CROP 590 Experimental Design in Agriculture
Lab exercise – 4th week
ANOVA assumptions
Transformations
SAS On-line Documentation
PROC GLM
PROC UNIVARIATE
PROC BOXPLOT
PROC GLIMMIX
Part 1. Data Entry
Up to this point we have entered data into SAS in the format of a SAS dataset. If you
are working with large datasets that are in a different format, you may prefer to write a
short program to rearrange the data in SAS. This can be achieved using Do loops and
the ‘@’ symbol, which tells SAS to read another data point from the same line. Two
‘@@’ symbols would tell SAS to continue reading from the same line until there are no
more data points to be read. Run the program below, and note how the data is
reformatted.
Data one;
Input herbicide
Do i=1 to 10;
Input weedcount
Output;
End;
Datalines;
H-A 33 21 48 18
H-B 25 28 20 15
H-C 4 5 2 5 4 1
H-D 8 11 9 13 6
;
Proc Print;
Run;
$ @;
@;
53 31
14 30
3 4 2
5 9 7
39 26 44 25
27 17 23 13
6
6 12
Part 2. Testing ANOVA assumptions
Conduct a one-way ANOVA of the above data set using herbicide as the independent
variable. Use the plots=diagnostics option in PROC GLM to obtain a standard group
of preformatted diagnostic plots for evaluating ANOVA assumptions. Adding the
plots=diagnostics(unpack) option will print each of the default dignostic plots as
a separate image. Request a Bartlett’s test for Homogeneity of Variances, or use the
default which is Levene’s test. Output the residuals and predicted values to a new data
set for further diagnosis.
PROC GLM plots=diagnostics;
Class herbicide;
Model weedcount = herbicide;
Means herbicide / hovtest=bartlett;
Means herbicide / hovtest;
output out=new r=residual p=predicted;
Run;
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Manually obtain residual plots, using the herbicide names as labels and the vref=0
option to include a reference line at eij = 0:
PROC GPLOT data=new;
plot residual*predicted = herbicide / vref=0;
run;
You can obtain box plots similar to the ones that SAS creates when you run PROC GLM
by using the BOXPLOT procedure.
PROC BOXPLOT data=new;
Plot residual*herbicide;
Run;
Proc Univariate can be used to test for normality (normal statement) and to obtain a
variety of descriptive plots, including normal probability plots (plots statement).
proc univariate data=new normal plots;
histogram residual/kernel;
QQPLOT residual /NORMAL(MU=EST SIGMA=EST L=1);
var residual;
run;
Part 3. Data Transformation
Are the residuals for the variable ‘weedcounts’ normally distributed? Do they have
homogeneous variance? What is your proof? If not, can you determine what
transformation is needed? Rerun your analysis on the transformed data and recheck the
ANOVA assumptions.
Tests for homogeneity of variance in SAS can only be run on one-way models. According
to the SAS help information, "homogeneity of variance testing for more complex models
is a subject of current research." Two approaches can be found in the literature for
testing for HOV in a Randomized Block Design. One is to simply ignore blocks and check
for HOV of treatment groups. Another is to adjust the data for blocks (remove the block
effects) and then run hovtests using a one-way model for the treatment groups.
If no suitable transformation can be identified, data with heterogeneous variance can
still be analyzed with PROC MIXED, using a Repeated statement with an unstructured
covariance option (Type=un). We will discuss this topic more in the lab exercise on
repeated measures.
Part 4. Generalized Linear Models
Generalized Linear Models are becoming the method of choice for analyzing data that
are not normally distributed, but follow another probability distribution in the
exponential family (which includes normal, binomial, Poisson, gamma, and negative
binomial distributions.) Appropriate use of Generalized Linear Models requires an
understanding of the underlying theory, which is beyond the scope of this class. To get
some idea about the SAS syntax and output for this type of analysis, run the following
program:
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proc glimmix data=one;
Class herbicide;
Model weedcount = herbicide / link=log s dist=poisson;
lsmeans herbicide/ilink diff CL;
run;
How do the F tests and estimates of the means compare to the analysis of transformed
data?
Later in the term, we will conduct combined analyses across multiple experiments and
learn how to determine if the variances for those experiments are homogeneous. PROC
MIXED and PROC GLIMMIX can both be used to account for heterogeneous variances
without the use of transformations.
Part 5. Detection of Outliers
In general, obvious outliers can be identified visually from residual plots. If you are
confident that a mistake or abnormality occurred during data collection, it may be best
to treat that observation as a missing plot. On the other hand, unusual variation that is
real may provide valuable insights and should not be ignored or discarded. We should
also avoid the temptation to massage our data to make it meet our expectations. If you
are not sure how to handle an outlier, you may want to “studentize” the residuals to
express them in standardized units. This may help in establishing an objective criterion
for outlier detection. For example, you might decide that values of studentized residuals
that are greater than 4 standard errors from a mean of zero are too extreme and were
likely the result of a mistake during data collection.
Replace one of the data points in the original data set with an outlier and rerun the
analysis. Various options can be used in PROC GLM to obtain diagnostic statistics for
outlier detection.
Proc GLM data=three plots=diagnostics;
Class herbicide;
Model weedcount = herbicide;
Means herbicide / hovtest=bartlett;
Means herbicide / hovtest;
output out=new r=residual p=predicted student=studres
stdr=rstderr cookd=cookct covratio=covrat dffits=dffit;
Run;
Proc print;
proc gplot data=new;
plot residual*predicted = herbicide;
plot studres*predicted = herbicide;
Run;
Note that the shapes of the two residual plots are the same, but values of studres are
expressed in standard units.
PROC MIXED also has some nice features for analyzing the influence of data outliers.
proc mixed data=three;
Class herbicide;
Model weedcount = herbicide / influence;
run;
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