency tables can be used to provide this evidence.

4 Contingency Tables/Chi Square Statistics When would you use them? Contingency tables and the corresponding chi-square statistic is very useful for those implementing programs, and should be used BEFORE important decisions are made. Any responsible extension employee would use correctly implemented evaluation research to evaluate their programs and measure their objectives. Properly interpreted Chi square statistics can be an important part of that evaluation. When applying for grants to support existing programs, it is a good idea to use statistics to validate claims that the program works. Chi square can be one of these statistics. When justifying grant monies spent on programs, evaluation research should be used. Responsible administrators should use accurate statistics to provide evidence that their objectives were met.

5 Examples of When to Use Them You should use contingency tables and chi square statistics: BEFORE you use any Intervention, so you can determine if there is evidence that it will work and for whom it will work. For instance You should be able to interpret contingency tables reported in the literature that have been used to evaluate similar programs. You want to know if there is evidence that a program like yours will work, and what factors could influence its effectiveness. BEFORE implementing and/or continuing any program, so you will know if it s worth your continued time and effort. For instance - Is the percent of students who received an A in school greater for those who belonged to your 4-H program relative to those who did not? For instance - What factors are most important when attempting to increase the effectiveness of this intervention? For instance - What percent of those involved in intervention 1 saw the program as effective compared to the percent involved in intervention 2.

6 Examples of When to Use Them BEFORE you report the results of your evaluation and/or make recommendations, so you can accurately explain the risks and probabilities. For instance If having access to computers related to scores on standardized tests, then (1) Are scores on standardized tests related to academic achievement, and (2) How many computers must you purchase to see a significant gain in standardized test scores for this group? For instance - What percent of your clients experienced increased economic stress after paying to participate in your program? Does this economic stress outweigh benefits? For instance, Can you identify the most important factors in your program? If you were forced to curtail activities which activities could you eliminate without significantly decreasing positive outcomes for your participants?

7 Assumptions of Chi Square The statistics generated by the computer for chisquare are only valid if the data meet the following qualifications: Both the independent and dependent variables are categorical.* Researchers used a random sample to collect data. Researchers had an adequate sample size. Generally the sample size should be at least 100. The number of respondents in each cell should be at least 5. If not, you can use a Fisher s Exact or other tests. *Generally the number of categories is somewhere between 3 and 7. More than 7 categories can be overwhelming and confusing to the reader.

8 Contingency Tables/Chi Square Statistics How do you interpret them? There are two parts of a contingency table that you must correctly interpret: The chi square statistic The numbers in the table

9 Contingency Tables/Chi Square Statistics How do you interpret them? The chi square statistic It is relatively easy to interpret a chi square statistic if you know three things First all else equal, the greater the chi square number, the stronger the relationship between the dependent and independent variable. Second the lower the probability associated with a chi-square statistic, the stronger the relationship between the dependent and independent variable. Third If your probability is.05 or less, then you can generalize from a random sample to a population, and claim the two variables are associated in the population.

10 Contingency Tables/Chi Square Statistics How do you interpret them? The numbers in the contingency table There are a few simple rules that makes it easier to interpret a contingency table. These include: First to avoid confusion, always put the independent variable on the side and the dependent variable on the top. Second focus on the percent not on the frequency. Third use the percent that totals to 100 percent for each independent variable (e.g., the row percent). Fourth compare the percent for each category of the independent variable across the independent variables.

11 Contingency Table. Mother s Racial Identification by Probability of Receiving Bad News about their Kindergarten Child from the Child s Teacher. A contingency table reported in the literature should look something like the one above. When interpreting this table, you compare the percent of each independent category. In this case, 10% of White mothers, compared to 44.83% of Black mothers and 35.71% of Hispanic mothers received bad news. The probability associated with the chi square statistic of is less than.01 indicating there is a strong relationship between whether or not the mom received bad news and her race.

12 Computer Printouts How do you Interpret them? How do you construct a table from a computer printout? How do you construct and interpret a bar chart from a contingency table?

