Lab 227
11/11/09
ANOVA
Overview
•
ANOVA is a procedure we use to test the null hypothesis when we want to evaluate the mean
differences between two or more groups.
•
The main advantage of ANOVA is that we can make multiple comparisons between groups while
keeping the alpha level constant.
Hypotheses
•
H
0
: µ
1
= µ
2
= µ
3
•
H
1
: At least one population mean is different
Definitions
•
Factor: this is what we call the IV in ANOVA
•
Level: the individual conditions that make up a factor
o
For example, when testing the effect of three types of therapy on depression, “type of
therapy” is the factor while the specific types (e.g. cognitive, behavioral, or
psychodynamic) are considered levels of the factor.
The F statistic
•
The ratio for the F statistic is similar to the tstatistic but uses variance differences instead of
mean differences
ܨ =
ܸܽݎ݅ܽ݊ܿ݁ ܾ݁ݐݓ݁݁݊ ݏ݈ܽ݉݁ ݉݁ܽ݊ݏ
ܸܽݎ݅ܽ݊ܿ݁ ݓ݅ݐℎ݅݊ ݃ݎݑݏ (݁ݔ݁ܿݐ݁݀ ݀ݑ݁ ݐ ܿℎܽ݊ܿ݁ ݎ ݁ݎݎݎ)
This can also be stated in another way:
ܨ =
ܶݎ݁ܽݐ݉݁݊ݐ ݂݂݁݁ܿݐ+݂݂݀݅݁ݎ݁݊ܿ݁ݏ ݀ݑ݁ ݐ ܿℎܽ݊ܿ݁
ܦ݂݂݅݁ݎ݁݊ܿ݁ݏ ݀ݑ݁ ݐ ܿℎܽ݊ܿ݁
If the null is true, the there will be no treatment effect and the ratio would be F=1
Notation
•
K
is the number of groups in the design
•
N
is the total sample size
•
N
is the sample size per group
•
T
is used instead of ∑X
•
If we add up
T
for all groups we will get
G
•
If we compute
∑X
2
for each group and add it up, we will get
σܺ
௧௧
ଶ
•
MS
is what we call the variance in ANOVA
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 Fall '09
 Shinkareva
 Statistics, Statistical hypothesis testing, Statistical significance

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