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HRP 223 - 2008
HRP223 2008
Topic 8 – Analysis of Means
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One Categorical Predictor
HRP223 2008
Normally Distributed
Not Normally Distributed
One sample vs. population
One sample t-test
Wilcoxon Signed Rank
Two paired samples
Paired t-test
Difference then Signed Rank
Two unpaired samples
T-test
Wilcoxon Rank-sum
Three or more unpaired samples
ANOVA
Kruskal-Wallis
Three or more paired samples
Mixed effects
Transform then mixed model
Normally Distributed
Not Normally Distributed
One sample vs. population
Describe > Distribution
Describe > Distribution
Two paired samples
Analyze >ANOVA>t-test
Describe > Distribution
Two unpaired samples
Analyze >ANOVA>t-test
Describe > Distribution
Three or more unpaired samples
Analyze >ANOVA>Linear
Analyze >ANOVA>Nonpar.
Three or more paired samples
Analyze >ANOVA>Mixed
Multiple Categorical Predictors
 Unpaired samples
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– ANOVA
 Paired samples
– Mixed Effects Models
 If data is not normally distributed
– There are spcialized statistics (Friedman’s test for
2 predictors).
– Try to transform into normally distributed.
Mean vs. Expected BMI
It would be nice to see the
actual Excel file.
Adds a link to source
Adds a link to source and
runs import wizard
This gives instant access to the
current state of the spreadsheet
but it is bugged if you mix
character and numeric data.
Take a Look at the Data
HRP223 2008
Prior to analysis,
do all 3 plots.
Histograms and
box plots show
outliers and
bimodal data but
are not ideal for
assessing
normality.
The formal tests for normality
are not great. They will not
find problems with small
samples and will declare
problems with large samples.
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1. normal distribution
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2. skewed-to-the-right distribution
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3. skewed-to-the-left distribution
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4. heavy-tailed distribution
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5. light-tailed distribution
1.
2.
Image from: Statistics I: Introduction to ANOVA, Regression, and
Logistic Regression: Course Notes. SAS Press 2008.
Inference 101
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 You only have one sample but you want to
make inferences to the world.
 Given what you see in this sample, you can
guess what the distribution of samples looks
like around the null distribution.
2
3
4
5
6
7
10
0
5
Frequency
0 2 4 6 8
Frequency
12
15
15
10
5
0
Frequency
1
1
2
3
5
6
7
1
2
3
4.06
4
5
6
7
4.13
How do you
compare this
sample vs. another
with a mean of 5?
8 10
Frequency
10
Frequency
2
3
4
5
6
7
1
2
3
5
6
6
4
7
1
0
3
4
3.78
5
6
7
4
5
6
7
5
6
7
12
Frequency
10
5
Frequency
15
8 10
6
4
2
3
3.9
2
1
2
3.84
0
Frequency
3.8
4
1
2
3
4
4.13
5
6
7
0 2 4 6 8
1
0
0
0
2
5
10
Make a histogram of the means
5
Frequency
15
15
4.26
4
If the population you
are sampling from
has a mean of 4,
you will not observe
a score of 4.
1
2
3
4
4.01
40
80
.75/sqrt(1) = .75
1
2
3
4
5
6
7
Mean: 4.04 SD: 0.74
150
.75/sqrt(5) = .34
0 50
Frequency
250
1000 samples of size 5
1
2
3
4
5
6
7
Mean: 3.99 SD: 0.34
1000 samples of size 25
100
300
.75/sqrt(25) = .15
0
Frequency
Distributions of the Means
0
Frequency
120
1000 samples of size 1
1
2
3
4
Mean: 4 SD: 0.15
5
6
7
Precision
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 Think of the “+/- something” imprecision in the
estimates of the political polls.
 You typically end up saying you are 95% sure you chose
an interval that has the true value inside the range
bracketed by the confidence limits (CLs). Either the
population value is or is not in the interval between the
lower and upper confidence limit, and if you repeated
the process on many samples, 95% of such intervals
would include the population value.
 The 99% CI is wider (more accurate) than the more
precise 95% CL.
Confidence Intervals from 10 Samples
The unobservable truth
You want to set the width of the
interval so that in 95% of the
experiments, the confidence
interval includes the true value.
In theory, you tweak the interval
and increase or decrease the width.
Axis with units showing your outcome
Benefits of CLs
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 You have information about the estimate's precision.
 The width of the CI tells you about the degree of
random error which is set by the confidence interval.
 Wide intervals indicate poor precision. Plausible
values could be across a broad range.
Estimation vs. Hypothesis Testing
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 P-value < .05 corresponds to a 95% CL that
does not include the null hypothesis value.
 CLs show uncertainty, or lack of precision, in
the estimate of interest and thus convey more
useful information than the p-value.
0 difference between groups or
odds ratio of 1
CLs vs. p-values
null value
Lower
CL
Upper
CL
P > .05 and the null value is inside of
the confidence limits (CLs)
Confidence
interval
null value
Lower
CL
P < .05 and the null value is
not inside of the confidence
limits
Upper
CL
Confidence
interval
null value
zone of clinical
indifference
Not statistically significant and not clinically
interesting
Not statistically significant, possibly clinically
interesting
Statistically significant but not clinically
interesting
Statistically significant and clinically
interesting
Compare Two Teachers
 Import the data
 Describe the data
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– Assign the method as a classification variable
 Do an unpaired T-test
 Do a one-way ANOVA with the predictor
having only two levels
SS total is the sum of the distance
between each point and the overall
mean line squared.
SS error is the sum of the total
squared distances between each
point and the group mean lines.
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Psoriasis
 Scores are arbitrary numbers 0 = < 0%
response, 5 = 26-50% response, etc.
If and only if you work on a fast machine!
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Weight Gain
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Postpartum Depression
After the Formats
Dementia
Wide to Long
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 You may have noticed that the data for these
analyses are all set up as long, skinny files where
there is a record for every observation on a
patient. Some people store data as wide records
with many variables with a single record for each
person.
 To convert from wide to long:
–
–
–
–
Do data step processing with arrays.
Use the Transpose option on the Data menu.
Combine proc transpose and data step code.
Use a macro I wrote. (It is brand new, so check it.)
Tolerance.sas7bdat is
dataset from the book
Save a copy of the macro in a file
after the fill in the blanks are done.
The stuff in the macro file:
The stuff in the blah.sas file:
tol: all variables starting with the letters tol
Narrow to Wide
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 Of course you can transpose back to wide
from narrow.
 If you download the keyboard macros today
you will see that proc transpose now gives you
a code template.