13 Purpose Chi- Square/Contingency Table Examine relationship between two categorical variables Determine if the dependent variable is contingent on the independent variable Definition of Terms Cells Squares that make up chi-square printout (sometimes referred to as table) Each cell contains 4 numbers. These are referred to as: Frequency (raw numbers or count) Percent Row Percent Column Percent Tabulates the number of times each possible combination of the values of the independent and dependent variables occur (in your sample) Rows (r) Cells that are attached horizontally are referred to as a row Row percents make up the numbers in the cells that percentage to 100 across these rows.

14 Columns (c) Cells that are attached vertically are referred to as a column Column percents make up the numbers in the cells that percentage to 100 down these columns. Degrees of Freedom A number that you would use to find the critical value of a chi square statistic using a chi square table. The formula you use to compute a chi square statistic is (r 1) (c 1) = df Critical Value of Chi-Square Statistic The value of the chi-square statistic associated with a.05 probability of making an error if you reject the null hypothesis. Your chi square statistic must be greater than this if your relationship is significant. This is not reported in the printout, but the reported value must be greater than this if you are to reject the null hypothesis. Computed Chi-Statistic The computed value of the chi-square statistic. Generally the greater the chi square statistic, the lower the probability that you make a mistake if you reject the null hypothesis. Generally the greater the chi square statistic, the stronger the relationship between the independent and dependent variable.

15 Chi Square Statistic reported here Probability reported here

16 Research Question: Is preferred ice cream flavor related to race? *Please note.the data is fabricated and to be used only for illustration.

17 Research Question: Is race related to ice cream flavor preference? One Interpretation: 65% of Blacks, compared to 35.96% of Hispanics and 34.18% of Whites prefer Butter Pecan. Blacks were almost twice as likely to prefer Butter Pecan. The relationship between race and ice cream preference is significant at the.0001 level. *Please note.the data is fabricated and to be used only for illustration.

18 Here is an example of a table (above) that was constructed from a printout (below). The table reports the row percent, the frequency in each cell and the chi square statistic.

19 Contingency Table. Mother s Racial Identification by Probability of Receiving Bad News about their Kindergarten Child from the Child s Teacher. Chi-square results can be presented in a contingency table. In this table you report, the frequency in each cell. If the independent (causal) variable is on the side, you report the row percent. If the independent (causal) variable is on the top, you report the column percent. When interpreting this table, you compare the percent of each independent category. In this case, 10% of White mothers, compared to 44.83% of Black mothers and 35.71% of Hispanics mothers received bad news.

20 Using data from the previous slide, you could construct the following graph: No Yes White Black Hispanic

21 Or you could use the same data to construct this graph: Black White Hispanic Yes No

22 100.00% 80.00% 60.00% 40.00% 20.00% 0.00% CHART 5 Middle/High School Students Perception of How Good They are at Finding Resources by Whether or Not They Made Decisions about Service Learning Projects 7% 9% Strongly Disagree 13% 24% 44% 43% 28% 17% (p <0.0001) 11% 7% Disagree Undecided Agree Strongly Agree Did Did Not Contingency tables are often used to construct two-variable bar charts. In this case, the extent to which students agree that they are good at finding resources is contingent on whether or not they made decisions about their Service Learning Project. Assuming the independent variable is on the side of the computer printout, the row percent is used to construct the bar chart. The probability is less than.0001 indicating a strong relationship between these two variables. All else equal, the less the probability, the stronger the relationship.

23 Interpreting Bar Charts CHART 5 Middle/High School Students Perception of How Good They are at Finding Resources by Whether or Not They Made Decisions about Service Learning Projects % 80.00% 60.00% 40.00% 20.00% 7% 9% 13% 24% 44% 43% 28% 17% (p <0.0001) 11% 7% Did Did Not 0.00% Strongly Disagree Disagree Undecided Agree Strongly Agree Interpreting the Bar Chart Interpret the most striking comparison for your audience. For instance, Twenty-eight percent of those who made decisions about their Service Learning Project agreed that they were good at finding resources, compared to only seventeen percent of those who did not make decisions about their projects.

24 100.00% 80.00% CHART 7 Middle/High School Students Perception of the Level to Which They Agree Teachers Listen to Their Ideas by Whether or Not They Made Decisions about Service Learning Projects 60.00% 40.00% 20.00% 9% 15% 21% 22% 35% 39% 27% 20% (p <0.0001) 8% 3% Did Did Not 0.00% Strongly Disagree Disagree Undecided Agree Strongly Agree In this case, the extent to which students feel teachers listen to them is contingent on whether or not they made decisions about their Service Learning Project. 8% of those who did make decisions about their Service Learning Project felt their teachers listened to them compared to only 3% of those who did not make decisions.

