Module 1 — Understanding Measurement Precision

• Definition of precision
• Precision versus trueness
• Standard deviation as a measure of dispersion
• Repeatability
• Repeatability standard deviation
• Intermediate precision
• Reproducibility
• Repeatability and reproducibility limits
• Factors affecting precision
• Different levels and sources of imprecision
• Effect of changing measurement conditions

The training begins with exactly these core concepts, including the distinction between precision and trueness and the definitions of repeatability, intermediate precision and reproducibility.

Module 2 — Describing and Interpreting Dispersion

• Standard deviation
• Interquartile range
• IQR as an alternative measure of dispersion
• Relationship between IQR and standard deviation
• Interpretation of interlaboratory data
• Standard deviation of the mean
• Effect of the number of observations on uncertainty in the mean

The course includes an interlaboratory example and introduces IQR and the standard deviation of the mean before moving into formal precision testing.

Module 3 — Comparing Precision with a Specified Value

• Purpose of variance comparison
• Chi-square test
• Comparing an observed standard deviation with a specified standard deviation
• Degrees of freedom
• Critical chi-square values
• Statistical interpretation of results
• Worked example using intermediate precision and published method performance

Exercise 1 — Chi-Square Test

Participants apply the chi-square approach to determine whether an observed precision estimate differs significantly from a specified value.

The presentation contains both the statistical approach and a worked example comparing an intermediate precision of 1.24 with a published value of 1.05, followed by Exercise 1.

Module 4 — Designing Precision Studies

• Principles of experimental design for precision evaluation
• Repeatability and intermediate precision studies
• Nested experimental designs
• Groups of measurements obtained under repeatability conditions
• Within-group variation
• Between-group variation
• Separating different sources of variability
• Practical considerations when planning a precision experiment

The training specifically introduces a nested design for obtaining repeatability and intermediate precision estimates

Module 5 — Estimating Precision Using ANOVA

• Introduction to analysis of variance
• ANOVA structure for grouped replicate measurements
• Within-group sums of squares
• Between-group sums of squares
• Mean squares
• F-statistic
• Repeatability standard deviation
• Between-group standard deviation
• Intermediate precision standard deviation
• Interpretation of ANOVA output
• Worked laboratory example
• Using Excel ANOVA output

Exercise 2 — ANOVA

Participants analyse grouped replicate measurements and estimate the components of precision.

The worked example in the training uses four analyst groups and demonstrates how the resulting ANOVA table can be converted into precision estimates.

Module 6 — Precision from Replicate Measurements

• Pooled standard deviation
• Combining precision information from several replicate sets
• Estimating repeatability from paired measurements
• Relative paired differences
• Mean relative range
• Repeatability relative standard deviation
• Use of the coefficient
• values for different numbers of replicates
• Estimating variance using duplicates
• Estimating variance using multiple measurements

The presentation specifically covers pooled SD, a relative-range approach using  for duplicate data, and coefficients for two to five replicates.

Module 7 — Comparing Variances Using the F-Test

• Purpose of the F-test
• Comparison of two variances
• Calculating the F-statistic
• Degrees of freedom
• Critical F-values
• Statistical interpretation
• Comparison of laboratory repeatability against method-performance requirements
• Worked manganese-in-steel example
• Worked fuel-oil example

Exercise 3 — F-Test

Participants determine whether laboratory precision differs significantly from an established precision criterion.

The slides include examples where one laboratory precision estimate is significantly different from the method criterion and another where no significant difference is found, which is useful pedagogically because participants see both possible outcomes.