Graphics Programs Reference
In-Depth Information
α
of a test is the maximum probability of accidentally rejecting a true null
hypothesis. Note that we cannot prove the null hypothesis, in other words
not guilty
is not the same as
innocent
(Fig. 3.12).
The t-test can be performed by the function
ttest2
. We load an example
data set of two independent series of measurements. The fi rst example shows
the performance of the t-test on two distributions with with the means 25.5
and 25.3, respectively, whereas the standard deviations are 1.3 and 1.5.
clear
load('organicmatter_two.mat');
The binary fi le
organicmatter_two.mat
contains two data sets
corg1
and
corg2
. First we plot both histograms in one single graph
[n1,x1] = hist(corg1);
[n2,x2] = hist(corg2);
h1 = bar(x1,n1);
hold on
h2 = bar(x2,n2);
set(h1,'FaceColor','none','EdgeColor','r')
set(h2,'FaceColor','none','EdgeColor','b'x)
Here we use the command
set
to change graphic objects of the bar plots
h1
and
h2
, such as the face and edge colors of the bars. Now we apply the
function
ttest2(x,y,alpha)
to the two independent samples
corg1
and
corg2
at an
alpha=0.05
or 5% signifi cance level. The command
[h,significance,ci] = ttest2(corg1,corg2,0.05)
yields
h =
0
significance =
0.0745
ci =
-0.0433 0.9053
The result
h=0
means that you cannot reject the null hypothesis without
another cause at a 5% signifi cance level. The signifi cance of 0.0745 means
that by chance you would have observed values of
t
more extreme than the
one in the example in 745 of 10,000 similar experiments. A 95% confi dence
interval on the mean is [-0.0433 0.9053], which includes the theoretical (and
