Therearebasicallytwotypesofrandomvariablesandtheyyieldtwotypesofdata:numericalandcategorical.Basicallycategoricalvariableyielddatainthecategoriesandnumericalvariablesyielddatainnumericalform.Responsestosuchquestionsas"Whatisyourmajor?"or"Doyouownacar?"arecategoricalbecausetheyyielddatasuchas"biology"or"no."Incontrast,responsestosuchquestionsas"Howtallareyou?"or"Whatisyourscore?"arenumerical.Numericaldatacanbeeitherdiscreteorcontinuous.

TypesofDataDataType

QuestionTypePossibleResponses

Categorical

Whatisyoursex?maleorfemale

NumericalDiscrete-Howmanycarsdoyouown?twoorthree

NumericalContinuous–Howtallareyou?

72inchesThetablebelowmayhelpyouseethedifferencesbetweenthesetwovariables.Noticethatdiscretedataarisefromacountingprocess,whilecontinuousdataarisefromameasuringprocess.WhatisChisquaretest?Achisquare(X2)statisticisusedtoinvestigatewhetherdistributionsofcategoricalvariablesdifferfromoneanother.TheChiSquarestatisticcomparesthetalliesorcountsofcategoricalresponsesbetweentwo(ormore)independentgroups.(note:Chisquaretestscanonlybeusedonactualnumbersandnotonpercentages,proportions,means,etc.)

χ2test有幾種不同的用法，在此我們只討論兩種，一種是所謂的「獨(dú)立性考驗(yàn)」(thetestforindependence)，另一為「適合度考驗(yàn)」(thetestofgoodnessoffit)。AChi-squaregoodness-of-fittestisusedtotestwhetherafrequencydistributionfitsanexpecteddistribution.AChi-squareindependencetestisusedtotesttheindependenceoftwovariables.Usingachi-squaretest,youcandeterminewhethertheoccurrenceofonevariableaffectstheprobabilityoftheoccurrenceoftheothervariable.某市初中聯(lián)考擬定三門課程，對(duì)各門課程的達(dá)標(biāo)人數(shù)統(tǒng)計(jì)如下表，請(qǐng)問(wèn)三門課程難度是否一致？課程語(yǔ)文數(shù)學(xué)英語(yǔ)達(dá)標(biāo)人數(shù)1019488原假設(shè)：難度一致

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語(yǔ)文：數(shù)學(xué)：英語(yǔ)=：1：1goodness-of-fittest若按照個(gè)體輸入，則需要輸入所有人數(shù)。課程達(dá)標(biāo)113021103120若直接輸入總數(shù)，則需要加權(quán)達(dá)標(biāo)人數(shù)課程1019488語(yǔ)文數(shù)學(xué)英語(yǔ)“課程”變量可以省略DataWeightCasesData/WeightCasesWeightCasesby達(dá)標(biāo)人數(shù)DonotweightcasesFrequencyVariable:OKAnalyzeNonparametricTestsChi-SquareAnalyze/NonparametricTests/Chi-SquareTestVariableList達(dá)標(biāo)人數(shù)OKExpectedValuesAllcategoriesequal某市初中聯(lián)考擬定三門課程，對(duì)各門課程的達(dá)標(biāo)人數(shù)統(tǒng)計(jì)如下表，已知語(yǔ)文考試人數(shù)是其他兩門課程人數(shù)的兩倍，請(qǐng)問(wèn)三門課程難度是否一致？課程語(yǔ)文數(shù)學(xué)英語(yǔ)達(dá)標(biāo)人數(shù)1019488原假設(shè)：難度一致

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語(yǔ)文：數(shù)學(xué)：英語(yǔ)=2：1：1goodness-of-fittestAnalyzeNonparametricTestsChi-SquareTestVariableList達(dá)標(biāo)人數(shù)OKExpectedValuesAllcategoriesequalValues:Add語(yǔ)文：數(shù)學(xué)：英語(yǔ)2：1：1根據(jù)變量順序（升序）輸入比值已知某校男生2000人，女生800人，現(xiàn)調(diào)查某課程的偏好是否存在性別差異，數(shù)據(jù)如下表：性別男生女生選擇該課程的人數(shù)507214原假設(shè)：性別無(wú)偏差

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男：女=5：2（2000/800）DataWeightCasesWeightCasesby選擇人數(shù)DonotweightcasesFrequencyVariable:OKAnalyzeNonparametricTestsChi-SquareTestVariableList選擇人數(shù)OKExpectedValuesAllcategoriesequalValues:Add男：女=5：2根據(jù)變量順序（升序）輸入比值某研究探討性格與人際交往的關(guān)系，抽樣結(jié)果顯示各類型人數(shù)如下表：

性格交往類型內(nèi)向一般外向主動(dòng)102565被動(dòng)57358原假設(shè)：性格與交往類型無(wú)關(guān)

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如：主動(dòng)內(nèi)向：主動(dòng)一般：主動(dòng)外向=1：1：1；外向主動(dòng)：外向被動(dòng)=1：1independencetest性格交往類型人數(shù)內(nèi)向主動(dòng)10內(nèi)向被動(dòng)57一般主動(dòng)25一般被動(dòng)35外向主動(dòng)65外向被動(dòng)8性格交往類型人數(shù)11101257212522353165328DataWeightCasesWeightCasesby人數(shù)DonotweightcasesFrequencyVa