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


 Marvin McDaniel
 2 years ago
 Views:
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 Chisquare statistic reflects the strength of this relationship. All else equal, the greater the chisquare statistic, the stronger the relationship. The chi square statistic is usually reported at the bottom of a contingency table. The probability associated with the chisquare 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 chisquare 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 chisquare 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 4H 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 chisquare 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 chisquare 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 ChiSquare Statistic The value of the chisquare 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 ChiStatistic The computed value of the chisquare 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. Chisquare 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 twovariable 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, Twentyeight 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? What are inferential statistics? Why learn about inferential statistics? Why use inferential statistics? When are inferential statistics utilized?
More informationModule 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 } OneSample ChiSquare Test
More information13.2 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 informationBivariate Statistics Session 2: Measuring Associations ChiSquare Test
Bivariate Statistics Session 2: Measuring Associations ChiSquare Test Features Of The ChiSquare Statistic The chisquare test is nonparametric. That is, it makes no assumptions about the distribution
More informationRecommend 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 informationPASS Sample Size Software
Chapter 250 Introduction The Chisquare 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 informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationCHI 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 informationWhen to use a ChiSquare test:
When to use a ChiSquare 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 informationUnit 29 ChiSquare GoodnessofFit Test
Unit 29 ChiSquare GoodnessofFit Test Objectives: To perform the chisquare hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni
More informationThe ChiSquare Test. STAT E50 Introduction to Statistics
STAT 50 Introduction to Statistics The ChiSquare Test The Chisquare test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed
More informationMATH 10: Elementary Statistics and Probability Chapter 11: The ChiSquare Distribution
MATH 10: Elementary Statistics and Probability Chapter 11: The ChiSquare Distribution Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,
More informationChi 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 informationChisquare test Fisher s Exact test
Lesson 1 Chisquare 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 informationGraphing 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 informationχ 2 = (O i E i ) 2 E i
Chapter 24 TwoWay Tables and the ChiSquare Test We look at twoway tables to determine association of paired qualitative data. We look at marginal distributions, conditional distributions and bar graphs.
More informationIs it statistically significant? The chisquare test
UAS Conference Series 2013/14 Is it statistically significant? The chisquare test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chisquare? Tests whether two categorical
More informationThe 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: TwoWay Tables The Problem of Multiple Comparisons Expected
More informationCHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY
CHAPTER 11 CHISQUARE: NONPARAMETRIC 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 informationElementary Statistics
lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chisquare Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page
More informationChiSquare Analysis (Ch.8) Purpose. Purpose. Examples
ChiSquare Analysis (Ch.8) Chisquare test of association (contingency) x tables rxc tables Posthoc Interpretation Running SPSS Windows CROSSTABS Chisquare test of goodness of fit Purpose Chisquare
More informationAP 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 informationDESCRIPTIVE 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 informationAssociation 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 informationHatice 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 informationCHISquared Test of Independence
CHISquared Test of Independence Minhaz Fahim Zibran Department of Computer Science University of Calgary, Alberta, Canada. Email: mfzibran@ucalgary.ca Abstract Chisquare (X 2 ) test is a nonparametric
More informationTesting 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 informationChapter 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 information4) 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 informationChapter 23. Two Categorical Variables: The ChiSquare Test
Chapter 23. Two Categorical Variables: The ChiSquare Test 1 Chapter 23. Two Categorical Variables: The ChiSquare Test TwoWay Tables Note. We quickly review twoway tables with an example. Example. Exercise
More informationChisquare test Testing for independeny The r x c contingency tables square test
Chisquare test Testing for independeny The r x c contingency tables square test 1 The chisquare distribution HUSRB/0901/1/088 Teaching Mathematics and Statistics in Sciences: Modeling and Computeraided
More informationSection 12 Part 2. Chisquare test
Section 12 Part 2 Chisquare 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 informationChapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other ChiSquare Tests
