Z-Scores - How to PDF

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Kukucka Stats 1

Z-Scores Example in SPSS The datafile Census.sav contains data for N = 360 individuals on 11 different variables. We want to compute Z-scores for the variable time spent online per day (in minutes).

Step 1: Why do we want to know Z-scores? For continuous variables, Z-scores allow us to estimate the percentage of people in the population who have scores that are higher (or lower) than a given number. In other words, we use Z-scores to estimate the probability that a person’s score on some variable of interest will be higher (or lower) than a given value.

Step 2: How do we get SPSS to calculate Z-scores?  Go to “Analyze”  “Descriptive Statistics”  “Descriptives”

 Select the variable for which you want to calculate Z-scores, and move it into the “Variable(s)” box by clicking the arrow button in the middle.  Check the box that says “Save standardized values as variables,” and then click OK.

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Step 3: How do we read the output from SPSS?

In the output window, SPSS gives us the sample size, mean, and standard deviation for this variable, which is great and all, but isn’t really what we’re interested in here. Go back into “Data View” by clicking the tab at the bottom left, and you will see that SPSS has created a new variable that wasn’t there before. It is called “Zonline.”

 This new variable gives us the Z-scores for “time spent online” for all N = 360 people in our sample. For example, a person who spends 90 minutes online per day has a Z-score of 1.40 (i.e., this person’s score is 1.40 standard deviations above the mean). A person who spends 18 minutes online per day has a Zscore of -1.69 (i.e., their score is 1.69 SDs below the mean).

Using our Z-distribution table, we can easily figure out the percentage of people who spend more (and less) time online than any given person in our sample. For example, the guy who spends 90 minutes online per day has a Z-score of 1.40...

If we look up Z = 1.40 in our table, we can estimate that this person spends more time online per day than 91.92% of other people. In other words, we would estimate that 8.08% of people spend more than 90 minutes online per day....