25 Contact Information Dr. Carol Albrecht Assessment Specialist USU Extension

Inferential Statistics. What are they? When would you use them?

Inferential Statistics. What are they? When would you use them? Inferential Statistics What are they? When would you use them? What are inferential statistics? Why learn about inferential statistics? Why use inferential statistics? When are inferential statistics utilized?

More information

Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests. The Applied Research Center Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

More information

13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations.

13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. 13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. Data is organized in a two way table Explanatory variable (Treatments)

More information

Bivariate Statistics Session 2: Measuring Associations Chi-Square Test

Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution

More information

Recommend Continued CPS Monitoring. 63 (a) 17 (b) 10 (c) 90. 35 (d) 20 (e) 25 (f) 80. Totals/Marginal 98 37 35 170

Recommend Continued CPS Monitoring. 63 (a) 17 (b) 10 (c) 90. 35 (d) 20 (e) 25 (f) 80. Totals/Marginal 98 37 35 170 Work Sheet 2: Calculating a Chi Square Table 1: Substance Abuse Level by ation Total/Marginal 63 (a) 17 (b) 10 (c) 90 35 (d) 20 (e) 25 (f) 80 Totals/Marginal 98 37 35 170 Step 1: Label Your Table. Label

More information

PASS Sample Size Software

PASS Sample Size Software Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial

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

CHI SQUARE DISTRIBUTION

CHI SQUARE DISTRIBUTION CI SQUARE DISTRIBUTION 1 Introduction to the Chi Square Test of Independence This test is used to analyse the relationship between two sets of discrete data. Contingency tables are used to examine the

More information

When to use a Chi-Square test:

When to use a Chi-Square test: When to use a Chi-Square test: Usually in psychological research, we aim to obtain one or more scores from each participant. However, sometimes data consist merely of the frequencies with which certain

More information

Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

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

MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution

MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,

More information

Chi Square for Contingency Tables

Chi Square for Contingency Tables 2 x 2 Case Chi Square for Contingency Tables A test for p 1 = p 2 We have learned a confidence interval for p 1 p 2, the difference in the population proportions. We want a hypothesis testing procedure

More information

Chi-square test Fisher s Exact test

Chi-square test Fisher s Exact test Lesson 1 Chi-square test Fisher s Exact test McNemar s Test Lesson 1 Overview Lesson 11 covered two inference methods for categorical data from groups Confidence Intervals for the difference of two proportions

More information

Graphing Data Presentation of Data in Visual Forms

Graphing Data Presentation of Data in Visual Forms Graphing Data Presentation of Data in Visual Forms Purpose of Graphing Data Audience Appeal Provides a visually appealing and succinct representation of data and summary statistics Provides a visually

More information

χ 2 = (O i E i ) 2 E i

χ 2 = (O i E i ) 2 E i Chapter 24 Two-Way Tables and the Chi-Square Test We look at two-way tables to determine association of paired qualitative data. We look at marginal distributions, conditional distributions and bar graphs.

More information

Is it statistically significant? The chi-square test

Is it statistically significant? The chi-square test UAS Conference Series 2013/14 Is it statistically significant? The chi-square test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chi-square? Tests whether two categorical

More information

The Chi Square Test. Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed.

The Chi Square Test. Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed. The Chi Square Test Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed.) Concepts: Two-Way Tables The Problem of Multiple Comparisons Expected

More information

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples

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

Chi-Square Analysis (Ch.8) Purpose. Purpose. Examples

Chi-Square Analysis (Ch.8) Purpose. Purpose. Examples Chi-Square Analysis (Ch.8) Chi-square test of association (contingency) x tables rxc tables Post-hoc Interpretation Running SPSS Windows CROSSTABS Chi-square test of goodness of fit Purpose Chi-square

More information

AP Statistics for Friday 4/15/16. 2) turn in work; hand back work. 3) lesson on Chi Square tests for Association with handouts