11/4/015 Chapter 11 Overview Chapter 11 Introduction 111 Test for Goodness of Fit 11 Tests Using Contingency Tables Other ChiSquare Tests McGrawHill, Bluman, 7th ed., Chapter 11 1 Bluman, Chapter 11
More informationComparing 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 informationResearch 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: CHISQUARE TESTS: When to use a ChiSquare test: Usually in psychological research, we aim to obtain one or more scores
More informationConstructing 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 informationChi Square Distribution
17. Chi Square A. Chi Square Distribution B. OneWay 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 informationDescriptive 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 informationHow 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. 147175 for additional details  Tables consist of words and numbers where spatial relationships
More informationChi 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 informationChapter 13. ChiSquare. Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running two separate
1 Chapter 13 ChiSquare This section covers the steps for running and interpreting chisquare analyses using the SPSS Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running
More informationCHAPTER 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 informationFirstyear Statistics for Psychology Students Through Worked Examples
Firstyear Statistics for Psychology Students Through Worked Examples 1. THE CHISQUARE TEST A test of association between categorical variables by Charles McCreery, D.Phil Formerly Lecturer in Experimental
More informationChi Squared and Fisher's Exact Tests. Observed vs Expected Distributions
BMS 617 Statistical Techniques for the Biomedical Sciences Lecture 11: ChiSquared and Fisher's Exact Tests Chi Squared and Fisher's Exact Tests This lecture presents two similarly structured tests, Chisquared
More informationHomework 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 informationChi 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 chisquare test is a statistical
More informationTABLE 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 (Oneway χ 2 )... 1 Test of Independence (Twoway χ 2 )... 2 Hypothesis Testing
More informationControlled 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 informationAnalysing Tables Part V Interpreting ChiSquare
Analysing Tables Part V Interpreting ChiSquare 8.0 Interpreting Chi Square Output 8.1 the Meaning of a Significant ChiSquare Sometimes the purpose of Crosstabulation is wrongly seen as being merely about
More informationChiSquare Test (χ 2 )
Chi Square Tests ChiSquare Test (χ 2 ) Nonparametric test for nominal independent variables These variables, also called "attribute variables" or "categorical variables," classify observations into a
More informationStatistical Impact of Slip Simulator Training at Los Alamos National Laboratory
LAUR1224572 Approved for public release; distribution is unlimited Statistical Impact of Slip Simulator Training at Los Alamos National Laboratory Alicia GarciaLopez Steven R. Booth September 2012
More informationSydney 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 information4. 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 informationChisquare test: Germination data Dan Flynn
Chisquare test: Germination data Dan Flynn This lab examines whether the germination rates of lettuce seeds differed across the herb treatments. The Chisquare test is one of the standard methods for
More informationHandout 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 informationIntroduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 91
Introduction to Hypothesis Testing 91 Learning Outcomes Outcome 1. Formulate null and alternative hypotheses for applications involving a single population mean or proportion. Outcome 2. Know what Type
More informationUNDERSTANDING THE TWOWAY ANOVA
UNDERSTANDING THE e have seen how the oneway 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 informationLecture 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 informationChiSquare Test. Contingency Tables. Contingency Tables. ChiSquare Test for Independence. ChiSquare Tests for GoodnessofFit
ChiSquare Tests 15 Chapter ChiSquare Test for Independence ChiSquare Tests for Goodness Uniform Goodness Poisson Goodness Goodness Test ECDF Tests (Optional) McGrawHill/Irwin Copyright 2009 by The
More informationResearch 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 informationHypothesis Testing for a Proportion
Math 122 Intro to Stats Chapter 6 Semester II, 201516 Inference for Categorical Data Hypothesis Testing for a Proportion In a survey, 1864 out of 2246 randomly selected adults said texting while driving
More informationHaving a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails.
Chisquare Goodness of Fit Test The chisquare test is designed to test differences whether one frequency is different from another frequency. The chisquare test is designed for use with data on a nominal
More informationSimulating ChiSquare Test Using Excel
Simulating ChiSquare 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 informationAnalyzing tables. Chisquared, exact and monte carlo tests. Jon Michael Gran Department of Biostatistics, UiO
Analyzing tables Chisquared, 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 informationCONTINGENCY 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 informationUsing SPSS to perform ChiSquare tests:
Using SPSS to perform ChiSquare tests: Graham Hole, January 2006: page 1: Using SPSS to perform ChiSquare tests: This handout explains how to perform the two types of ChiSquare test that were discussed
More informationCATEGORICAL DATA ChiSquare Tests for Univariate Data
CATEGORICAL DATA ChiSquare Tests For Univariate Data 1 CATEGORICAL DATA ChiSquare Tests for Univariate Data Recall that a categorical variable is one in which the possible values are categories or groupings.
