1. Z-Test
Dr. Kalman J. Andrassy

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

3. 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 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).

4. 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.

5. 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.

6. 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.”

7. 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 standard deviations from the mean, while a 100 is standard deviations from the mean.
The 0 score (not pictured) is standard deviations from the mean, beyond even the 99.7th percentile, past the fourth standard deviation. A true outlier.

8. Z Table