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*The chi-square independence test is a procedure for testing if two categorical variables are related in some population. Example: a scientist wants to know if education level and marital status are related for all people in some country. A good first step for these data is inspecting the contingency table of marital status by education.*

- Goodness-of-Fit Tests and Model Validity
- Introduction
- SPSS Tutorials: Chi-Square Test of Independence

## Goodness-of-Fit Tests and Model Validity

This lesson explains how to conduct a chi-square test for independence. The test is applied when you have two categorical variables from a single population. It is used to determine whether there is a significant association between the two variables. For example, in an election survey, voters might be classified by gender male or female and voting preference Democrat, Republican, or Independent. We could use a chi-square test for independence to determine whether gender is related to voting preference. The sample problem at the end of the lesson considers this example.

## Introduction

This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The specific tests considered here are called chi-square tests and are appropriate when the outcome is discrete dichotomous, ordinal or categorical. For example, in some clinical trials the outcome is a classification such as hypertensive, pre-hypertensive or normotensive. We could use the same classification in an observational study such as the Framingham Heart Study to compare men and women in terms of their blood pressure status - again using the classification of hypertensive, pre-hypertensive or normotensive status. The technique to analyze a discrete outcome uses what is called a chi-square test.

By Benjamin Frimodig , published There are three types of Chi-square tests, tests of goodness of fit, independence and homogeneity. All three tests also rely on the same formula to compute a test statistic. The Chi-square goodness of fit test is used to compare a randomly collected sample containing a single, categorical variable to a larger population. This test is most commonly used to compare a random sample to the population from which it was potentially collected. The test begins with the creation of a null and alternative hypothesis.

How do we test the independence of two categorical variables? It will be done using the Chi-square test of independence. As with all prior statistical tests we need to define null and alternative hypotheses. Also, as we have learned, the null hypothesis is what is assumed to be true until we have evidence to go against it. In this lesson, we are interested in researching if two categorical variables are related or associated i. Therefore, until we have evidence to suggest that they are, we must assume that they are not.

Chapter Chi-Square Tests: Solutions. Goodness of Fit Test. In this section, we consider experiments with multiple outcomes. The probability of each.

## SPSS Tutorials: Chi-Square Test of Independence

A chi-square test is a statistical test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying. Therefore, a chi-square test is an excellent choice to help us better understand and interpret the relationship between our two categorical variables. To perform a chi-square exploring the statistical significance of the relationship between s2q10 and s1truan , select Analyze , Descriptive Statistics , and then Crosstabs. Find s2q10 in the variable list on the left, and move it to the Row s box.

Our tutorials reference a dataset called "sample" in many examples. If you'd like to download the sample dataset to work through the examples, choose one of the files below:. The Chi-Square Test of Independence determines whether there is an association between categorical variables i.

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field. The background history of Pearson's paper is thoroughly covered as well as the fundamentals of this very important topic.

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