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Also known as: Standard Score
A standardized value expressing how many standard deviations an observation is from the mean.
DESCRIPTION
The z-score transforms data to a standard scale with mean zero and unit variance, enabling comparisons across distributions and features. It supports outlier detection, hypothesis testing (z-tests), and normalization for models. Under normality assumptions, z-scores map directly to probabilities via the standard normal CDF. Care is needed with small samples or non-normal distributions.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, the standard score (also called z-score) is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.
Precise, widely accepted description of standardized value.
NIST/SEMATECH e-Handbook of Statistical Methods
A standardized value (z-value) is a dimensionless quantity indicating how many standard deviations a value is from the mean.
Emphasizes dimensionless nature of z-values.
Investopedia
A z-score is a numerical measurement that describes a value’s relationship to the mean of a group of values.
General-purpose explanation emphasizing relationship to mean.
RELATED TERMS
Feature Scaling Normal Distribution t-score Data Anomaly Detection z-test p-value Confidence Interval Effect Size Sigma
COMPETING TERMS
Percentile Rank Raw Score
KNOWLEDGE AREAS
Mathematics Data Science Testing & Validation
TARGET AUDIENCE
Data Scientist Data Analyst Information Analyst
EXTERNAL SOURCES
- Wikipedia - Standard score
- NIST - Z-values in EDA handbook
- Penn State Statistics - Standardization and z-scores
- Khan Academy - Educational review of z-scores
TOP QUESTIONS
When should I use Z-scores?
Use them to compare values across different scales, detect outliers, or apply tests relying on the normal distribution.
Category: Guidance
What is a typical Z-score threshold for outliers?
Common cutoffs are |z| > 3, though domain context may warrant stricter or looser thresholds.
Category: Practice
How do Z-scores differ from t-scores?
Z-scores assume known population variance or large samples; t-scores account for small samples via the t-distribution.
Category: Comparison
What’s a common mistake with Z-scores?
Applying them to skewed or heavy-tailed data without transformations or robust methods can mislead outlier detection.
Category: Mistakes
Do Z-scores require normality?
They are most interpretable under normality; standardization works regardless, but probability interpretations depend on distributional assumptions.
Category: Misunderstanding
How do I compute a Z-score?
Subtract the mean from the value and divide by the standard deviation. Use population or sample parameters as appropriate.
Category: How-to
How are Z-scores used in machine learning?
As a scaling method to normalize features and as a basic outlier detection tool in preprocessing.
Category: Application
What is Z-score standardization vs. min–max scaling?
Z-score centers and scales by standard deviation; min–max rescales to a range. Choice depends on model assumptions.
Category: Comparison
Where to learn more about Z-scores?
Consult NIST’s EDA handbook and university statistics courses for theory and practice.
Category: Learning