The variance is defined as the sum of the squares of the deviations of the observation data from a specific value, divided by the degrees of freedom /. The variance — sometimes called the mean square — is denoted by V (Steiner S. H. & MacKay R. J., 2005).

3.5.1. Analysis of variance

The relative magnitude of the effect of different factors can be obtained by the decomposition of the variance, namely ANOVA — this is given in table (1). The experimental design permits the effects of numerous factors to be investigated at the same time. When many different factors dynamically affect a given quality characteristic, ANOVA is a systematic and meaningful way of statistically evaluating experimental results (Montgomery D. C., 2009).

Sources of variation

Degrees of freedom

F

Sum of squares SS

Mean

square

V

Pure sum of

squares

S

F-

ratio

Percent

contribution

(%)

Factor(a)

1

sa

va

Sa

Fa

a

Error(e)

n-1

se

Ve

Se

1

е

Total (t)

N

st

St

100.0

Table 1. ANOVA table

Where:

1. Variance ratio

(7)

(7) (9)

(10)

Fa =

2. Sum of squares

s’ = s — ( f x v|

a a J a e J

s’„ = s„ + (fn x v„)

e e V-‘ a e /

3. %age contribution:

a’ = | ^ I x 100

After n pieces of experimental data are collected and after the values of a and e are calculated, significant testing provides the criterion for making such decisions. The F-tests are used to statistically determine whether the constituents — the total sum of squares which are decomposed — are significant with respect to the components that remain in the error variance. The specific numerical confidence levels, depending upon which F-table is used, are called the level of significance. When the variance ratios Fa are larger than the F-table at the 5% level, then the effect is called significant at the 5% level (Montgomery D. C., 2009).