Instructor: Hello students.
Welcome to Biostats ER, Example 3, Chapter 7.
In this example, we will learn
how to perform hypothesis testing
for two sample independent continuous outcome data.
The problem is from our textbook, Problem 30.
And the problem states, a study is performed
to examine the relationship between
the concentration of plasma antioxidant vitamins
and cancer risk.
The table shows data
for plasma vitamin A concentration
in stomach cancer patients
and controls, participants similar to the cancer patients,
but free of disease.
Is there a significant difference in the mean concentration
of plasma antioxidant vitamins
between the patients with stomach cancer and controls?
Run the appropriate test
at a 5% level of significance.
So here the two samples are independent
because this is an example of a case control study.
The outcome, plasma vitamin A concentration,
is measured on a continuous scale,
and here we will use a t-test
because the sample size for the stomach cancer patients
is less than 30.
So with that, we will move forward with step one,
where we will set up the hypothesis
and determine the level of significance.
So the hypothesis here,
for null will state
that the means are equal and mu1 is equal to mu2.
And the alternative will state that the means are not equal
and mu1 is not equal to mu2.
The level of significance here is 0.05.
Now for step two, as per the guidelines,
if the ratio of the sample variance
is between 0.5 and two,
the assumption of equality of population variance
is considered appropriate.
Therefore, when we check the ratio of the variance,
we find out that it is 0.62,
which is between 0.5 and two.
Therefore, we can proceed.
Here, I have provided you
with the t-test that we will be using
and the degrees of freedom will be calculated
by adding the two sample sizes, n1 plus n2,
and then deducting two because we have two samples.
And then we will get our degree of freedom, which is 68.
Then we will set up the decision rule.
And based on the degrees of freedom being 68
and alpha being 0.05,
we will reject null if our t calculated
is less than or equal to negative 1.995,
or if our t calculated is greater than
or equal to positive 1.995.
Now we will move forward
and compute the test statistics.
First we will calculate the Sp,
and here the n1 is 20
and the s1 is 0.15.
The n2 is 50,
and the s2 is 0.19.
And for the denominator, n1 again is 20,
n2 is 50.
And then we will deduct two.
So once we perform the calculation,
we find out that Sp is 0.18.
Then we will move to our calculation
to obtain the t-value.
And here for the numerator,
we will insert the two mean values,
2.41 and 2.78.
And then for the denominator, we'll insert Sp,
which is 0.18
and then the n1,
which is 20,
and n2, which is 50.
Once we perform the calculation here,
we obtain our t calculated,
which is negative 7.77.
Now in step five, we are going to reach our conclusion.
And here we will reject null
because negative 7.77
is actually less than negative 1.995.
So we have statistically significant evidence
at the alpha of 0.05
to show that there is a significant difference
in the mean concentration of plasma antioxidant vitamins
between patients with stomach cancer and controls.
Thank you for your time and attention
and I'll see you in the next video.