BSI PD ISO/TS 17503:2015

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Statistical methods of uncertainty evaluation. Guidance on evaluation of uncertainty using two-factor crossed designs

Published By	Publication Date	Number of Pages
BSI	2015	28

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This Technical Specification describes the estimation of uncertainties on the mean value in experiments conducted as crossed designs, and the use of variances extracted from such experiments and applied to the results of other measurements (for example, single observations).

This Technical Specification covers balanced two-factor designs with any number of levels. The basic designs covered include the two-way design without replication and the two-way design with replication, with one or both factors considered as random. Calculations of variance components from ANOVA tables and their use in uncertainty estimation are given. In addition, brief guidance is given on the use of restricted maximum likelihood estimates from software, and on the treatment of experiments with small numbers of missing data points.

Methods for review of the data for outliers and approximate normality are provided.

The use of data obtained from the treatment of relative observations (for example, apparent recovery in analytical chemistry) is included.

PDF Catalog

PDF Pages	PDF Title
6	Foreword
7	Introduction
8	1 Scope 2 Normative references 3 Terms and definitions
9	4 Symbols
11	5 Conduct of experiments 6 Preliminary review of data — Overview 7 Variance components and uncertainty estimation 7.1 General considerations for variance components and uncertainty estimation
12	7.2 Two-way layout without replication 7.2.1 Design 7.2.2 Preliminary inspection 7.2.3 Variance component estimation
13	7.2.4 Standard uncertainty for the mean of all observations 7.2.5 Degrees of freedom for the standard uncertainty
14	7.3 Two-way balanced experiment with replication (both factors random) 7.3.1 Design 7.3.2 Preliminary inspection 7.3.3 Variance component extraction
15	7.3.4 Standard uncertainty for the mean of all observations
16	7.3.5 Degrees of freedom for the standard uncertainty
17	7.4 Two-way balanced experiment with replication (one factor fixed, one factor random) 7.4.1 Design 7.4.2 Preliminary inspection
18	7.4.3 Variance component extraction 7.4.4 Standard uncertainty for the mean of all observations
19	7.4.5 Degrees of freedom for the standard uncertainty 8 Application to observations on a relative scale 9 Use of variance components in subsequent measurements
20	10 Alternative treatments 10.1 Restricted (or residual) maximum likelihood estimates 10.2 Alternative methods for model reduction 11 Treatment with missing values
21	Annex A (informative) Examples
26	Bibliography