Because a random sample of cases well represents the population of cases
from which it was drawn, we can use a random sample to create a comparison
group when our research design is unbalanced. This is a huge data set with
more than 20,000, de-identified cases, about patients in a hypothetical
intensive care unit. One of the variables tells us whether or not the patient died.
That variable is called "Expired" and it is coded as 1 = "expired" or died, and
0 = "no" or did not die. Let's look at these numbers. Right-click on the
variable name and choose Descriptive Statistics. It looks like about 90% of
the patients survived and 10% died; and at 10% is about 2100 cases, so if
this researcher wanted to do comparisons between those who survived and those who
did not, that 90/10 split is just too different to use a t-test. This is called
an "unbalanced research design". Because the groups are different sizes, the
t-test assumes that the groups are equally sized, and when that assumption
is violated, our test becomes less accurate; and when the group sizes are
this unbalanced, the results of the t-test are likely to be wrong. One way to
deal with an unbalanced research design is to make your comparison group smaller.
You can do this by randomly selecting a comparison group of equal size from the
larger group. In our case, we can randomly select about 2,100 cases from among the
90% of patients who survived. These groups are independent: people
belong in either the group that survived, or the group that did not
survive, you cannot be in both groups, you cannot be in neither group. We would like
to select a random sample of cases from among those who survived so that we can
compare them to the cases that died, but we have a problem.
SPSS will not allow us to select a random sample from among only the cases
that survived, so we will need to do this in several steps. Because we will be
deleting cases, I recommend that you create a duplicate of your raw data set
and then do this technique on that duplicate file, so that you keep all of
your original data. I renamed my original data set "ICU Data Combo" and you will
see why in a moment.
Step one: we're going to isolate only the cases that did not survive, put them in a
new data set, and then delete them from the original data set, leaving only the
cases that survived. From the menus choose Data -> Select Cases
This opens the Select cases dialog box. We want to create a data set containing
only the cases that did not survive. This option says "select if condition is
satisfied". Click on IF, in the select cases dialog box. Our conditional
expression is "Expired = 1". These are the cases of the people who died.
You select the cases and then choose "copy selected cases to a new data set." We will
call it "ExpiredData." Click OK. You get a new SPSS data set containing only your
selected cases, but leaving the original data set unaffected. I am going to save
this new data set to the Desktop. Before we do anything els,e let's check the
exported data to see how many cases there are. That will be the total number
of cases that we need for our comparison. (2097) We will remember this number for later.
I want to do one more thing.Tthis is completely unnecessary, but it will help
me illustrate another technique later. In the "ExpiredData" set, find the variable
for "Discharge Date" and delete it from the data set. We now return to our combo
data set and delete the cases that expired. We will use the recently used
dialogues box to get back to Select Cases. This time, we will modify our
conditional expressions so that we will
select the cases where Expired = 0, and then change the settings to
"delete unselected cases". This will delete the cases that died leaving us with a
data set of only the cases that survived. As before, we should check our data set
to see how many cases remain. We will need that information for our random
sample. Select cases that we need from among those who survived. To obtain a
random sample, choose Data -> Select Cases. We will click the Reset button and OK to
clear out the existing filters, and then return to Select Cases. Select random
sample of cases in the select cases dialog box. Click sample: select exactly
2097 cases from among the first 18,785 cases. Delete the unselected cases.
This leaves us with two data sets, one containing all of the cases that expired
and the second containing an equal number of cases - randomly selected from
among those that survived.
The last step will be to combine the datasets. Because we started with the
same data all of our variables will match, but let's prove that to ourselves.
With the "ICU Data Combo" selected, go to Data -> Compare Datasets; select the open
data set "ExpiredData" and Continue. The matched fields box shows us all of the
data fields that are available to compare; presumably those that are common
to both data sets. Because we duplicated the data, all of our fields should match,
but we could make sure by clicking unmatched fields. Remember that we
deleted that variable for discharge date in the "ExpiredData" set. The active data
set has the discharge date that is missing from the compare data set.
This is a way that we can compare two unfamiliar data sets that should be the
same and to make sure that they are actually the same. I am going to cancel
out of this dialog box.
Go to Data -> Merge Files -> Add Cases. We are going to add cases from the "ExpiredData"
set to our combo data set. Click Continue. We see that there is only one unpaired
variable: discharge date, but of course we already knew about that. All of the other
paired variables are already in the new active data set, so click OK. Our combined
data set now contains only the paired variables. Let's check the expired
variable once again. We now have a single data set with exactly 2097 cases in each
group.
To conclude, let's do a t-test on our groups. Go to Analyze -> Compare Means ->
-> Independent Samples t-tests. We will compare the average length of stay for
our two groups. The grouping variable is Expired. Define the groups as 1 and 0.
The group statistics show us the average length of stay for each group and the
results for the t-test shows us that patients who expired stayed
statistically significantly longer than patients who survived. And because our
group sizes are now the same, the assumption for the t-test has been met
and we can feel much more confident that our findings are accurate.