Instructor: Hello, students.
Welcome to our biostat ER example from Chapter 6.
In this example, we are going to learn
how to calculate the 95% confidence interval
for risk difference.
First, I'm going to read the problem.
The problem here states, "A clinical trial is conducted
to compare an experimental medication to a placebo
to reduce the symptoms of asthma.
200 participants are enrolled to the study
and randomized to receive
either the experimental medication or the placebo.
The primary outcome
is a self-reported reduction of symptoms.
Among 100 participants
who received the experimental medication,
38 report reduction in symptoms
as compared to 21 participants of 100 assigned to placebo."
So for your convenience here, I have generated a table
and inserted the numbers in the respective cells.
So, 38 participants from 100 in the experimental group
reported reduction in symptoms,
whereas 21 participants from the placebo group out of 100
reported reduction in symptoms.
The next thing I have done here is type the formula
that we will be using
to calculate the 95% confidence interval
for risk difference.
The first thing for this formula we have to do
is calculate the p1-hat,
which is x1 divided by n1.
And as you can see, the x1 here is 38,
and the n1 is 100.
So p1-hat is going to be 0.38.
And next we have to calculate p2-hat.
And x2 here is 21, and n2 here again is 100.
So when we do the division, we get 0.21.
Now we have to plug this number into the formula.
So here is 0.38, which is p1-hat,
minus 0.21, which is p2-hat.
Then we have the z value 1.96.
Then again we have the p1-hat, which is 0.38,
and then we have 1 minus p1-hat, which is 0.62,
and then we have 0.21, which is p2-hat,
and 1 minus p2-hat, which is 0.79.
Once we have inserted all the numbers into the formula,
what we have to do is solve the equation algebraically.
And once we do that,
we get that the 95% confidence interval
is going to be 0.046 to 0.294.
So as you can see,
this confidence interval does not include a 1,
therefore, we can state with 95% confidence
that there is a statistically significant difference
between the two groups,
which is the exposed experimental group,
and the unexposed, which is the placebo.
Thank you for your time and attention,
and I will see you in the next video.