686 P.J. Mart ́ın-Alvarez ́
Table 13.7Results of two-way ANOVA for 1-propanol content in wines resulting from the fer-
mentation of a same must with or without skins and in the presence or absence of sulfur dioxide
(SO 2 ). ANOVA table:
Degrees of Sums of Mean square
Source of variation: freedom (df) Squares (SS) (MSS) F-values P-Values
SO 2 (Factor A) 1 41.95 41.95 7.007 0.057157
Skins (Factor B) 1 1011.15 1011.15 168.882 0. 000202 ∗
SO 2 ∗Skins (Interaction) 1 1.14 1.14 0.190 0.685095
Error 4 23.95 5.99
Total 7 1078.19
∗The skins factor has a significant influence (P<0.05)
Table 13.8Means and standard error values for 1-propanol content in wines:
Factors:
SO 2 (A) Skins (B) Mean Std. Err. 95% Confidence interval N
Without Without 38.60 0.10 37.33 39.87 2
Without With 61.84 0.46 56.00 67.68 2
With Without 34.78 3.36 –7.85 77.40 2
With With 56.50 0.71 47.55 65.46 2
Table 13.9S-N-K test for comparison of means values for 1-propanol content in wines according
to skins’ factor:
Homogenous Groups
(α= 0 .05):Skins Mean 1 2
Without 36.68750 ∗∗∗∗
With 59.17250 ∗∗∗∗
Fcal^2 <F 1 −α,(b−1),ab(m−1)or,PB>α,thenH 03 is accepted, factor B does not influence
the analyzed variable. When the interaction exists, the influence of one of the factors
will depend on the levels of another factor.
13.1.4.5 Example of Application of Two-Way ANOVA
Tables 13.5 to 13.9 show the results of applying two-way ANOVA to the 1-propanol
content in wines resulting from fermentation of the same must with or without
skins and in the presence or absence of sulfur dioxide, that corresponds to a 2^2
factorial design (Herraiz et al. 1990; Mart ́ın-Alvarez et al. 2006), obtained with the ́
STATISTICA program (Factorial ANOVAprocedure, in theANOVAmodule). They
include the two-way ANOVA table (only the skins factor has a significant influence
at the 95% confidence level,P<0.05), the mean and the standard error values
of 1-propanol content for each combination of levels of factors (greater values in
wines elaborated with the addition of skins), and the results of the S-N-K test for
comparison of means of the skins’ factor. Figure 13.2 shows plots of the means of
1-propanol content for each level of factors.