STATISTICS
describe the whole measuring interval (Table 2).
Worked example: a 5 x 5 precision study A laboratory performs a short precision verification study for a generic quantitative serum assay on an automated analyser. The values in Table 3 are used as a teaching example and do not represent a specific commercial method. Two concentration levels are tested. Each level is measured five times in each of five groups, giving 25 results per level. In practice, the groups might represent days, analytical runs or series. The first statistical step is to calculate
the mean, SD and CV within each group. These within-group summaries show the short-term scater of replicate results. The second step is to compare the group means. If the group means differ more than expected from replicate scater alone, there is evidence of an additional between-group component. The ANOVA and variance component
results are shown in Table 4. The F-test is included because it is part of the variance component output, but it should not be misread as the final decision about whether the method is acceptable. It asks whether between-group variation is larger than would be expected from within- group scater alone. At both levels, the repeatability CV
is approximately 3%, showing that replicate measurements within a group are relatively close. However, the within- laboratory CV is higher because the study also includes between-group variation. In this example, the between-group component is the larger contributor to the total within-laboratory variance at both concentrations. At Level 1, the repeatability variance is
0.889 and the between-group variance is 1.947. These variances add to give a within- laboratory variance of 2.835. Taking the square root gives a within-laboratory SD of 1.684 units/L. Dividing by the mean of
Statistic
Number of groups Replicates per group
Number of observations Mean
Average within-group SD Average within-group CV
Level 1 5 5
25
32.808 units/L 0.943 units/L 2.87%
Table 3. Example 5 x 5 precision data structure.
Statistic MSwithin
MSbetween F ratio
P value
Repeatability variance Between-group variance Within-laboratory variance Repeatability SD Between-group SD Within-laboratory SD Repeatability CV Between-group CV Within-laboratory CV
Level 1 0.889 10.622 11.95
<0.001 0.889 1.947 2.835
0.943 units/L 1.395 units/L 1.684 units/L 2.87% 4.25% 5.13%
Level 2 4.481 77.189 17.23
<0.001 4.481
14.542 19.023
2.117 units/L 3.813 units/L 4.361 units/L 2.83% 5.10% 5.83%
Table 4. ANOVA and variance component summary from the example precision study.
32.808 units/L gives a within-laboratory CV of 5.13%. The same logic applies at Level 2 (Fig 2).
This is the main statistical lesson
of the example. The within-laboratory CV is not produced by adding CVs. It is produced by adding variance components, returning to an SD, and then calculating the CV.
Interpreting variance components and CVs The calculation is not the end of a precision study. The result still needs to
be interpreted in relation to the study design, the concentration tested and the intended use of the measurement procedure. The F ratio and P value in the ANOVA output answer a specific statistical question: is the between-group variation larger than expected from within- group scatter alone? They do not decide whether the observed imprecision is acceptable for clinical use. A statistically detectable between-group component may be practically unimportant, while an imprecision estimate with
Level 2 5 5
25
74.768 units/L 2.117 units/L 2.83%
August 2026
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