AP Statistics for Friday 4/15/16. 2) turn in work; hand back work. 3) lesson on Chi Square tests for Association with handouts AP Statistics for Friday 4/15/16 1) go over schedule 2) turn in work; hand back work 3) lesson on Chi Square tests for Association with handouts 4) Assign #105 p 631 / 19, 23, 31 schedule... Normal Distribution

More information

DESCRIPTIVE STATISTICS & DATA PRESENTATION*

DESCRIPTIVE STATISTICS & DATA PRESENTATION* Level 1 Level 2 Level 3 Level 4 0 0 0 0 evel 1 evel 2 evel 3 Level 4 DESCRIPTIVE STATISTICS & DATA PRESENTATION* Created for Psychology 41, Research Methods by Barbara Sommer, PhD Psychology Department

More information

Association Between Variables

Association Between Variables Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi

More information

Hatice Camgöz Akdağ. findings of previous research in which two independent firm clusters were

Hatice Camgöz Akdağ. findings of previous research in which two independent firm clusters were Innovative Culture and Total Quality Management as a Tool for Sustainable Competitiveness: A Case Study of Turkish Fruit and Vegetable Processing Industry SMEs, Sedef Akgüngör Hatice Camgöz Akdağ Aslı

More information

CHI-Squared Test of Independence

CHI-Squared Test of Independence CHI-Squared Test of Independence Minhaz Fahim Zibran Department of Computer Science University of Calgary, Alberta, Canada. Email: mfzibran@ucalgary.ca Abstract Chi-square (X 2 ) test is a nonparametric

More information

Testing differences in proportions

Testing differences in proportions Testing differences in proportions Murray J Fisher RN, ITU Cert., DipAppSc, BHSc, MHPEd, PhD Senior Lecturer and Director Preregistration Programs Sydney Nursing School (MO2) University of Sydney NSW 2006

More information

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately

More information

4) The goodness of fit test is always a one tail test with the rejection region in the upper tail. Answer: TRUE

4) The goodness of fit test is always a one tail test with the rejection region in the upper tail. Answer: TRUE Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 13 Goodness of Fit Tests and Contingency Analysis 1) A goodness of fit test can be used to determine whether a set of sample data comes from a specific

More information

Chapter 23. Two Categorical Variables: The Chi-Square Test

Chapter 23. Two Categorical Variables: The Chi-Square Test Chapter 23. Two Categorical Variables: The Chi-Square Test 1 Chapter 23. Two Categorical Variables: The Chi-Square Test Two-Way Tables Note. We quickly review two-way tables with an example. Example. Exercise

More information

Chi-square test Testing for independeny The r x c contingency tables square test

Chi-square test Testing for independeny The r x c contingency tables square test Chi-square test Testing for independeny The r x c contingency tables square test 1 The chi-square distribution HUSRB/0901/1/088 Teaching Mathematics and Statistics in Sciences: Modeling and Computer-aided

More information

Section 12 Part 2. Chi-square test

Section 12 Part 2. Chi-square test Section 12 Part 2 Chi-square test McNemar s Test Section 12 Part 2 Overview Section 12, Part 1 covered two inference methods for categorical data from 2 groups Confidence Intervals for the difference of

More information

Chapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other Chi-Square Tests

Chapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other Chi-Square Tests 11/4/015 Chapter 11 Overview Chapter 11 Introduction 11-1 Test for Goodness of Fit 11- Tests Using Contingency Tables Other Chi-Square Tests McGraw-Hill, Bluman, 7th ed., Chapter 11 1 Bluman, Chapter 11

More information

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Comparing Multiple Proportions, Test of Independence and Goodness of Fit Comparing Multiple Proportions, Test of Independence and Goodness of Fit Content Testing the Equality of Population Proportions for Three or More Populations Test of Independence Goodness of Fit Test 2

More information

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1: Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 000: Page 1: CHI-SQUARE TESTS: When to use a Chi-Square test: Usually in psychological research, we aim to obtain one or more scores

More information

Constructing and Interpreting Confidence Intervals

Constructing and Interpreting Confidence Intervals Constructing and Interpreting Confidence Intervals Confidence Intervals In this power point, you will learn: Why confidence intervals are important in evaluation research How to interpret a confidence

More information

Chi Square Distribution

Chi Square Distribution 17. Chi Square A. Chi Square Distribution B. One-Way Tables C. Contingency Tables D. Exercises Chi Square is a distribution that has proven to be particularly useful in statistics. The first section describes

