Translate the value directly
| Z-score | Position |
|---|---|
| −2.0 | Two reference SDs below the mean |
| −0.5 | Half an SD below the mean |
| 0 | At the reference mean |
| 1.3 | 1.3 SDs above the mean |
The sign gives direction, not desirability. Whether a high value is favorable depends on what the variable measures.
Percentiles require a distribution
Under a standard normal reference, z can be mapped to a cumulative probability. But standardization alone does not make the data normal. A z of 2 is not universally the 97.7th percentile unless the reference model justifies that mapping.
Common flagging rules such as |z| > 2 or 3 are rules of thumb, not automatic error diagnoses. They can over-flag in heavy-tailed data and under-describe skewed or mixed distributions. Verify the record and inspect the distribution before exclusion.
Standard deviation interpretation explains the denominator; a histogram shows whether a normal percentile mapping is plausible.
Sample versus reference standardization
A score standardized within the current sample answers “where is this case relative to these observations?” A score based on an external norm answers “where is it relative to that reference population?” Those can differ materially. Record the reference group, weighting, time period, and treatment of missing values.
A defensible reporting sentence
“The observation had z = −1.4 relative to the stated reference sample, placing it 1.4 standard deviations below that sample mean. No normal percentile or outlier conclusion was assumed without checking the reference distribution.”