Z-Test Dr. Kalman J. Andrassy

The Z-Test X is the individual value you are examining μ is the mean score of the variable σ is the standard deviation

Interpreting the Z-score The Z-score from a Z-test shows how far the individual score is from the mean using a normal distribution as your guide. It is a reflection of how many standard distributions from the mean the score ultimately is. A score of 1.00, for example, would be exactly one standard deviation from the mean (in which 68% of all scores would be under the 68-95-99.7 rule). A score of 2.00 would be exactly two standard deviations away (in the 95th percentile), and 3.00 would be exactly three standard deviations away (in the 99.7th percentile).

Z-Score on a Graph Since the z-test yields a z-score that is a reflection of the values on a normal distribution graph, it is considered the “universal language” of statistics.

SPSS – Z-Scores Z-Scores are a function of Descriptive Statistics in SPSS. You will get them in a similar way as when you display a frequency distribution.

Saving Standardized Values Getting your z-scores are as simple as clicking on “Save Standardized values as Variables.” Each individual score for your variable will be saved as a specific z- score in a new variable that will be z(variable name). Here, the new variable for the z-scores of the variable “score” will become “zscore.”

Z-Scores in Data View In the Data View tab of SPSS, you can see what each individual score for the variable “score” corresponds to in z- scores. A score of 92 is 0.35735 standard deviations from the mean, while a 100 is .78404 standard deviations from the mean. The 0 score (not pictured) is -4.54956 standard deviations from the mean, beyond even the 99.7th percentile, past the fourth standard deviation. A true outlier.

Z Table