Chi-square
distribution
This program calculates
the tail-end and percentile values
for points on a Chi-square
(X2)
distribution
curve.
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You must provide
the value of X2
and the degrees of freedom. No special instruction or
Matlab toolbox is used. Since the summation in
the calculation of Z cannot
actually extend to infinity, we
stop summation when the next term is less than a chosen level of
precision. Our precision is limited to approx. 1×10-7.
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The Matlab program to accomplish this, is:
%
Clears
screen and variables in workspace
clc;
clear
%
Asks the
user for the relevant input
v
= input('Degrees
of
freedom: ');
w = input('Chi-square:
');
%
Calculates the denominator product
r
= 1;
for
i = v : -2 : 2
r
= r*i;
end
%
Calculates the numerator product
k
=
w^(floor((v+1)/2))*exp(-w/2)/r;
%
If
degrees of freedom are odd, then uses the pi factor
if
floor(v/2) ==
v/2
j
= 1;
else
j =
sqrt(2/(w*pi));
end
l
= 1;
m = 1;
v = v + 2;
m = m*w/v;
%
Summation factor
while
m >= 1e-7
l
= l + m;
v
= v + 2;
m
= m*w/v;
end
%
Displays
results
str
= ['Tail
end
value: '
num2str(1-j*k*l)];
disp(str)
str = ['Percentile:
'
num2str(j*k*l)];
disp(str)
Example
- Calculate tail-end and percentile
A X2 statistic for
a given study was computed to be 2.571108 with one degree of freedom.
What are the tail-end and percentile values?
Running the Matlab program above, we enter and get:
Degrees of freedom: 1
Chi-square:
2.571108
Tail-end
value: 0.10883
Percentile:
0.89117
From
'Chi-square' to home
From
'Chi-square' to 'Probability and Stats'
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