Introduction to variance analysis

When it's necessary to compare two populations, the Student test is generally used. But for populations larger than two, the Fisher test is used. In this test, the "factorial" S ² variance is divided by the "residual" S ² variance. The factorial variance corresponds to the dispersion obtained by varying the factor studied (e.g.: 3 operators / interseries). The residual variance generally corresponds to the dispersion of results obtained under repeatability conditions (e.g. 10 measurements / intraseries). Thus, by taking the ratio of the two variances ( S ² factorial/ S ² residual), we seek to demonstrate that this ratio is :

• not significant, indicating that changing operator has no more impact on the result than repeating the measurement ten times;

• significant, indicating that changing operator has an impact on the result.

In this sheet, we present various experimental designs, the basis of the study, up to the performance of an analysis of variances and its interpretation.