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This quantlet illustrates the concept of the -value,
which is used extensively for hypothesis testing. The
main idea is that, if the probability of getting an observed
value
is very small, then we most likely have the wrong
assumptions in computing this probability.
More formally, suppose we take a sample value from the binomial probability distribution:
To activate this quantlet, the following should be typed in:
twpvalue()After this, the user should see the following window:
Here, the user is asked to input the number of Bernoulli
trials (), the null hypothesis probability of success
in the Bernoulli trials (
), and the observed binomial
value (
). The values above are the default values.
After choosing the desired values, clicking on the OK
button results in the window below, asking which probability
should be visually displayed.
After choosing the desired choice, the next window is displayed (here, for choosing P(X=5)):
On the computer screen, the desired probability from
the last window will be represented in black, with the rest
of the distribution portrayed in red. In the above window,
the second bar from the right, representing , will be
in black.
One intention of this quantlet is to demonstrate why the -value
is
and not
. Indeed, through experimenting,
the user can observe that
depends strongly on
, and
gets small even when there is clearly no strong evidence against
.
, on the other hand, is stable for increasing
, and stays large when there is no strong evidence against
.
Additionally, for testing the null hypothesis that
(i.e. for a given
considerably smaller than
), this
quantlet demonstrates that as the observed value
becomes larger,
the
-value decreases (i.e. evidence against
becomes stronger),
and that when
becomes larger, the
-value becomes larger
(i.e. evidence against
becomes weaker).