More information

Descriptive Analysis

Descriptive Analysis Research Methods William G. Zikmund Basic Data Analysis: Descriptive Statistics Descriptive Analysis The transformation of raw data into a form that will make them easy to understand and interpret; rearranging,

More information

How to Make APA Format Tables Using Microsoft Word

How to Make APA Format Tables Using Microsoft Word How to Make APA Format Tables Using Microsoft Word 1 I. Tables vs. Figures - See APA Publication Manual p. 147-175 for additional details - Tables consist of words and numbers where spatial relationships

More information

Chi Square (χ 2 ) Statistical Instructions EXP 3082L Jay Gould s Elaboration on Christensen and Evans (1980)

Chi Square (χ 2 ) Statistical Instructions EXP 3082L Jay Gould s Elaboration on Christensen and Evans (1980) Chi Square (χ 2 ) Statistical Instructions EXP 3082L Jay Gould s Elaboration on Christensen and Evans (1980) For the Driver Behavior Study, the Chi Square Analysis II is the appropriate analysis below.

More information

Chapter 13. Chi-Square. Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running two separate

Chapter 13. Chi-Square. Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running two separate 1 Chapter 13 Chi-Square This section covers the steps for running and interpreting chi-square analyses using the SPSS Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running

More information

CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS

CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS Hypothesis 1: People are resistant to the technological change in the security system of the organization. Hypothesis 2: information hacked and misused. Lack

More information

First-year Statistics for Psychology Students Through Worked Examples

First-year Statistics for Psychology Students Through Worked Examples First-year Statistics for Psychology Students Through Worked Examples 1. THE CHI-SQUARE TEST A test of association between categorical variables by Charles McCreery, D.Phil Formerly Lecturer in Experimental

More information

Chi Squared and Fisher's Exact Tests. Observed vs Expected Distributions

Chi Squared and Fisher's Exact Tests. Observed vs Expected Distributions BMS 617 Statistical Techniques for the Biomedical Sciences Lecture 11: Chi-Squared and Fisher's Exact Tests Chi Squared and Fisher's Exact Tests This lecture presents two similarly structured tests, Chi-squared

More information

Homework Questions? A Look at Categorical Variables. Math 140. Chapter 3 1. Two Types of Questions

Homework Questions? A Look at Categorical Variables. Math 140. Chapter 3 1. Two Types of Questions Homework Questions? Two Types of Questions 1. Conceptual questions Answered in the beginning of class, as part of class Just ask. 2. HW questions on specific problems Answered during office hours Answered

More information

Chi Square Test. PASSS Research Question 4: Chi Square Test

Chi Square Test. PASSS Research Question 4: Chi Square Test Chi Square Test Is there a statistically significant relationship between a student s Year 11 truancy and his or her enrolment in full time education after secondary school? A chi-square test is a statistical

More information

TABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2

TABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2 About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (One-way χ 2 )... 1 Test of Independence (Two-way χ 2 )... 2 Hypothesis Testing

More information

Controlled Science Investigation NCATE Competency Assessment for SCE 4350 Indicator 8.1 and 8.2

Controlled Science Investigation NCATE Competency Assessment for SCE 4350 Indicator 8.1 and 8.2 Controlled Science Investigation NCATE Competency Assessment for SCE 4350 Indicator 8.1 and 8.2 The following guide provides steps for helping students learn how to 1) plan and conduct a simple investigation

More information

Analysing Tables Part V Interpreting Chi-Square

Analysing Tables Part V Interpreting Chi-Square Analysing Tables Part V Interpreting Chi-Square 8.0 Interpreting Chi Square Output 8.1 the Meaning of a Significant Chi-Square Sometimes the purpose of Crosstabulation is wrongly seen as being merely about

More information

Chi-Square Test (χ 2 )

Chi-Square Test (χ 2 ) Chi Square Tests Chi-Square Test (χ 2 ) Nonparametric test for nominal independent variables These variables, also called "attribute variables" or "categorical variables," classify observations into a

More information

Statistical Impact of Slip Simulator Training at Los Alamos National Laboratory

Statistical Impact of Slip Simulator Training at Los Alamos National Laboratory LA-UR-12-24572 Approved for public release; distribution is unlimited Statistical Impact of Slip Simulator Training at Los Alamos National Laboratory Alicia Garcia-Lopez Steven R. Booth September 2012

