In this tutorial we're going to examine how to calculate and interpret z-scores
in SPSS. So here notice we have the variable, scores, and on this variable we
have a score for each of 23 people in total.
Now to calculate z scores on this variable what we want to do is go to
Analyze on the menu bar, select Descriptive Statistics, and then select
our option Descriptives here.
Move the variable, scores, over to the Variable(s) box. And then right here Save
standardized values as variables we want to click on this box, and when we do that
this is what is going to produce the z-scores in SPSS. Let's go ahead and go
to Options as well. And under Options
notice we have the Mean and Standard deviation selected by default as well as
Minimum and Maximum.
Let's go ahead and deselect Minimum and Maximum for now.
Click Continue.
And then click OK. The SPSS output window opens
and here we have just one table of output where we have the mean and
standard deviation for the variable, scores.
OK so you may ask yourself what happened, where are the z-scores? Well the z-scores
are actually provided in the Data Editor window.
So if we click here we'll go back to our Data Editor and notice this column now,
Zscores. So we have a z-score for each of the original scores, a
z-score is calculated and provided in SPSS.
If we go to our output here by clicking on Window and select Output then you will
see here in our output we have a mean if we round to a whole number place
the mean is equal to 47, rounding once again to a whole number.
OK so a mean of 47, keep that in mind. Let's go back to our data.
Let's take a few of these as an example. Here we have a score of 32. Recall that
the mean was 47 when we rounded. 32 is below 47 and notice how our z score is
negative. 39 is also less than 47 and notice how our z-score is once again negative.
Moving down here to observation 7, 54 that's greater than or mean of 47, and
notice now that our z-score is positive. Taking one more example, 76,
that's also greater than the mean of 47, and once again our z-score is positive.
This illustrates a property of z-scores. And that is, values that are less than
the mean of 47 would produce negative z- scores,
whereas values that are greater than the mean of 47 would produce positive z-
scores.
OK that's a basic property of the z-score distribution. Now something else that's
interesting and you may have learned in your introductory statistics course is
what the mean and standard deviation of a z-score distribution is equal to. Let's
take a look at that on our own.
Go to Analyze, Descriptive Statistics, and then go to Descriptives once again. And
then now let's move our new variable notice this variable here Zscore. This
is new, we produced it by checking on this box before.
Let's move it over and then let's deselct this this time because we already
have our z-score variable.
Click OK. And now notice what we get here in our output, in this second table here.
We have the same mean and standard deviation for scores as we did before
which shouldn't be surprising since it's the same variable. But this is where it's
interesting.
Notice the mean and standard deviation for the z-score variable.
Now this here is scientific notation zero e to the negative 7
and what that means is it's point six zeros and a number so .000000 and then some
number.
In other words, it's very, very small and what that really means is just rounding
error.
This value is really zero for all intents and purposes.
It's just a rounding error. So the mean is equal to 0 and the standard deviation
is equal to 1, which is another property of a z-score distribution.
If you take any variable in SPSS no matter what the values are and you
calculate z-scores on that variable and you obtain a mean and standard deviation
of the new z-score variable, the z-score variable will always have a mean of zero
and a standard deviation of one just as we see right here.
Just keep in mind there may be a little bit of rounding error.
This concludes the tutorial on obtaining z-scores in SPSS.