1. Today: Feb 28 Reading Data from existing SAS dataset One-way ANOVA
Reading Le 7:5
Reading C&S 7:A-H

2. Reading SAS Datasets
Sometimes your “raw” data is already a SAS dataset
LIBNAME tomhs 'c:/my documents/ph5415/';
PROC CONTENTS DATA=tomhs.bpstudy;
PROC PRINT DATA=tomhs.bpstudy (obs=10);
RUN;
The libname statement tells SAS which directory (folder) the dataset is in.
DATA=tomhs.bpstudy
Tells SAS to look for a SAS dataset called bpstudy in the directory referenced by tomhs.

3. PROC CONTENTS OUTPUT The CONTENTS Procedure
Data Set Name: TOMHS.BPSTUDY Observations:
Member Type: DATA Variables:
Engine: V Indexes:
Created: :07 Saturday, February 26, Observation Length: 128
Last Modified: 9:07 Saturday, February 26, Deleted Observations: 0
-----Alphabetic List of Variables and Attributes-----
# Variable Type Len Pos
3 AGE Num
6 CHOL Num
2 GROUP Num
8 HDL Num
9 PULSE Num
10 PULSEBL Num
4 SBP Num
5 SBPBL Num
1 SEX Num
7 TRIG Num
11 WT Num
12 WTBL Num
13 cholbl Num
14 hdlbl Num
16 id Char
15 trigbl Num

4. PROC PRINT – 10 Observations
C T U U c t
G S S H R H L L h h r
R B B O I D S S W W o d i
O S O A P P L G L E E T T l l g
b E U G B B B b b b i
s X P E L L L l l l d
A00001
A00010
A00021
A00023
A00056
A00075
A00083
A00105
A00133
A00143

5. Reading a SAS Dataset DATA temp; SET tomhs.bpstudy;
sbpdif = sbp12-sbpbl;
PROC MEANS DATA=temp;
Reads in an observation. Replaces the infile and input statements when reading in text data
The MEANS Procedure
Variable N Mean Std Dev Minimum Maximum
SEX
GROUP
AGE
SBP
SBPBL
CHOL
TRIG
HDL
PULSE
PULSEBL WT
WTBL
cholbl
hdlbl
trigbl
sbpdif

6. One-Way Analysis of Variance
Two-sample t-test; compare means of two groups
Are the means different?
What if we have more than two groups?
Examples;
compare three different behavioral interventions
compare 5 different BP drugs

7. Analysis of Variance Could compare all pairs of means with t-tests
three groups: A-B, B-C, A-C
five groups:
A-B, A-C, A-D, A-E
B-C, B-D, B-E
C-D, C-E
D-E

8. Analysis of Variance Problem - multiple comparisons!!
When performing many tests, may reject null hypothesis by chance (Type I error)
With  = 0.05, you allow for possibility of rejecting 1 out of 20 tests by chance
Even if all group means are equal then there is a fairly large chance that one-pair will be different
Think of the largest – smallest. This will get bigger as the number of groups gets larger.

9. Analysis of Variance
ANOVA simultaneously tests for difference in k means
Y - continuous
k samples from k normal distributions
each size ni, not necessarily equal
each with possibly different mean
each with constant variance 2

10. Constant variance
ANOVA is robust for violations of constant variance (and normality)
Rule of thumb:
If largest standard deviation is less than twice the smallest standard deviation, you’re ok.
Can sometimes transform to achieve equal variance or normality

11. Analysis of Variance Ho: 1 = 2= ... = k Ha: Not all i equal
For each group i;
ni = number of observations
= sample mean
= sample variance
= overall mean
Two-sample t-test is
special case; k = 2
Sometimes referred to as a global or omnibus test

12. Two-sample T-test - y y = t 1 1 + s n n Compared means for two groups
This compares variation between groups with variation within groups
Variation Between Groups - y y = 1 2 t 1 1 + s p n n 1 2
Variation Within Groups

13. ANOVA F-test F = s Compared means for all groups
This compares variation between groups with variation within groups
Variation Between Groups – Compared to Grand Mean F = 2 s p
Variation Within Groups

14. Analysis of Variance Variation for all observations:
Called the “(corrected) total sum of squares” or SST
Can be divided into two parts:
deviation of individual observation from its sample mean
deviation of sample means from overall mean
Similar to regression