More information

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p. Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under

More information

4. Sum the results of the calculation described in step 3 for all classes of progeny

4. Sum the results of the calculation described in step 3 for all classes of progeny F09 Biol 322 chi square notes 1. Before proceeding with the chi square calculation, clearly state the genetic hypothesis concerning the data. This hypothesis is an interpretation of the data that gives

More information

Chi-square test: Germination data Dan Flynn

Chi-square test: Germination data Dan Flynn Chi-square test: Germination data Dan Flynn This lab examines whether the germination rates of lettuce seeds differed across the herb treatments. The Chi-square test is one of the standard methods for

More information

Handout 7: Understanding Relationships Between Two Categorical Variables

Handout 7: Understanding Relationships Between Two Categorical Variables In this handout, we will continue to discuss ways to investigate the relationship between two categorical variables. Recall that a categorical variable takes on a value that is the name of a category or

More information

Introduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 9-1

Introduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 9-1 Introduction to Hypothesis Testing 9-1 Learning Outcomes Outcome 1. Formulate null and alternative hypotheses for applications involving a single population mean or proportion. Outcome 2. Know what Type

More information

UNDERSTANDING THE TWO-WAY ANOVA

UNDERSTANDING THE TWO-WAY ANOVA UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables

More information

Lecture 7: Binomial Test, Chisquare

Lecture 7: Binomial Test, Chisquare Lecture 7: Binomial Test, Chisquare Test, and ANOVA May, 01 GENOME 560, Spring 01 Goals ANOVA Binomial test Chi square test Fisher s exact test Su In Lee, CSE & GS suinlee@uw.edu 1 Whirlwind Tour of One/Two

More information

Chi-Square Test. Contingency Tables. Contingency Tables. Chi-Square Test for Independence. Chi-Square Tests for Goodnessof-Fit

Chi-Square Test. Contingency Tables. Contingency Tables. Chi-Square Test for Independence. Chi-Square Tests for Goodnessof-Fit Chi-Square Tests 15 Chapter Chi-Square Test for Independence Chi-Square Tests for Goodness Uniform Goodness- Poisson Goodness- Goodness Test ECDF Tests (Optional) McGraw-Hill/Irwin Copyright 2009 by The

More information

Research Methods & Experimental Design

Research Methods & Experimental Design Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and

More information

Hypothesis Testing for a Proportion

Hypothesis Testing for a Proportion Math 122 Intro to Stats Chapter 6 Semester II, 2015-16 Inference for Categorical Data Hypothesis Testing for a Proportion In a survey, 1864 out of 2246 randomly selected adults said texting while driving

More information

Having a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails.

Having a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails. Chi-square Goodness of Fit Test The chi-square test is designed to test differences whether one frequency is different from another frequency. The chi-square test is designed for use with data on a nominal

More information

Simulating Chi-Square Test Using Excel

Simulating Chi-Square Test Using Excel Simulating Chi-Square Test Using Excel Leslie Chandrakantha John Jay College of Criminal Justice of CUNY Mathematics and Computer Science Department 524 West 59 th Street, New York, NY 10019 lchandra@jjay.cuny.edu

More information

Analyzing tables. Chi-squared, exact and monte carlo tests. Jon Michael Gran Department of Biostatistics, UiO

Analyzing tables. Chi-squared, exact and monte carlo tests. Jon Michael Gran Department of Biostatistics, UiO Analyzing tables Chi-squared, exact and monte carlo tests Jon Michael Gran Department of Biostatistics, UiO MF9130 Introductory course in statistics Thursday 26.05.2011 1 / 50 Overview Aalen chapter 6.5,

More information

CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont

CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont To most people studying statistics a contingency table is a contingency table. We tend to forget, if we ever knew, that contingency

More information

Using SPSS to perform Chi-Square tests:

Using SPSS to perform Chi-Square tests: Using SPSS to perform Chi-Square tests: Graham Hole, January 2006: page 1: Using SPSS to perform Chi-Square tests: This handout explains how to perform the two types of Chi-Square test that were discussed

More information

CATEGORICAL DATA Chi-Square Tests for Univariate Data

CATEGORICAL DATA Chi-Square Tests for Univariate Data CATEGORICAL DATA Chi-Square Tests For Univariate Data 1 CATEGORICAL DATA Chi-Square Tests for Univariate Data Recall that a categorical variable is one in which the possible values are categories or groupings.

