Hypotheses testing

Based on the outcomes of table 9, the proposed hypotheses will be tested. The values for the different categories of the predictor variables, along with the beta coefficients of these variables will be used to calculate the predicted values of the parent brand evaluation, as well as the values for the categories, mentioned in table 10. That way, a regression formula will be composed that can calculate the predicted value for each condition of the variables used in this research. The outcome of these predicted values for the different conditions will be compared with the proposed hypotheses.

Table 10. Values of predictor variables.

Variables Values

brand extension strategy 0 = existing line 1 = green line extension

fit 0 = low

1 = high

environmental involvement 0 = low → (# − %) 1 = high → (# + %)

The first hypothesis explains the direct effect that I propose: Compared to the existing product, the green line extension will lead to a more positive brand evaluation. There was no significant effect found for the direct effect of brand extension strategy on the parent brand evaluation (" = -2.10, p = 0.15), as seen in table 9. This means that the brand extension strategy (existing line vs. green line extension) does not significantly change the parent brand evaluation, and hypothesis 1 cannot be accepted. Nevertheless, the predicted values for both

categories are calculated for illustrative purposes. The predicted values of parent brand evaluation, based on the existing line was calculated by the following formula:

#$%"!#$%#&' )#&"&

= ) + "_*∗ ,,,,,_+#%+ "_-∗ -,./0.12 3.1- + "_.∗ ,"&/+ "₀∗ ,_1'",,,,,, + "₂∗ ,"&/,,,,,∗+4%+ "₂∗ ,"!4$%4&' )4&"∗+4%+ "₅∗ ,"!4$%4&' )4&"∗"&/,,,,,

+ "₆∗ ,"!4$%4&' )4&"∗"&/∗+4%

#$%"!#$%#&' )#&"& = 5.5 + (−2.14 ∗ 0.47) + (−2.10 ∗ 0) + (−0.39 ∗ 5.760) +

(0.003 ∗ 38.1) + (0.51 ∗ 5.76 ∗ 0.47) + (0.37 ∗ 0 ∗ 5.76) + (−0.28 ∗ 0 ∗ 5.76 ∗ 0.47)

= 3.79

As seen in the formula, predictor variables fit, environmental involvement, and age are held constant by taking their means into this formula so that the effect of that predictor variable is held constant. The mean coefficients that were used for these variables are mentioned in table 7. Moreover, as seen in the formula, the value “0” is used for the brand extension strategy, which corresponds with the existing line (as seen in table 10). To calculate the predicted value for the green line extension, the value “1” instead of “0” will be used for the brand extension strategy variable, in the above-mentioned formula.

After running the formula for both categories of the brand extension strategy, the parent brand evaluation was calculated for both conditions. As seen in graph 3, the green brand extension resulted in a more positive parent brand evaluation (y = 3.94), than the existing line (y = 3.70), as proposed in hypothesis 1. However, no conclusions can be made, based on these predicted values due to the insignificant result of the brand extension strategy on the parent brand evaluation.

Graph 3. Brand extension strategy's effect on parent brand evaluation.

The second hypothesis explained the effect of the fit conditions on the evaluation of the parent brand: under high fit, the green line extension leads to a higher evaluation of the parent brand, in comparison with the existing product; and under low fit, the green line extension leads to a lower evaluation of the parent brand, in comparison with the existing product. When examining the interaction effect of brand extension strategy and fit on the parent brand evaluation (table 9), this effect was, unfortunately, insignificant (" = 1.84, p = 0.45). This means that there is no difference in parent brand evaluations between the high fit or low fit conditions. Moreover, for illustrative purposes, the predicted values of the 2x2 conditions are calculated, based on the regression formula. Again, the formula below is an example of how the parent brand evaluation of one condition (high fit, green line extension) is calculated:

#$%7#'7+#%,'9""& )#&" "!%"&$#:&&

= ) + "_-∗ ℎ.2ℎ C.0 + "_-∗ 2D--1 3.1- -,0-1/.E1 + "_. ∗ ,"&/+ "₀∗ ,_1'",,,,,, + "₂∗ ,"&/,,,,,∗;<=; ><?+ "₂∗ ,'9""& )4&" "!%"&$4:&∗74'7 +4%

