Instructor: Hello students, and welcome
to Biostat Chapter 8:Example 6.
In this example, we will learn how to calculate sample size
for one-sample dichotomous outcome
to perform hypothesis testing.
The problem here is not from our textbook,
and first I will read the problem.
The issue here is that we have performed an intervention
for older adult females to improve their bone health.
From published literature, we have been able to determine
that bone fracture for similar population is 63%.
We are hypothesizing that after the intervention,
bone health will improve.
Hence we will see a reduction in fracture down to 59%.
We want to test the hypothesis
that with a 90% statistical power,
if there is a true difference in bone fracture
after the intervention. How many subjects are required?
So here I have provided you
with all the information in a summary format,
and I have also inserted the formula here.
And now, as we move forward, we first need
to determine the effect size, and for the effect size,
the numerator here is the difference
between the hypothesized value and the established value.
And the denominator is the square root
of the established value multiplied by one minus that value.
So here I have inserted all the values
as they were provided in the problem,
and after that, once we perform the algebra, we get
that the effect size is equal to 0.083.
Now we have to determine the other values that
we need to insert in the formula
to determine our sample size.
So the value for Z1 minus alpha divided by two.
The Z 97.5th percentile is 1.96,
which is a value we have used multiple times by now.
The value of Z one minus beta here would be
the Z 90th percentile because one minus beta
is the power of the study,
and that is going to be 1.282.
So now we will insert these values
and once we insert these values
and perform the algebra,
we get 1528.81.
So once we round it up, we get 1,529.
So 1,529 subjects are required.