STAT 200
Chapter 12
Inference for OneWay Analysis of Variance
OneWay Analysis of Variance
(Section 12.1)
•
Objective: to compare the means of three or more independent populations
•
Examples:
–
Comparison of mean annual income among 4 populations: university graduates
who have a major in computer science, civil engineering, statistics and actuarial
science.
–
Comparison of the mean reduction in blood pressure in hypertensive patients
randomized to three different treatment groups: antihypertensive drug A, B and
C.
•
Analysis of Variance (ANOVA) is a statistical method that tests the equality of three
or more population means by analyzing sample variances or variation in the data.
When there is only one characteristic that we can use to classify the populations,
we fit the oneway ANOVA model.
•
The oneway ANOVA model:
X
ij
=
μ
i
+
ij
,
i
= 1
,
2
, ..., I,
j
= 1
,
2
, ..., n
i
–
there are
I
populations
–
within population
i
, there are
n
i
individuals
–
the population mean for population
i
is given by
μ
i
–
X
ij
represents the measurement on the
j
th individual in the
i
th population
X
ij
varies about the population mean
μ
i
; its value is expressed as the population
mean
μ
i
plus an error term
ij
–
the error term
ij
is a random variable
Assumptions:
–
For each fixed
i
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 Spring '10
 eee
 Normal Distribution, Variance, Oneway ANOVA model, SG M SE M SG M SE

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