Formulas for Exam 2• Estimated Main EffectFull Effect: Yhigh− YloworP(coef∗mean)2p−1Half Effect:Yhigh− Y orP(coef∗mean)2p• Replication ErrorSSrepError=X(ni− 1)s2idfrepError=X(ni− 1)MSrepError=SSrepErrordfrepError• Standard error of an estimated full effectvuuutMSrepError4N• Critical effect sizetα2,dfvuuutMSrepError4N(use t=3 for most situations.)• Prediction IntervalˆY ± tα2,dfvuuutMSrepErrorN + k + 1Nwhere k is the number of variables in the prediction equationand t is usually betweem 2 and 3.1• Combining higher order interactionsSSEf f ect=N4(Effect)2SS“Error00=X(SSEf f ect)df“Error00= number of effects in sum.• Test for Curvaturet =YF− YCss21NF+1NCsignificant if t is greater than 3.• Randomized Complete Block DesignSSBlock=Xm(Yj− Y )2dfBlock= #Blocks − 1SSError= SSrepError− SSBlockdfError= dfrepError−
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