SUMMARY OF STATISTICS FORMULAS

[Pages:2]95206_Graveter_Front_Endpapers 4/12/06 2:17 PM Page 2

SUMMARY OF STATISTICS FORMULAS

THE MEAN Population: X

N

Sample: M X n

SUM OF SQUARES Definitional: SS (X )2 Computational: SS X 2 (X)2

N

VARIANCE Population: 2 SS

N

Sample: s2 n S S 1

STANDARD DEVIATION

Population: SS N

Sample: s n SS1

z-SCORE (FOR LOCATING AN X VALUE) z X

BINOMIAL (NORMAL APPROXIMATION)

z X pn or z X/n p

npq

p q/n

z-SCORE (FOR LOCATING A SAMPLE MEAN)

z MM

where M n

2 n

t STATISTIC (SINGLE SAMPLE)

t M sM

where sM

s2 n

t STATISTIC (INDEPENDENT MEASURES)

t (M1 M 2) ( 1 2) s(M1M2)

where s(M1M2)

s2p s2p n1 n2

and

s2p SdSf11 SdSf22

t STATISTIC (RELATED SAMPLES)

t MD D sMD

where sMD

s2 n

ESTIMATION t Statistic (Single Sample)

M tsM t Statistic (Independent Measures)

1 2 M1 M2 ts(M1 M2) t Statistic (Related Samples)

D MD tsMD

INDEPENDENT-MEASURES ANOVA

SStotal

X 2

G2 N

dftotal N 1

SSbetween

T2 n

G2 N

dfbetween k 1

SSwithin SSinside each treatment

dfwithin N k

F MSbe tween MSwithin

where each MS SS df

REPEATED-MEASURES ANOVA

SSbetween

T2 n

G2 N

dfbetween k 1

SSerror SSwithin SSsubjects

dferror (N k) (n 1)

where SSwithin SSinside each treatment

and

SSsubjects

P2 k

G2 N

F MSbe tween MSerror

where each MS SS df

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TWO-FACTOR ANOVA

SSbetween

treatments

T2 n

G2 N

dfbetween treatments number of cells 1

SSwithin treatments SSeach treatment

dfwithin treatments dfeach treatment

SSA

TR2OW nROW

G2 N

dfA (number of levels of A) 1

SSB

T C2 OL nCOL

G2 N

dfB (number of levels of B) 1

SSAB SSbetween treatments SSA SSB

dfAB dfbetween treatments dfA dfB

FA

MS A MSwithin

FB

MS B MSwithin

FAB

MSA B MSwithin

where each MS SS df

PEARSON CORRELATION

r SP SSXSSY

where

SP

(X

MX)(Y

MY)

XY

(X) (Y) n

SPEARMAN CORRELATION rs 1 n(6n2 D21)

LINEAR REGRESSION

Y^ bX a

where b SP SSX

and

a MY bMX

SSregression r2SSY

df 1

MSregression

SS df

SSresidual (1 r2)SSY

df n 2

MSresidual

SS df

MULTIPLE REGRESSION

Y^ b1X1 b2X2 a

R2 b1SPX1 Y b2 SPX2Y SSY

SSregression R2SSY

df 2

MSregression

SS df

SSresidual (1 R2)SSY

df n 3

MSresidual

SS df

LINEAR AND MULTIPLE REGRESSION

Standard error of estimate MSresidual F MSreg ression

MSresidual

CHI-SQUARE STATISTIC 2 ( fo fe)2

fe

MANN-WHITNEY U

UA

nAnB

nA(nA 1) 2

RA

UB

nAnB

nB(nB 1) 2

RB

KRUSKAL-WALLIS TEST

H N(N1 2 1)

T2 n

3(N 1)

FRIEDMAN TEST 2r nk(k1 2 1) R2 3n(k 1)

MEASURES OF EFFECT SIZE

Cohen's d mean dif ference standard deviation

r 2 and 2 (Percentage of Variance Accounted For)

r2 t 2 t 2 df

(for Independent and Repeated t)

2 SStreatmSe SnttreatmSeSn etrror term

(for Analysis of Variance)

2

phi n

Cram?r's V 2 n(df)

(for Chi-square Test for Independence)

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