15. Analysis of Variance Measures variation within samples
Measures variation between samples
Each has a corresponding “sum of squares”
Sum of squares within (SSW)
Sum of squares between (SSB)

16. Analysis of Variance Each has a corresponding degrees of freedom (DF)
SST = n-1 df
SSB = k-1 df
SSW = (n-1) - (k-1) = n-k df
Ratio of each sum of squares over its degrees of
freedom gives us the mean squares
MSW = SSW / (n-k) = average variation within k samples
MSB = SSB / (k-1) = average variation between k samples

17. Analysis of Variance MSW is estimate of the total variance, 2
MSW = SSW/(n-k)
SSW =
Sample variance for ith group,
= Pooled variance for k groups

18. Analysis of Variance
The null hypothesis is tested by looking at F ratio:
F = MSB/MSW, compare to F distribution with k-1, n-k df
If variation between groups much greater than variation
within groups;
F >> 1, reject null hypothesis
F  1, fail to reject null hypothesis

19. Analysis of Variance Results often presented in an ANOVA table
SAS uses “Model” for “Between” and “Error” for “Within”

20. ANOVA in SAS; two ways PROC ANOVA DATA = LIPID; CLASS diet;
MODEL lipid = diet;
RUN;
PROC GLM DATA = LIPID;
Both test for difference
in mean lipid reduction
for the two diets

21. PROC ANOVA and GLM Almost exactly the same for this case
GLM is a more general procedure

22. 6 Treatment groups (Variable GROUP)
TOMHS Study
6 Treatment groups (Variable GROUP)
Beta-blocker
Calcium channel blocker
Diuretic
Alpha-blocker
ACE inhibitor
Placebo
All Treatments given lifestyle intervention to lower BP

23. ANOVA – TOMHS Study PROC GLM DATA=temp; CLASS group;
MODEL sbpdif = group;
MEANS group;
RUN;
Creates 5 dummy variables for you
OUTPUT
The GLM Procedure
Class Level Information
Class Levels Values
GROUP
Number of observations
NOTE: Due to missing values, only 848 observations can be used in this analysis

24. GLM – OUTPUT ANOVA TABLE Pooled (over 6 groups) standard deviation
The GLM Procedure
Dependent Variable: sbpdif
Sum of
Source DF Squares Mean Square F Value Pr > F
Model <.0001
Error
Corrected Total
R-Square Coeff Var Root MSE sbpdif Mean
ANOVA TABLE
If H0 is true than F should be near 1
F = /194.52
Pooled (over 6 groups) standard deviation
Estimates s

25. GLM – OUTPUT
Source DF Type I SS Mean Square F Value Pr > F
GROUP <.0001
Source DF Type III SS Mean Square F Value Pr > F
If no covariates are in the model this portion of the output will be the same as the ANOVA table because the model includes only GROUP.
The GLM Procedure
Level of sbpdif
GROUP N Mean Std Dev

26. Contrasts PROC GLM DATA=temp; CLASS group; MODEL sbpdif = group;
MEANS group;
ESTIMATE 'BB vs Placebo' group ;
ESTIMATE 'CCB vs Placebo' group ;
ESTIMATE 'Diur vs Placebo' group ;
ESTIMATE 'AB vs Placebo' group ;
ESTIMATE 'ACE vs Placebo' group ;
RUN;
The GLM Procedure OUTPUT
Dependent Variable: sbpdif
Standard
Parameter Estimate Error t Value Pr > |t|
BB vs Placebo <.0001
CCB vs Placebo <.0001
Diur vs Placebo <.0001
AB vs Placebo
ACE vs Placebo <.0001

27. Compare all Groups PROC GLM DATA=temp; CLASS group;
MODEL sbpdif = group;
LSMEANS group/PDIF;
RUN;

28. GLM – OUTPUT The GLM Procedure Least Squares Means sbpdif LSMEAN
GROUP LSMEAN Number
Least Squares Means for effect GROUP
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable: sbpdif
i/j
<.0001
<.0001
<.0001
<.0001
< < < <.0001
NOTE: To ensure overall protection level, only probabilities associated with pre-planned
comparisons should be use
P-value: Group 1 v Group 2