In this video, I will illustrate how to state
your hypothesis when you're
comparing the averages between two entity.
We will use basketball as an example,
using Michael Jordan and Wilt Chamberlain,
the two highest scorers in
the history of basketball, as examples.
If you were to recall,
you would know that Michael Jordan, on average,
scored 30.12 point in each game,
and Chamberlain averages around 30.06 points per game.
If you were to compare
the two averages between Michael Jordan and Chamberlain,
and even though they are very similar looking numbers,
we need to set up a statistical hypothesis testing.
We are interested in comparing
the average points scored by the two basketball players,
and the comparison of means or
averages is available in three flavors.
First, we can assume that
the average points per game scored by the two players,
Jordan and Chamberlain, are the same.
That is, the difference between
their mean scores is zero.
If their averages are the same,
average of one minus average of other should be zero,
this becomes a null hypothesis.
Let's say if Mu_j
represents the average points
per game scored by Michael Jordan,
and Mu_c represents the average points
per game scored by Wilt Chamberlain,
we can state the null hypothesis to be Mu_j equal Mu_c,
that is the average scored by
Jordan and average scored by Chamberlain are the same.
The alternative hypothesis would be that no,
these averages are not the same, they are different.
The alternative hypothesis H_a
compared to null hypothesis H_0 or o.
The alternative is that the averages are not the same,
their average scores are different.
Now, the other option, the second option,
is to assume that Jordan scored better or higher.
In that case, our null hypothesis is
the average score by
Michael Jordan is greater than or
equal to the average score by Wilt Chamberlain.
In this particular case,
the alternative hypothesis would be different.
It wouldn't be not equal to,
but it would be less than.
The alternative would be that the average scored by
Jordan is less than that by Wilt Chamberlain.
By the same account,
our third option will be
that the null hypothesis is that in fact Jordan scored
less than Wilt Chamberlain and
the alternative hypothesis will be the reverse of it,
saying that no, Michael Jordan scored
higher than Wilt Chamberlain.
In a nutshell, we have three options.
We can say the averages are the
same and the null would be,
no, they are not the same, not equal.
We can say the average is less than,
the null is that Jordan's average
is higher than Chamberlain,
and the alternative would be the reverse of it.
The third option is to say that
the average scored by
Jordan is less than average scored by Chamberlain,
and the reverse of it will be the alternative hypothesis.
So, three ways of defining a hypothesis.