Chapter 13- Inference For Tables: Chi-Chapter 13- Inference For Tables: Chi-square Proceduressquare Procedures

Section 13.1- Test for goodness of fitSection 13.1- Test for goodness of fitSection 13.2- Inference for Two-Way Section 13.2- Inference for Two-Way

tables tables

Presented By: Tyesha BaileyPresented By: Tyesha Bailey

Introduction: Things to learn throughout the chapterIntroduction: Things to learn throughout the chapter Goodness of FitGoodness of Fit Calculate expected values for every category in a Calculate expected values for every category in a

distribution, chi-squared statistic, and P-valuedistribution, chi-squared statistic, and P-value State the null and alternative hypothesis for State the null and alternative hypothesis for

differences between two distributionsdifferences between two distributions Use components of the chi-square statistic to Use components of the chi-square statistic to

identify the most important deviations between identify the most important deviations between observed and expected countsobserved and expected counts

Two-Way TablesTwo-Way Tables Arrange data for successes and failures into a two-Arrange data for successes and failures into a two-

way tableway table

Introduction: Things to learn throughout the chapter Introduction: Things to learn throughout the chapter Continued….Continued….

Use percents to describe relationships between Use percents to describe relationships between two categorical variablestwo categorical variables

Interpreting Chi-square tests of IndependenceInterpreting Chi-square tests of Independence Identify expected cell counts, chi-square statistic, Identify expected cell counts, chi-square statistic,

and its P-value using the calculatorand its P-value using the calculator Explain what the null hypothesis the chi-square Explain what the null hypothesis the chi-square

statistic tests in a specific two-way tablestatistic tests in a specific two-way table Determine the deviations from the null hypothesis Determine the deviations from the null hypothesis

by using percents, comparison of expected and by using percents, comparison of expected and observed counts, and the components of chi-observed counts, and the components of chi-square statisticsquare statistic

Introduction: Things to learn throughout the chapter Introduction: Things to learn throughout the chapter Continued….Continued….

Doing Chi-square TestsDoing Chi-square Tests Calculate the expected value of any observed Calculate the expected value of any observed

count in a two-way tablecount in a two-way table Calculate the component of the chi-square statistic Calculate the component of the chi-square statistic

for any cell,for any cell, Give the degrees of freedom for the chi-square Give the degrees of freedom for the chi-square

statisticstatistic Use chi-square critical values to approximate the Use chi-square critical values to approximate the

P-value of a chi-square testP-value of a chi-square test

Vocabulary: Words to be familiar with throughout Vocabulary: Words to be familiar with throughout the chapterthe chapter

Chi-square test for goodness of fitChi-square test for goodness of fit- test that - test that shows the difference between the observed sample shows the difference between the observed sample and the hypothesis population distributionsand the hypothesis population distributions

Chi-square distributionsChi-square distributions- Family of distributions - Family of distributions that take only positive values and are skewed rightthat take only positive values and are skewed right

Degrees of freedomDegrees of freedom- chi-square distribution - chi-square distribution specified by one parameterspecified by one parameter

Goodness of fit testGoodness of fit test- helps determine whether a - helps determine whether a population has a certain hypothesized distribution, population has a certain hypothesized distribution, and expressed as percents of populationand expressed as percents of population

Vocabulary: Words to be familiar with throughout Vocabulary: Words to be familiar with throughout the chapterthe chapter

Expected countsExpected counts- any cell - any cell of a two-way table when of a two-way table when the alternative hypothesis the alternative hypothesis is trueis true

Chi-square statisticChi-square statistic- a - a measure of how far the measure of how far the observed counts in a two-observed counts in a two-way table are from the way table are from the expected counts.expected counts.

Examples Of Topics/ EquationsExamples Of Topics/ Equations

Two-way tableTwo-way table

Expected CountExpected Count

Chi-square, Degrees of Chi-square, Degrees of freedom, P-valuefreedom, P-value

Conclusion of Chapter 13/ Need to know TopicsConclusion of Chapter 13/ Need to know Topics

Chi-square test for Chi-square test for goodness of fitgoodness of fit

Chi-square test for Chi-square test for independenceindependence

Goodness of fit testGoodness of fit test Degrees of freedomDegrees of freedom Two-way tablesTwo-way tables P-valuesP-values

Expected CountsExpected Counts Chi-square StatisticChi-square Statistic All equations in the All equations in the

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