406 Novel food packaging techniques Table 19.2 Packaging and storage conditions used in the models developed in Bro and Jakobsen(2002) modelling factor Abbreviation No. of levels Setting of levels Storage time(days) Day 4333 3,7,8,10 2.5.8 Light exposure (% Light O2 level (% 40.60.8 model for the experiment in Table 19.2 would look like equation 19.4(before removal of any insignificant effects a-value +1·Day+B2·Temp+B3· Light+B4·O2+Bs Temp+A6· Day. Light+Day.O2+B·Temp· Light+·Temp O2+A10· Light.O2 194 where betas are regression coefficients (before removal of any insignificant effects). The interpretation of the GEMANOVA model is much more simple than the ANOVA model as is discussed in detail in Bro (1997)and Bro and Jakobsen(2002) a-value= Day. Temp. Light. O2 Since the effect of the O2 level is insignificant in the interval between 40-80% O2, the resulting gEMANOVA model can be written as equation 19.6(Bro and Jakobsen 2002). The interaction term Day TempLightcoz describes deviations parameters can be performed from Fig. 192, and interpretation of the model 19.6 where a-valueo is the a-value at day 0 and co is a constant For all settings of the factors the a-value is simply calculated as the starting level of the a-value(a-valueo) plus the product of the four effects read from the ordinates in Fig. 19.2. Example: a-value a-valueo+ Day(10).Temp(2).Light(O) co2(constant)N a-valueo +(-2.3).1.1-1.7.1.9 N a-valueo -8.2, meaning that after ten days storage, at 2 C and no exposure to light the a-value has decreased by approximately 8.2 The interaction term is 0 on day o(the factor Day is 0) All changes in colour a-value during storage are negative(colour becomes less red) compared to the starting colour. The change is calculated as themodel for the experiment in Table 19.2 would look like equation 19.4 (before removal of any insignificant effects). a-value ˆ 0 ‡ 1
Day ‡ 2
Temp ‡ 3
Light ‡ 4
O2 ‡ 5
Day
Temp ‡ 6
Day
Light ‡ 7
Day
O2 ‡ 8
Temp
Light ‡ 9
Temp
O2 ‡ 10
Light
O2 19:4 where betas are regression coefficients. On the other hand, when applying the GEMANOVA model the interactions are modelled as one higher-order multiplicative effect, resulting in equation 19.5 (before removal of any insignificant effects). The interpretation of the GEMANOVA model is much more simple than the ANOVA model as is discussed in detail in Bro (1997) and Bro and Jakobsen (2002). a-value ˆ Day
Temp
Light
O2 19:5 Since the effect of the O2 level is insignificant in the interval between 40–80% O2, the resulting GEMANOVA model can be written as equation 19.6 (Bro and Jakobsen 2002). The interaction term DayTempLightcO2 describes deviations from the a-value on day 0 in a very simple way, and interpretation of the model parameters can be performed from Fig. 19.2. a-value ˆ a-value0 ‡ Day
Temp
Light
cO2 19:6 where a-value0 is the a-value at day 0 and cO2 is a constant. Interpretation: • For all settings of the factors the a-value is simply calculated as the starting level of the a-value (a-value0) plus the product of the four effects read from the ordinates in Fig. 19.2. Example: a-value ˆ a-value0 ‡ Day(10)
Temp(2)
Light(0)
cO2 (constant)  a-value0 +(ÿ2.3)
1.1
1.7
1.9  a-value0 ÿ8.2, meaning that after ten days storage, at 2ºC and no exposure to light the a-value has decreased by approximately 8.2. • The interaction term is 0 on day 0 (the factor Day is 0). • All changes in colour a-value during storage are negative (colour becomes less red) compared to the starting colour. The change is calculated as the Table 19.2 Packaging and storage conditions used in the models developed in Bro and Jakobsen (2002) Modelling factor Abbreviation No. of levels Setting of levels Storage time (days) Day 4 3, 7, 8, 10 Temperature (ºC) Temp 3 2, 5, 8 Light exposure (%) Light 3 0, 50, 100 O2 level (%) O2 3 40, 60, 80 406 Novel food packaging techniques