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
95206_Graveter_Front_Endpapers 4/12/06 2:17 PM Page 3
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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