Casio FX-9750G, FX-9860GII ITest, 9. Statistic Formula, r n, F = MS/MSe, MS = SS/Fdf, MSe = SSe/Edf

9. Statistic Formula

ITest

Test

1-Sample Z Test

 = (o – 0)/(/' )

Z



o1

o2

 1



2

2-Sample

Test

= (

–

)/ (

12/

) + (

22/

)

1-Prop Z Test

z = (x/n – p0)/

p0(1 – p0)/n

2-Prop Z Test

z = (x1/n1 – x2/n2)/

pˆ (1 – pˆ )(1/n1 + 1/n2)

1-Sample t Test

 = (o – 0)/(s/' )

t = (o1 – o2)/ sp2(1/n1 + 1/n2)

2-Sample t Test (pooled)

sp =

((n1 – 1)sx12

+ (n2 – 1)sx22)/(n1 + n2 – 2)

df = n1 + n2 − 2

t = (o1 – o2)/ sx12/n1 + sx22/n2

2-Sample t Test (not pooled)

df = 1/(C2/(n1 – 1) + (1 – C)2/(n2 – 1))

C= (sx12/n1)/(sx12/n1 + sx22/n2)

	n		n
	b = (xi – o)(yi – p)/ (xi – o)2				a = p – bo
LinearReg t Test	i=1		i=1
	t = r n – 2)/(1 – r2)
				Oi: The i-th element of the observed
	k			list
Χ2 GOF Test	2 = (Oi − Ei)2 /Ei			Ei: The i-th element of the expected
	i
				list
	k	R		Oij: The element at row i, column j of
	2 = (Oij		− Eij)2 /Eij
Χ2 two-way Test	i	j		the observed matrix
	k	R		Eij: The element at row i, column j of
	Eij = xij • xij / n
				the expected matrix
	i=1	j=1
2-Sample F Test	F = sx12/sx22
	F = MS/MSe		MS = SS/Fdf		MSe = SSe/Edf
	k			k
ANOVA Test	SS = ni (oi − o)2			SSe = (ni – 1)sxi2
	i=1			i=1
				k
	Fdf = k − 1			Edf = (ni – 1)
				i=1

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