14.2 Power Point

8/7/2019 14.2 Power Point

1/11

Inference for TwoInference for Two--Way TablesWay Tables

(Chi(Chi--Square Test for Homogeneity)Square Test for Homogeneity)

Section 14.2Section 14.2 Part 1Part 1


2/11

A chiA chi--square test of homogeneity testssquare test of homogeneity tests

whether it is reasonable to believe that,whether it is reasonable to believe that,when several different populations arewhen several different populations arebroken down into the same categories,broken down into the same categories,they have the same proportion ofthey have the same proportion ofmembers in each category. Suchmembers in each category. Suchpopulations are calledpopulations are called homogeneoushomogeneous..


3/11

Example: Paper TowelsExample: Paper Towels Justine decides to test the dry strengthJustine decides to test the dry strength

of three brands of paper towels. Sheof three brands of paper towels. She

cannot take a true random sample, butcannot take a true random sample, butshe believes that it is reasonable toshe believes that it is reasonable toassume that all paper towels of theassume that all paper towels of thesame brand are pretty much identical.same brand are pretty much identical.

So she buys one roll of each of theSo she buys one roll of each of thethree brands and uses the first 25three brands and uses the first 25towels from each.towels from each.


4/11

Justine stretches each towel tightly,Justine stretches each towel tightly,

drops a golf ball from a height of 12drops a golf ball from a height of 12inches, and records whether the golfinches, and records whether the golfball goes through the towel. Justineball goes through the towel. Justine

tests the 75 towels in random ordertests the 75 towels in random orderbecause she knows that it will bebecause she knows that it will beimpossible to hold her testing procedureimpossible to hold her testing procedurecompletely constant. The next displaycompletely constant. The next displayshows the results from Justines tests.shows the results from Justines tests.


5/11

BrandBrand

BrainyBrainy MountyMounty SteveSteve TotalTotal

TowelTowel YesYes 1818 77 55 3030

Breaks?Breaks? NoNo 77 1818 2020 4545

TotalTotal 2525 2525 2525 7575

This is called a twoThis is called a two--way table because eachway table because each

outcome is classified in two ways, according tooutcome is classified in two ways, according tothe type of paper towel and whether or not itthe type of paper towel and whether or not itbreaks. Disregarding the labels and totals, itbreaks. Disregarding the labels and totals, it

has two rows and three columns.has two rows and three columns.

This is called a twoThis is called a two--way table because eachway table because each

outcome is classified in two ways, according tooutcome is classified in two ways, according tothe type of paper towel and whether or not itthe type of paper towel and whether or not itbreaks. Disregarding the labels and totals, itbreaks. Disregarding the labels and totals, it

has two rows and three columns.has two rows and three columns.


6/11

We Need a New TestWe Need a New Test Are the results from Justines threeAre the results from Justines three

samples consistent with the hypothesissamples consistent with the hypothesisthat the percentage of towels thatthat the percentage of towels thatbreak is the same for each brand?break is the same for each brand?


7/11

What You Need Before You TestWhat You Need Before You Test Formula for the expected count,Formula for the expected count, EE

As before:As before:

dfdf = (= (rr -- 1)(1)(cc -- 1)1)

( )( )row total column totalE

grand total!

! E

EO 22 )(G


8/11

ChiChi--Square Test for HomogeneitySquare Test for Homogeneity Name of test:Name of test:22 Test forTest for

HomogeneityHomogeneity

State the Hypotheses:State the Hypotheses:

HH00: The distribution of the response: The distribution of the response

variable is the same in all populationsvariable is the same in all populationsof interest.of interest.

HHaa: These distributions are not all the: These distributions are not all thesame.same.


9/11

Check Conditions:Check Conditions:

S.S. Separate, independent randomSeparate, independent randomsamplessamples

E.E. All expected counts are at least 5All expected counts are at least 5(or all are(or all are 1 and no more than1 and no more than20% are < 5)20% are < 5)

State the df, compute the test statisticState the df, compute the test statistic

and theand the PP --valuevalue

Interpretation in contextInterpretation in context


10/11

Family FulfillmentFamily Fulfillment In November 1997, the Gallup OrganizationIn November 1997, the Gallup Organization

released the results of a poll on family valuesreleased the results of a poll on family values

for different nations of the world. Resultsfor different nations of the world. Resultsfrom each country were based on samples offrom each country were based on samples of1000 adults in each country. One of the1000 adults in each country. One of thequestions asked was this: For youquestions asked was this: For you

personally, do you think it is necessary or notpersonally, do you think it is necessary or notnecessary to have a child at some point innecessary to have a child at some point inyour life in order to feel fulfilled?your life in order to feel fulfilled?


11/11

Table of Observed CountsTable of Observed Counts

CountryCountry

ResponseResponse

USUS IndiaIndia MexicoMexico CanadaCanada GermanyGermany TotalTotal

YesYes 460460 930930 610610 590590 490490 30803080

NoNo 510510 6060 380380 370370 450450 17701770

UndecidedUndecided 3030 1010 1010 4040 6060 150150

TotalTotal 10001000 10001000 10001000 10001000 10001000 50005000

14.2 Power Point

Documents

Transcript of 14.2 Power Point