BS704_HypothesisTesting-Anova_print.html.pdf - Hypothesis...

Hypothesis Testing - Analysis of Variance (ANOVA)
Introduction
This module will continue the
discussion of hypothesis
testing, where a specific
statement or hypothesis is
generated about a
population parameter, and
sample statistics are used to
assess the likelihood that the
hypothesis is true. The
hypothesis is based on
available information and the
investigator's belief about
the population parameters.
The specific test considered here is called analysis of variance (ANOVA) and is a test of
hypothesis that is appropriate to compare means of a continuous variable in two or
more independent comparison groups. For example, in some clinical trials there are
more than two comparison groups. In a clinical trial to evaluate a new medication for
asthma, investigators might compare an experimental medication to a placebo and to a
standard treatment (i.e., a medication currently being used). In an observational study
such as the Framingham Heart Study, it might be of interest to compare mean blood
pressure or mean cholesterol levels in persons who are underweight, normal weight,
overweight and obese.
The technique to test for a difference in more than two independent means is an
extension of the two independent samples procedure discussed previously which
applies when there are exactly two independent comparison groups. The ANOVA
technique applies when there are two or more than two independent groups. The
ANOVA procedure is used to compare the means of the comparison groups and is
conducted using the same five step approach used in the scenarios discussed in
previous sections. Because there are more than two groups, however, the computation
of the test statistic is more involved. The test statistic must take into account the sample
sizes, sample means and sample standard deviations in each of the comparison groups.
Learning Objectives
After completing this module, the student will be able to:
Perform analysis of variance by hand 1.
Appropriately interpret results of analysis of variance tests 2.
Distinguish between one and two factor analysis of variance tests 3.
Identify the appropriate hypothesis testing procedure based on type of outcome
variable and number of samples
4.
The ANOVA Approach

Consider an example with four independent groups and a continuous outcome
measure. The independent groups might be defined by a particular characteristic of the
participants such as BMI (e.g., underweight, normal weight, overweight, obese) or by the
investigator (e.g., randomizing participants to one of four competing treatments, call
them A, B, C and D). Suppose that the outcome is systolic blood pressure, and we wish
to test whether there is a statistically significant difference in mean systolic blood
pressures among the four groups. The sample data are organized as follows:
Group 1 Group 2 Group 3 Group 4
Sample Size n
1
n
2
n
3
n
4
Sample Mean
Sample
Standard
Deviation
s
1
s
2
s
3
s
4
The hypotheses of interest in an ANOVA are as follows:
H
0
: μ
1
= μ
2
= μ
3
... = μ
k
H
1
: Means are not all equal.