**Hypothesis
Testing**

We need to compare two distributions of data

The two
samples will always be different

Sampling
error and measurement error are unavoidable

Statistics are used to distinguish between trivial and
meaningful differences

A statistical test works much like a jury in criminal trial

Both
situations operate without absolute proof

You
may make wrong decision

A jury
trial is a test for guilt, while a statistical test is a test for differences

You
do not stand trial to show you are innocent

You
do not design experiment unless you expect an effect

Both situations consider one of
two mistakes more serious

Finding
innocent man guilty in a jury trial

Concluding
a difference was "real" when it was not

A statistical test

Is based on
the data

Begins by
assuming "no difference" (= null hypothesis)

It is
difficult to reject the null hypothesis

Must
be __>__ 95% differences observed did not occur by chance

Now
you accept the alternative hypothesis

Science progress by rejecting null
hypotheses

To carry out most kinds of statistical tests

Use data to
calculate test statistic

Look up the
critical value of the test statistic

Compare to
see if the test statistic is in the rejection region