Descriptives Analysis: Z-Scores

Descriptive statistics are informative statistics that describe datasets. Z-scores are a type of descriptive statistics. Z-scores represent the number of standard deviations between each data point and the mean. A positive z-score indicates that the data point is above the mean, and a negative z-score indicates that the data point is below the mean. Z-scores are helpful in identifying outliers.

 

To generate z-scores, click on 'Analyze' in the toolbar at the top of the Data Editor window. Then, click 'Descriptive Statistics' in the dropdown menu and 'Descriptives...' in the side menu.

 

In the Descriptives dialog box that pops up, double click on the variable of interest (Age of Respondents, age) in the variable list to add it to the 'Variable(s):' field. Then, make sure the 'Save standardized values as variables' box is selected, because selecting this option instructs SPSS to create a new variable of z-scores named 'Z and the original variable’s name' (for example: Zage) in the Data Editor. While creating z-scores, SPSS can also generate a descriptives analysis in the SPSS Viewer output window. To do so, click 'Options...'

 

In the Descriptives: Options dialog box that pops up, check off any statistics you would like to be displayed in the SPSS Viewer output window. Here, we selected Mean because we would like the average age of the respondents to be displayed in the output (in addition to the creation of z-scores as a new variable). Then, click 'Continue.' Back in the Descriptives dialog box, click OK, and the z-scores will be added as a new variable (Zage) with each individual case having a z-score in the Data Editor. Additionally, a table with the descriptives information requested in the Options dialogue box is displayed in the SPSS Viewer output window.

 

In the Data View of the Data Editor window, the z-scores have been added as a new variable (Zage) with each individual case having a z-score.

 

In the SPSS Viewer window, the output is displayed. The descriptive statistics (the Mean of the Age of Respondents variable) that were requested are displayed in the Descriptive Statistics table. The average age of the respondents is 48.32 years old. Please note that this descriptives table is completely independent from the z-score calculations.