More information

Inferential Statistics

Inferential Statistics Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

More information

Bivariate Analysis. Comparisons of proportions: Chi Square Test (X 2 test) Variable 1. Variable 2 2 LEVELS >2 LEVELS CONTINUOUS

Bivariate Analysis. Comparisons of proportions: Chi Square Test (X 2 test) Variable 1. Variable 2 2 LEVELS >2 LEVELS CONTINUOUS Bivariate Analysis Variable 1 2 LEVELS >2 LEVELS CONTINUOUS Variable 2 2 LEVELS X 2 chi square test >2 LEVELS X 2 chi square test CONTINUOUS t-test X 2 chi square test X 2 chi square test ANOVA (F-test)

More information

Mind on Statistics. Chapter 15

Mind on Statistics. Chapter 15 Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,

More information

DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS. Posc/Uapp 816 CONTINGENCY TABLES

DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS. Posc/Uapp 816 CONTINGENCY TABLES DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 816 CONTINGENCY TABLES I. AGENDA: A. Cross-classifications 1. Two-by-two and R by C tables 2. Statistical independence 3. The interpretation

More information

Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to

More information

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS

CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHAPTER 11 CHI-SQUARE AND F DISTRIBUTIONS CHI-SQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chi-square tests of independence we use the hypotheses. H0: The variables are independent

More information

Two Categorical Variables: the Chi-Square Test

Two Categorical Variables: the Chi-Square Test CHAPTER 22 Two Categorical Variables: the Chi-Square Test 22.1 22.2 22.3 22.4 Data Analysis for Two-Way Tables Inference for Two-Way Tables Goodness of Fit Selected Exercise Solutions Introduction We saw

More information

Odds ratio, Odds ratio test for independence, chi-squared statistic.

Odds ratio, Odds ratio test for independence, chi-squared statistic. Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review

More information

American Journal Of Business Education July/August 2012 Volume 5, Number 4

American Journal Of Business Education July/August 2012 Volume 5, Number 4 The Impact Of The Principles Of Accounting Experience On Student Preparation For Intermediate Accounting Linda G. Carrington, Ph.D., Sam Houston State University, USA ABSTRACT Both students and instructors

More information

Statistics. Annex 7. Calculating rates

Statistics. Annex 7. Calculating rates Annex 7 Statistics Calculating rates Rates are the most common way of measuring disease frequency in a population and are calculated as: number of new cases of disease in population at risk number of persons

More information

Test Positive True Positive False Positive. Test Negative False Negative True Negative. Figure 5-1: 2 x 2 Contingency Table

Test Positive True Positive False Positive. Test Negative False Negative True Negative. Figure 5-1: 2 x 2 Contingency Table ANALYSIS OF DISCRT VARIABLS / 5 CHAPTR FIV ANALYSIS OF DISCRT VARIABLS Discrete variables are those which can only assume certain fixed values. xamples include outcome variables with results such as live

More information

Chi-Square Tests. In This Chapter BONUS CHAPTER

Chi-Square Tests. In This Chapter BONUS CHAPTER BONUS CHAPTER Chi-Square Tests In the previous chapters, we explored the wonderful world of hypothesis testing as we compared means and proportions of one, two, three, and more populations, making an educated

More information

DETERMINING STATISTICAL SIGNIFICANCE FOR OMS DATA: STEP-BY-STEP GUIDE May 2016

DETERMINING STATISTICAL SIGNIFICANCE FOR OMS DATA: STEP-BY-STEP GUIDE May 2016 DETERMINING STATISTICAL SIGNIFICANCE FOR OMS DATA: STEP-BY-STEP GUIDE May 2016 This document is part of several training modules created to assist in the interpretation and use of the Maryland Behavioral

More information

Distribution is a χ 2 value on the χ 2 axis that is the vertical boundary separating the area in one tail of the graph from the remaining area.

