Categorical Independent Variables - Department of Statistical Sciences

[Pages:47]CategoricalIndependent Variables

Andmultiplecomparisons

One-wayAnalysisofvariance

? CategoricalIV ? QuantitativeDV ? pcategories(groups) ? H0:Allpopulationmeansequal ? Normalconditionaldistributions ? Equalvariances

Analysismeanstosplitup

? WithnoIV,bestpredictoristheoverallmean ? VariationtobeexplainedisSSTO,sumofsquared

differencesfromtheoverallmean ? WithanIV,bestpredictoristhegroupmean ? VariationstillunexplainedisSSW,sumofsquared

differencesfromthegroupmeans

SSTO=SSB+SSW

ANOVASummaryTable

Source Model Error Corrected Total

Sum of DF Squares

Mean Square

F Value Pr > F

p - 1 SSB M SB = SSB/(p - 1) M SB/M SW p-value

n - p SSW M SW = SSW/(n - p)

n - 1 SSTO

H0 : ?1 = . . . = ?p

R2istheproportionofvariation explainedbytheindependentvariable

Contrasts

c = a1?1 + a2?2 + ? ? ? + ap?p c = a1Y 1 + a2Y 2 + ? ? ? + apY p

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