Overview
ISO 3301:1975, "Statistical interpretation of data - Comparison of two means in the case of paired observations," specifies a standardized method for comparing the mean of a population of paired differences to zero or any preassigned value. It formalizes the method of paired observations (a paired t‑test approach) for cases where each measurement from one treatment is paired with a corresponding measurement from another treatment on the same or similar element. The standard is intended for statistical hypothesis testing when comparing two related treatments, test methods, measuring instruments or laboratories.
Key topics and requirements
- Paired observations: Two results xi and yi form a pair when they are made on the same element under different conditions (or on matched elements). The analysis is applied to differences di = xi − yi.
- Conditions for valid use:
- The series of differences di must be treated as independent random items.
- The distribution of differences should be normal or approximately normal. If the distribution departs from normality, the method remains valid for sufficiently large samples (the document suggests sample sizes of about 100 or more for substantial deviations).
- Statistical procedure: Calculate the sample mean and variability of the differences, use Student’s t with degrees of freedom v = n − 1, and compare the test statistic to the appropriate critical t value for chosen significance level (two‑sided or one‑sided tests). The standard provides tabulated critical ratios and a worked example.
- Decision rules: The standard gives rejection criteria for two‑sided and one‑sided hypotheses and addresses Type I (false positive) and Type II (false negative) errors.
- Power considerations: Power depends on the true mean difference expressed in units of the standard deviation of differences (D/σd), the sample size, and the significance level. Graphs/tables in the standard illustrate power for typical α levels.
Applications and users
- Practical applications include:
- Comparing two analytical test methods on the same samples
- Evaluating two measuring instruments or two laboratory procedures
- Assessing treatment effects in paired experimental designs
- Typical users:
- Laboratory analysts and quality engineers
- Statisticians in R&D and testing organizations
- Metrologists and method validation specialists
- Regulatory bodies and conformity assessment personnel
Related standards
- ISO 2854 - Statistical interpretation of data - Techniques of estimation and tests (ISO 3301 is a special case of methods described in ISO 2854)
- ISO 3301 complements broader standards and guidance on statistical methods and method validation in testing and calibration contexts.
Keywords: ISO 3301:1975, paired observations, paired differences, paired t‑test, Student’s t, statistical interpretation of data, comparison of two means, sample size, hypothesis test, test methods, measurement comparison.
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