Distribution is a χ 2 value on the χ 2 axis that is the vertical boundary separating the area in one tail of the graph from the remaining area. Section 8 4B Finding Critical Values for a Chi Square Distribution The entire area that is to be used in the tail(s) denoted by. The entire area denoted by can placed in the left tail and produce a Critical

More information

Today s lecture. Lecture 6: Dichotomous Variables & Chi-square tests. Proportions and 2 2 tables. How do we compare these proportions

Today s lecture. Lecture 6: Dichotomous Variables & Chi-square tests. Proportions and 2 2 tables. How do we compare these proportions Today s lecture Lecture 6: Dichotomous Variables & Chi-square tests Sandy Eckel seckel@jhsph.edu Dichotomous Variables Comparing two proportions using 2 2 tables Study Designs Relative risks, odds ratios

More information

Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools

Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................

More information

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

More information

DATA ANALYSIS AND INTERPRETATION OF EMPLOYEES PERSPECTIVES ON HIGH ATTRITION

DATA ANALYSIS AND INTERPRETATION OF EMPLOYEES PERSPECTIVES ON HIGH ATTRITION DATA ANALYSIS AND INTERPRETATION OF EMPLOYEES PERSPECTIVES ON HIGH ATTRITION Analysis is the key element of any research as it is the reliable way to test the hypotheses framed by the investigator. This

More information

Simple Linear Regression Inference

Simple Linear Regression Inference Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

More information

2013 Parking and Transportation Services Survey Analysis

2013 Parking and Transportation Services Survey Analysis 2013 Parking and Transportation Services Survey Analysis Contents Summary... 3 Results... 5 Response Rate... 5 Overall Satisfaction... 6 All Respondents... 6 Faculty... 7 Staff... 8 Students... 9 Most

More information

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check

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

2. DATA AND EXERCISES (Geos2911 students please read page 8)

2. DATA AND EXERCISES (Geos2911 students please read page 8) 2. DATA AND EXERCISES (Geos2911 students please read page 8) 2.1 Data set The data set available to you is an Excel spreadsheet file called cyclones.xls. The file consists of 3 sheets. Only the third is

More information

SOME NOTES ON STATISTICAL INTERPRETATION. Below I provide some basic notes on statistical interpretation for some selected procedures.

SOME NOTES ON STATISTICAL INTERPRETATION. Below I provide some basic notes on statistical interpretation for some selected procedures. 1 SOME NOTES ON STATISTICAL INTERPRETATION Below I provide some basic notes on statistical interpretation for some selected procedures. The information provided here is not exhaustive. There is more to

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

Unit 24 Hypothesis Tests about Means

Unit 24 Hypothesis Tests about Means Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a two-sample t test To perform a paired t test To perform a two-sample t test A measure of the amount

More information

Directions for Chi-Square for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav. One-way Chi-square

Directions for Chi-Square for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav. One-way Chi-square Directions for Chi-Square for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav One-way Chi-square 1. Open the dataset containing the already grouped frequency of student

More information

Nonparametric Tests. Chi-Square Test for Independence

Nonparametric Tests. Chi-Square Test for Independence DDBA 8438: Nonparametric Statistics: The Chi-Square Test Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Nonparametric Statistics: The Chi-Square Test." My name is Dr. Jennifer Ann Morrow. In

More information

Understanding and Interpreting the Chi-square Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVU-School of Nursing Charleston Division

Understanding and Interpreting the Chi-square Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVU-School of Nursing Charleston Division Understanding and Interpreting the Chi-square Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVU-School of Nursing Charleston Division Inferential statistics Make judgments about accuracy of given sample in

More information

AP Statistics 2004 Scoring Guidelines

AP Statistics 2004 Scoring Guidelines AP Statistics 2004 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought

More information

Testing Research and Statistical Hypotheses

Testing Research and Statistical Hypotheses Testing Research and Statistical Hypotheses Introduction In the last lab we analyzed metric artifact attributes such as thickness or width/thickness ratio. Those were continuous variables, which as you

More information

Crosstabulation & Chi Square

Crosstabulation & Chi Square Crosstabulation & Chi Square Robert S Michael Chi-square as an Index of Association After examining the distribution of each of the variables, the researcher s next task is to look for relationships among

More information

AP: LAB 8: THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics

AP: LAB 8: THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics Ms. Foglia Date AP: LAB 8: THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,

More information