Univariate Statistics - MATLAB Recipes for Earth Sciences - page 89

the 5% signii cance level. h is is a two-sample t -test, i.e., the means are not
equal. Computing the two-tailed critical tcrit value by entering 1-0.05/2
yields the upper (positive) tcrit value, which we compare with the absolute
value of the dif erence between the means.
tcrit = tinv(1-0.05/2,na+nb-2)
tcrit =
1.9803
Since the tcalc value calculated from the data is smaller than the critical
tcrit value, we cannot reject the null hypothesis without another cause. We
conclude therefore that the two means are identical at a 5% signii cance
level. Alternatively, we can apply the function ttest2(x,y,alpha) to the two
independent samples corg1 and corg2 at an alpha=0.05 or a 5% signii cance
level. h e command
[h,p,ci,stats] = ttest2(corg1,corg2,0.05)
yields
h =
0
p =
0.4681
ci =
-0.3028
0.6547
stats =
tstat: 0.7279
df: 118
sd: 1.3241
h eresult h=0 means that we cannot reject the null hypothesis without another
cause at a 5% signii cance level. h e p -value of 0.4681 or ~47% (which is
much greater than the signii cance level of 0.05 or 5%) suggests that the
chances of observing more extreme t -values than the values in this example
from similar experiments would be 4,681 in 10,000. h e 95% coni dence
interval on the mean is [-0.3028,0.6547], which includes the theoretical
(and hypothesized) dif erence between the means of 25.5-25.3=0.2.
h e second synthetic example shows the performance of the two-sample
t -test in an example with very dif erent means of 24.3 and 25.5, while the
standard deviations are again 1.3 and 1.5, respectively.
clear