% Hazel Data on Magnesium Oxide
% Mg-CaO Data. In many ways magnesium (symbol Mg) is
% very similar to calcium (Ca), and determination of the quantity of one may
% be influenced by the presence of the other. Extremely small amounts of
% calcium, especially in the presence of much magnesium, as in magnesites
% and fused magnesia, cannot be determined satisfactorily by direct precipitation
% as oxalate. Hazel and Eglof (1946) proposed a new method, denoted
% as method B. Its performance was compared to the traditional alcohol
% method (treatment with a mixture of ethyl alcohol, methyl alcohol and
% sulfuric acid), denoted here as method A.
% The column y is obtained by using the method A, while the column z
% is obtained by a Hazel-Eglof method B. Column x is the exact amount of
% CaO present in MgO + CaO, India Magnesite, and Magnesite 104. Part of
% this data ( hazel.dat|mat) was analyzed also by Youden (1951, p.44).
hazel=[...
4.0 3.7 3.9
8.0 7.8 8.1
8.5 7.7 8.9
9.1 8.4 9.2
9.7 9.4 10.0
9.9 9.5 9.9
12.5 12.1 12.4
16.0 15.6 16.0
20.0 19.8 19.8
25.0 24.5 25.0
26.8 26.1 27.1
31.0 31.1 31.1
36.0 35.5 35.8
40.0 39.4 40.1
40.0 39.5 40.1 ];
%load 'hazel.dat'
x=hazel(:,1); y=hazel(:,2); z=hazel(:,3); n=length(x);
mycor = @(x,y) (x(:)-mean(x(:)))'*(y(:)-mean(y(:))) / ...
sqrt( (x(:)-mean(x(:)))'*(x(:)-mean(x(:)) ) * ...
(y(:)-mean(y(:)))'*(y(:)-mean(y(:))) );
rxy=mycor(x,y); rxz = mycor(x,z); ryz=mycor(y,z);
% 0.9998 0.9999 0.9996
ryz_x = (ryz - rxy * rxz)/sqrt((1-rxy^2)*(1-rxz^2)) %-0.3861
t= ryz_x * sqrt(n-2-1)/sqrt(1-ryz_x^2) %-1.5717
pval =2 * tcdf(-abs(t), n-2-1) %0.1420