Overview
ISO 5479:1997 - Statistical interpretation of data - Tests for departure from the normal distribution provides guidance on selecting and applying tests to decide whether a sample can be treated as coming from a normal distribution. The standard covers graphical methods, moment- and regression-based tests, characteristic-function tests and joint/multidirectional procedures. It is intended for complete (uncensored, ungrouped) data sets of size eight or greater and supplements statistical methods that assume normality.
Keywords: ISO 5479:1997, tests for normality, normal distribution, normal probability plot, Shapiro–Wilk, Epps–Pulley, tests for departure from normality
Key topics and requirements
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Scope and applicability
- Tests apply to independent observations from a single population.
- Recommended for sample sizes n ≥ 8; tests are ineffective for smaller samples.
- Intended for complete data (unsuitable for grouped or censored data).
- Can be applied to transformed variables (e.g., log, square root).
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Categories of methods
- Graphical method: Normal probability plot using specific plotting formula Pk = (k − 3/8)/(n + 1/4). Annex A supplies blank normal probability graph paper.
- Moment tests: Skewness and kurtosis based tests (e.g., empirical b1, b2).
- Regression tests: Includes Shapiro–Wilk (W) and related regression-type statistics.
- Characteristic-function tests: Epps–Pulley type tests and other omnibus procedures.
- Joint and multidirectional tests: Combination tests for skewness and kurtosis or multiple samples.
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Statistical practice
- Pre-specify significance level (commonly α = 0.05 or 0.01); critical values/tables provided for standard α levels.
- Use at least six significant digits in intermediate computations.
- Start with a normal probability plot to guide whether to use directional or omnibus tests.
Applications and users
ISO 5479 is practical for:
- Quality engineers, metrologists and laboratory analysts validating assumptions for parametric methods.
- Statisticians and researchers assessing normality before applying t-tests, ANOVA or control-chart methods.
- Standards developers and technical committees that rely on normality assumptions in measurement and testing procedures.
Practical uses include checking measurement distributions, verifying assumptions in conformity assessment, and guiding data transformation or subgrouping when mixtures or systematic departures are evident.
Related standards
- ISO 3534-1:1993 - Statistics - Vocabulary and symbols (referenced normative definitions)
- ISO 2854 (mentioned) - examples of methods that often assume normality
ISO 5479:1997 is a reference for anyone needing standardized, practical procedures to assess departures from normality in ungrouped data.
Open preview (PDF)Statistical interpretation of data — Tests for departure from the normal distribution
