HLTH211
Clinical Epidemiology and Biostatistics
for Health Sciences
Lecture 7: Hypothesis Testing – One and Two
Groups

o
Research questions often have essentially true or
false answers.
o
We may want to determine whether one treatment
has better outcomes than an alternative treatment,
or we may want to determine whether patients with
a particular characteristic have better outcomes than
patients without that characteristic, or we may be
interested in determining whether a treatment
results in a particular change.
o
These types of questions are
answered using hypothesis
testing.
Introduction to Hypothesis Testing
2

o
We set a null hypothesis which, in the case of a one
sample test, states that a parameter in the target
population takes a particular value (the null value)
o
If we were to take repeated samples from this target
population, we would expect to see variation in sample
statistics for estimating this parameter, ie. these statistics
would have some distribution. Some statistics may be close
to the null value set as our null hypothesis, others may be
further away.
o
We use a test statistic to measure the discrepancy between
a sample statistic and the null value.
o
The larger that test statistic is, the more unlikely it is that
the null hypothesis is true, so we reject the null hypothesis.
We use a probability (p-value) to make this decision.
3
Basis of Hypothesis Testing

Hypothesis:
State the
null
and the alternative hypotheses in
terms of the parameter of interest.
Assumptions:
Check the underlying assumptions of the test.
Test Statistic:
Calculate the test statistic. This can be done using software.
p-value:
Obtain the p-value (again, you can use software) for the test
Decison:
Use the p-value to decide whether or not you have enough evidence to
reject the null hypothesis
Conclusion:
Write a conclusion framed in terms of the original research question.
Steps in Hypothesis Testing
4
P
T
H
A
D
C
Hypothesis Test

o
The null hypothesis represents an assumption or
claim of ‘no effect’. The hypothesis test is used to
determine whether we have evidence against this null
hypothesis.
o
In the methods we use, null hypotheses will be fairly
simple and will be based on the equality of a
parameter to either another parameter or to a
constant.
o
Important: null hypotheses always refer to population
parameters, not to samples. This is because we are
attempting to draw conclusions about populations, not
about samples.
The Null Hypothesis
5

Examples of null hypotheses:
o
The average age at which Type 1 diabetes is
diagnosed in females is 54 years:
𝐻𝐻
0
:
𝜇𝜇
= 54
o
The average survival time for people diagnosed
with dementia is 4.5 years:
𝐻𝐻
0
:
𝜇𝜇
= 4.5
o
Later in the lecture we will consider hypotheses
such as – The average pain scores after treatment
are equal for Treatment A and Treatment B:
𝐻𝐻
0
:
𝜇𝜇
𝐴𝐴
=
𝜇𝜇
𝐵𝐵
6
Examples of Null Hypotheses

o
For a one sample test, the null hypothesis is a statement
(or claim) that a population parameter has a specified
value:
𝐻𝐻
0