Page 64 - MATLAB Recipes for Earth Sciences

3.6 The F–Test 55

ssmaller =
1.2097

Now we compare the calculated F with the critical F. This can be accom-
plished using the function finv on a 95% signifi cance level. The function
finv returns the inverse of the F distribution function with df1 and df2
degrees of freedom, at the value of 0.95. Typing
Freal = slarger^2/ssmaller^2

Ftable = finv(0.95,df1,df2)
yields

Freal =
1.0762

Ftable =
1.5400

The F calculated from the data is smaller than the critical F. We therefore
cannot reject the null hypothesis without another cause. The variances are
identical on a 95% signifi cance level.
We now apply this test to two distributions with very different standard
deviations, 2.0 and 1.2, respectively.

load('organicmatter_five.mat');

Now we compare the calculated F with the critical F at a 95% signifi cance
level. The critical F can be computed using the function finv. We again type

s1 = std(corg1);
s2 = std(corg2);

df1 = length(corg1) - 1;
df2 = length(corg2) - 1;

if s1 > s2
slarger = s1;
ssmaller = s2;
else
slarger = s2;
ssmaller = s1;
end
Freal = slarger^2/ssmaller^2

Ftable = finv(0.95,df1,df2)