WEBVTT

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In this video, you learn 
how to perform an Analysis of 

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Covariance model using SAS 
Studio. From the Tasks list, 

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click the Tasks drop-down 
arrow, and click Statistics to 

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expand the list of available 
options. After browsing the 

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list of options, I'll double 
click Analysis of Covariance. 

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To maximize the screen space, I 
will click the Maximize View 

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button. The data I am using 
comes from the FISH data set, 

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which is available in the 
SASHELP library. Height will be 

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my continuous dependent 
variable. I will regress Height 

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on the weight of the fish and 
the species of the fish. Weight 

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is my covariate (or continuous 
independent variable). Species 

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is my categorical variable. It 
consists of seven different 

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types of fish species: Bream, 
Roach, Whitefish, Parkki, 

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Perch, Pike, and Smelt. To 
access the data, I'll first 

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click the Select a Table button 
on the Data tab. Next, I'll 

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click the drop-down arrow next 
to SASHELP, and scroll down to 

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the FISH data set. After I find 
it, I'll highlight it and click 

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OK. You will notice that my 
screen is split. On the left 

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side are the settings for the 
analysis, and on the right side 

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are tabs for my code, log, and 
results. I can choose whether 

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to view just the settings, 
just the code and results, or 

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I can split the screen between 
them and view both. That is 

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what I want to do right now. 
Click the plus button to the 

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right of Dependent variable. 
I'm presented with only numeric 

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variables as potential options 
for my dependent variable. 

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Select Height and click OK. 
Next, click the plus button to 

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the right of Categorical 
variable. Select Species, and 

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click OK. Immediately below, 
click the plus button 

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corresponding to Continuous 
covariate. Select Weight and 

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click OK. In the Code/Results 
section, notice that the code 

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for our model is being 
generated. There is one thing 

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to point out before we move 
forward: Notice that the MODEL 

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statement also includes the 
interaction between the two 

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independent variables. As 
Weight changes, the height of 

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the fish can change at 
different rates for different 

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types of fish in the study, so 
it's included as well. For this 

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analysis, we don't want to 
center the covariate, so I'll 

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move to the Options tab. Here I 
can select from a wide array 

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of, for lack of a better term, 
options, or specifications to 

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customize the model. For 
example, if I believed that the 

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slopes were equal, I could 
change the default settings 

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accordingly. When I select 
Equal, my code is automatically 

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adjusted. I'm going to revert 
back to Unequal for this 

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analysis. When I click the 
drop-down icons next to 

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Multiple Comparisons and Plots, 
I'm given additional options 

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concerning pairwise comparison 
methods, covariate values, and 

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the significance level. When I 
change the Display plots option 

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from Default plots to Selected 
plots, I can specify which 

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plots I want. Select the check 
box next to Diagnostic plots to 

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include them in the model. 
Moving to the Output tab, I can 

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choose to create an output data 
set with a variety of results 

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corresponding to predicted 
values, residuals, standard 

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errors, and influence 
statistics. I don't want an 

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output data set for this 
analysis. The Information tab 

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provides properties information 
as well as additional resources 

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to better understand the 
procedures being used and to 

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help better navigate the SAS 
Studio interface. This is my 

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GO-TO resource when I have a 
question about SAS Studio. To 

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run the analysis, I'll click 
the Run button right above the 

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Information tab. I would like 
to view only the results, 

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without the options on the 
left, so I will click the 

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Code/Results button and then 
click the Results tab to view 

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the results of my analysis. I'm 
first given Class-level 

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information about my 
categorical variable, Species, 

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followed by the number of 
observations read from the data 

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set and the number used in my 
model. It looks as if there is 

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one observation with missing 
data, so it is excluded. Below 

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are several charts that list 
the specific statistics of my 

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model. I'll highlight a few as 
I scroll down the page. It's 

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here where I'm first able to 
judge how well my predictor 

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variables explain the response. 
Assuming an alpha of .05, I 

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conclude my model is 
significantly different from 

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the mean model. Notice that my 
R-square term is very high. 

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This and the significant p-
values for each predictor 

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variable are good initial 
indications that I might have a 

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good fitting model. Below, 
we're given Fit Diagnostics for 

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the response variable. Here, I 
can visually assess model 

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assumptions, evaluate model 
fit, and spot potential 

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influential observations that 
might be adversely influencing 

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model results. Below Fit 
Diagnostics is the ANCOVA plot. 

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Here, I can visually observe 
the relationship between Weight 

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and Height for each Species of 
fish in my model. The next two 

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tables list least square means 
for each Species and then test 

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whether their least square 
means significantly differ from 

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one another. Because I kept 
alpha at the default level, 

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alpha is .05. Continuing the 
least square means output, the 

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graph below shows box plots for 
each value of Species. Here I 

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can visually assess 
similarities, differences, and 

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potential model assumption 
violations. The final graph 

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lists all pairwise comparisons 
between the different species. 

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The pairwise comparisons with a 
blue line indicate they are 

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significantly different from 
one another. A red line 

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indicates non-significance. 
This confirms what we have 

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already seen previously. This 
analysis can be saved with a 

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name that you specify and then 
reopened later. I'm going to 

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exit the Maximized View and 
click the Split option to 

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return to all three views. I 
can choose to rerun the model 

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with different criteria, choose 
a new model, choose a new data 

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set, or explore other features 
in SAS Studio. In this video, 

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you learned to perform an 
analysis of covariance using 

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the Analysis of Covariance  
task in SAS Studio.