6-539. Statistic FormulaI TestTest1-Sample Z Test = (o – 0 )/(/' )2-Sample Z Test = (o1 – o2)/ (/1 ) + (/2 )21221-Prop Z Test z = (x/n – p0)/ p0(1 – p0)/n2-Prop Z Test z = (x1/n1 – x2/n2)/ pˆ (1 – pˆ )(1/n1 + 1/n2 )1-Sample t Test = (o – 0 )/(s/' )2-Sample t Test (pooled)t = (o1 – o2)/ sp2(1/n1 + 1/n2)df = n1 + n2 − 2sp = ((n1 – 1)sx12 + (n2 – 1)sx22)/(n1 + n2 – 2)2-Sample t Test (not pooled)t = (o1 – o2)/ sx12/n1 + sx22/n2C = (sx12/n1)/(sx12 /n1 + sx22/n2)df = 1/(C2 /(n1 – 1) + (1 – C )2 /(n2 – 1))LinearReg t Testt = r (n – 2)/(1 – r2)b = (xi – o)(yi – p)/(xi – o)2 a = p – boi=1ni=1nC2 GOF TestO i: The i-th element of the observedlistEi: The i-th element of the expectedlistC2 two-way TestO ij: The element at row i, column j ofthe observed matrixEij: The element at row i, column j ofthe expected matrix2-Sample F Test F = sx12 /sx22ANOVA TestF = MS/MSeSS = n i (oi − o) 2MS = SS/Fdf MSe = SSe/Edfi=1kFdf = k − 1 Edf = (ni – 1)SSe = (ni – 1)sxi2i=1ki=1k2 = (O i − Ei) 2 /Eiik2 = (O i − Ei) 2 /Eiik2 = (O ij − Eij) 2 /EijikjREij = xij • xij / ni=1kj=1R2 = (O ij − Eij) 2 /EijikjREij = xij • xij / ni=1kj=1R
