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1
Hypothesis Testing
Differences Between Groups
BME 423 Lecture Notes
 Sept. 17, 2008
II. Analysis of Variance (ANOVA or F Test)
C. Summary
III. Examples
B. HR in Men and Women in BME 423
C. HDL Concentration and Exercise
2. Variance of each group
12
1
1
,,,
n
mi
i
x
xx
x
x
n
=
⎛⎞
=
⎜⎟
⎝⎠
∑
…
C. Summary of ANOVA
(F Test)
Experiment:
m
 # of treatment groups
n
 # number of subjects per group
Null Hypothesis:
RV X is measured
H0:
()
2
22
2
2
1
1
1
n
i
s
ss
s
x
x
n
=
=−
−
∑
…
1. Mean of each group
m
μ
μμ
==
=
"
Alternative hypo: at least 2
diff
'
s
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22
1
1
m
wit
i
i
s
s
m
=
=
∑
3. Calculate the within groups
variance
1
1
m
i
i
Xx
m
=
=
∑
4. Compute the overall (grand) mean
6. Calculate the between groups
variance
2
2
X
bet
ns
s
=
5. Compute standard error of the mean
()
2
2
1
1
1
m
i
X
i
s
xX
m
=
=−
−
∑
7. Compute the F Statistic
2
2
bet
wit
s
F
s
=
1
(1
)
n
d
m
mn
ν
=
−
=
−
Obtained form F Table
Denominator degrees of freedom
8. Compare F with the Fcrit (critical value of F)
.05
(,
)
crit
n
d
FF
νν
≡
)
crit
n
d
α
≡
In general
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 Fall '06
 D'Argenio
 Biomedical Engineering

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