Comparing Two Independent Means  Unpooled and Pooled
Submitted by gfj100 on Wed, 11/11/2009  13:41
We determine whether to apply "pooled" or "unpooled" procedures by comparing the sample
standard deviations. RULE OF THUMB: If the larger sample standard deviation is MORE
THAN twice the smaller sample standard deviation then perform the analysis using unpooled
methods.
Example 1 (Unpooled):
Cholesterol levels are measured for 28 heart attack patients (2 days after their attacks) and 30
other hospital patients who did not have a heart attack. The response is quantitative so we
compare means. It is thought that cholesterol levels will be higher for the heart attack patients, so
a onesided alternative hypothesis is used.
Step 1:
null is
H
0
: μ
1
− μ
2
= 0 and alternative is
H
a
: μ
1
− μ
2
> 0, where groups 1 and 2 are heart
attack and control groups, respectively.
Minitab Output that can be used for Steps 25
Step 2:
test statistic is given in last line of output as t = 6.15, degrees of freedom given as 37.
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 Spring '11
 AndyRegards
 Statistics, Normal Distribution, Standard Deviation, Sample standard deviation

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