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationBivariate 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 ttest X 2 chi square test X 2 chi square test ANOVA (Ftest)
More informationMind 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 informationDEPARTMENT 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. Crossclassifications 1. Twobytwo and R by C tables 2. Statistical independence 3. The interpretation
More informationElementary 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 informationCHAPTER 11 CHISQUARE AND F DISTRIBUTIONS
CHAPTER 11 CHISQUARE AND F DISTRIBUTIONS CHISQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chisquare tests of independence we use the hypotheses. H0: The variables are independent
More informationTwo Categorical Variables: the ChiSquare Test
CHAPTER 22 Two Categorical Variables: the ChiSquare Test 22.1 22.2 22.3 22.4 Data Analysis for TwoWay Tables Inference for TwoWay Tables Goodness of Fit Selected Exercise Solutions Introduction We saw
More informationOdds ratio, Odds ratio test for independence, chisquared statistic.
Odds ratio, Odds ratio test for independence, chisquared 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 informationAmerican 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 informationStatistics. 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 informationTest Positive True Positive False Positive. Test Negative False Negative True Negative. Figure 51: 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 informationChiSquare Tests. In This Chapter BONUS CHAPTER
BONUS CHAPTER ChiSquare 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 informationDETERMINING STATISTICAL SIGNIFICANCE FOR OMS DATA: STEPBYSTEP GUIDE May 2016
DETERMINING STATISTICAL SIGNIFICANCE FOR OMS DATA: STEPBYSTEP GUIDE May 2016 This document is part of several training modules created to assist in the interpretation and use of the Maryland Behavioral
More informationDistribution 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 informationToday s lecture. Lecture 6: Dichotomous Variables & Chisquare tests. Proportions and 2 2 tables. How do we compare these proportions
Today s lecture Lecture 6: Dichotomous Variables & Chisquare tests Sandy Eckel seckel@jhsph.edu Dichotomous Variables Comparing two proportions using 2 2 tables Study Designs Relative risks, odds ratios
More informationData 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 informationCalculating PValues. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating PValues Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating PValues" (2014). A with Honors Projects.
More informationDATA 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 informationSimple 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 information2013 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 informationStats for Strategy Exam 1 InClass Practice Questions DIRECTIONS
Stats for Strategy Exam 1 InClass 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 informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More information2. 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 informationSOME 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 informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationUnit 24 Hypothesis Tests about Means
Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a twosample t test To perform a paired t test To perform a twosample t test A measure of the amount
More informationDirections for ChiSquare for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav. Oneway Chisquare
Directions for ChiSquare for One and for Two Variables Datasets: One_way_chi_square.sav and Two_way_Chi_square.sav Oneway Chisquare 1. Open the dataset containing the already grouped frequency of student
More informationNonparametric Tests. ChiSquare Test for Independence
DDBA 8438: Nonparametric Statistics: The ChiSquare Test Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Nonparametric Statistics: The ChiSquare Test." My name is Dr. Jennifer Ann Morrow. In
More informationUnderstanding and Interpreting the Chisquare Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVUSchool of Nursing Charleston Division
Understanding and Interpreting the Chisquare Statistic (x 2 ) Rose Ann DiMaria, PhD, RN WVUSchool of Nursing Charleston Division Inferential statistics Make judgments about accuracy of given sample in
More informationAP 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 informationTesting 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 informationCrosstabulation & Chi Square
Crosstabulation & Chi Square Robert S Michael Chisquare 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 informationAP: LAB 8: THE CHISQUARE TEST. Probability, Random Chance, and Genetics
Ms. Foglia Date AP: LAB 8: THE CHISQUARE 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