Instructor: Hello students and welcome to Biostat ER,
Chapter Eight, Example One.
In this example we will learn how to calculate sample size
for one-sample continuous outcome
to perform hypothesis testing.
This problem is not from the textbook
and I will read it first.
"The issue here is that we have collected some data
"and we need to know if our sample mean is different
"from some previous established mean, which is 100.
"We want a hypothesis test with 80% power
"and we know that we will fail to reject the null hypothesis
"within a margin of error of five.
"Therefore, if our mean is between 95 and 105,
"we know that we will fail to reject the null hypothesis.
"From publications for similar studies,
"we know that the standard deviation is between 8.5 and 9.5.
"So how many subjects are required?"
So here I have basically summarized the information
that has been provided and I have also stated the formula.
Now the standard deviation which was obtained
from previous literature, and as you can see it is a range
and we always want you to use the highest value
from this range as it will give us the most variation
and ensure that we have enough subjects in the study
because we always want to error on the side of caution
and ensure that we are enrolling enough subjects.
So as we proceed with the calculation,
we will first calculate the denominator, that is ES.
For ES, the numerator here is the difference
between the means.
Now because we want to fail to reject the null hypothesis
with a margin of error of five.
So this can be the high end minus the mean
or the low end minus the mean,
but the difference must be five.
So we will insert 105 and 100,
but we can also insert 95 and 100.
Both will give us the same result
because we are utilizing the absolute difference.
And here I have inserted 105 and 100 and the sigma,
which is 9.5.
And once we perform the algebra here, we get 0.526.
Now after we calculate the denominator,
we need to calculate the numerator.
So the value for Z, one minus alpha divided by two,
is basically the Z of the 97.5 percentile,
and that is going to be 1.96.
So this is the Z value
for which 97.5% of probability lies below.
So the value of Z one minus beta is going to be
the Z of the 80th percentile
because one minus beta is the power of the study
and that is going to be 0.84.
So, both of these values, of course,
were obtained from the Z table.
So now we are going to insert these numbers
and we are going to perform the algebra
and we will get 28.33.
So we always round off our sample size calculation,
therefore, it is going to be 29,
so 29 subjects are required.
So thank you for your attention
and I'll see you in the next video.