... definitions into sums of various powers of the data, e.g., the familiar Var ( x 1 ...x N )= 1 N−1 N j=1 x 2 j − N x 2 ≈ x 2 − x 2 (14.1.7) but this can magnify the roundoff error by ... few semi-invariants, denoted I k are given by I 2 = M 2 I 3 = M 3 I 4 = M 4 − 3M 2 2 I 5 = M 5 − 10M 2 M 3 I 6 = M 6 − 15M 2 M 4 − 10M 2 3 +30M 3 2 (14.1.11) Notice...
... 609 610 Chapter 14. Statistical Description of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5) Copyright (C) 1988-19 92 by Cambridge University ... http://www.nr.com or call 1-800-8 72- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Chapter 14. Statistical Description of Data 14....
... x); float var1,var2,svar,df,ave1,ave2; avevar (data1 ,n1,&ave1,&var1); avevar (data2 ,n2,&ave2,&var2); df=n1+n2 -2; Degrees of freedom. svar=((n1-1)*var1+(n2-1)*var2)/df; Pooled variance. ... var1,var2,ave1,ave2,df1,df2; avevar (data1 ,n1,&ave1,&var1); avevar (data2 ,n2,&ave2,&var2); if (var1 > var2) { Make F the ratio of the larger variance to the small...
... ((d1 =data1 [j1]) <= (d2 =data2 [j2])) fn1=j1++/en1; Next step is in data1 .
if (d2 <= d1) fn2=j2++/en2; Next step is in data2 .
if ((dt=fabs(fn2-fn1)) > *d) *d=dt;
}
en=sqrt(en1*en2/(en1+en2));
*prob=probks((en+0. 12+ 0.11/en)*(*d)); ... 1-800-8 72- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).
sort(n1 ,data1 );
sort(n2 ,data2 );
en1=n1;...
... of
red males
N
11
# of
red females
N
21
# of
green females
N
22
# of
green males
N
12
# of
males
N
1
⋅
# of
females
N
2
⋅
2.
green
# of red
N
⋅
1
# of green
N
⋅
2
total #
N
Figure ... [1]
Anderson, T.W., and Darling, D.A. 19 52,
Annals of Mathematical Statistics
, vol. 23 , pp. 193 21 2.
[2]
Darling, D.A. 1957,
Annals of Mathematical Statistics
,...
... exp
−
1
2
(a
11
x
2
− 2a
12
xy + a
22
y
2
)
dxdy (14.5.3)
where a
11
,a
12
, and a
22
are arbitrary constants. For this distribution r has the value
r = −
a
12
√
a
11
a
22
(14.5.4)
There are occasions ... z
2
|
√
2
1
N
1
−3
+
1
N
2
−3
(14.5.10)
where z
1
and z
2
are obtained from r
1
and r
2
using (14.5.6), and where N
1
and N
2
are, respectively, the n...
... member of pair,
for (k=(j+1);k<=n;k++) { and second member.
a1 =data1 [j] -data1 [k];
a2 =data2 [j] -data2 [k];
aa=a1*a2;
if (aa) { Neither array has a tie.
++n1;
644
Chapter 14. Statistical Description ... respectively.
crank(n,wksp1,&sf);
sort2(n,wksp2,wksp1);
crank(n,wksp2,&sg);
*d=0.0;
for (j=1;j<=n;j++) Sum the squared difference of ranks.
*d += SQR(wksp1[j]-wksp2[j]...
... one, and
a statistical universe of data sets that are drawn from it!
658
Chapter 15. Modeling of Data
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)
Copyright ... deviations σ of these normal distributionsare the same for all points. Then
the probability of the data set is the product of the probabilities of each point,
P...