+ "₅∗ ,'9""& )4&" "!%"&$4:&∗"&/,,,,, + "₆∗ ,'9""& )4&" "!%"&$4:&∗"&/∗74'7 +4%

"#$!"#! %"&,#())* +"*) ),&)*-".*%

= 5.5 + (−2.1 ∗ 1) + (−2.1 ∗ 1) + (−0.4 ∗ 5.76) + (0.003 ∗ 38.1) + (0.5

∗ 5.76 ∗ 1) + (1.8 ∗ 1 ∗ 1) + (0.4 ∗ 1 ∗ 5.76) + (−0.3 ∗ 1 ∗ 5.76 ∗ 1) = 4.37

As seen in this formula, only the environmental involvement (-1FGGGGG) and age (H2-GGGGG) are held constant, by making use of their mean scores (table 7), to mediate their effects on the parent brand evaluation. This means that this formula only calculates the effects of the fit and the brand extension strategy on the parent brand evaluation. Moreover, the high fit condition is valued as “1” and the green line extension is valued as “1” in this formula, which corresponds with the correct category that is being investigated in this example, when taking table 10 into account.

As seen in graph 4, and, after running the formula for this 2x2 hypothesis, in the high fit condition, the green brand extension led toward a higher parent brand evaluation (y = 4.37), in comparison with the existing line (y = 4.09). This finding is in line with hypothesis 2a. When zooming in on the low fit condition, the green brand extension led toward a higher parent brand evaluation (y = 3.51), in comparison with the existing line (y = 3,31) which is not in line with hypothesis 2b. However, based on the insignificant outcome of the interaction effect of brand extension strategy and fit, no further assumptions can be made based on these predicted values.

Graph 4. Graphic image of parent brand evaluation, based on strategy and fit.

The last hypothesis considered the environmental involvement that would influence the effect of fit on the parent brand evaluation, besides the brand extension strategy. In this proposed formula, only the age is being held constant. This hypothesis measures the 3-way interaction because the environmental involvement moderates the moderating effect of fit on the parent brand evaluation. Unfortunately, this three-way interaction effect was not significant, as seen in table 9: " = -0.28, p = 0.51. Therefore, Hypothesis 3 cannot be accepted.

For illustrative purposes, the predicted values of parent brand evaluation are calculated for these eight (2x2x2) groups. The formula that is used to measure the effect of one of the 8 conditions is mentioned below:

#$%7#'7+#%,'9""& )#&" "!%"&$#:&,):@ "&/&

= ) + "_-∗ ℎ.2ℎ C.0 + "_-∗ 2D--1 3.1- -,0-1/.E1 + "_.∗ -1FGGGGG − σ + "₀∗ ,_1'",,,,,,+ "₂∗ ,,,,,,AB∗;<=; ><?"&/ + "₂ ∗ ,'9""& )4&" "!%"&$4:&∗74'7 +4%

+ "₅∗ ,'9""& )4&" "!%"&$4:&∗"&/,,,,,AC + "₆∗ ,'9""& )4&" "!%"&$4:&∗"&/AB∗74'7 +4%

4,37

3,51 4,09

3,31

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00

High fit Low fit

Green line extension Existing line

"#$!"#! %"&,#())* +"*) ),&)*-".*,+./ )*0%

= 5.5 + (−2.1 ∗ 1) + (−2.1 ∗ 1) + (−0.4 ∗ 4.76) + (0.003 ∗ 38.1) + (0.5

∗ 4.76 ∗ 1) + (1.8 ∗ 1 ∗ 1) + (0.4 ∗ 1 ∗ 4.76) + (−0.3 ∗ 1 ∗ 4.76 ∗ 1) = 4.17

As seen in this formula, the only predictor variable that is held constant is the control variable age. Moreover, to recode the scale variable environmental involvement into high and low categories, I chose to add the standard deviation to the mean score of environmental involvement (-1FGGGGG + J) for the high category and subtract the standard deviation of the mean of environmental involvement (-1FGGGGG − J) for the low category, as seen in table 10, since the mean of environmental involvement of this sample was quite high (M= 5.76, SD = 0.99).

When calculating the predicted value, first, the low fit conditions (hypotheses 3b and 3c) will be discussed in which I proposed that “When the environmental involvement is low and the fit is low, the green line extension will lead to a more positive brand evaluation, in comparison with the existing line” and “When the environmental involvement is high and the fit is low, the green line extension will lead to a more negative brand evaluation, in comparison with the existing line”. As seen in graph 3, in the low environmental involvement condition, the existing line led to a more positive parent brand evaluation (y = 3.71) than the green brand extension (y = 3.51), which is not in line with hypotheses 3b. In the high environmental involvement condition, the green brand extension led to a higher parent brand evaluation (y = 3.51) than the existing line (y = 2.91), which is the opposite in comparison with hypothesis 3c.

However, due to the insignificant result of the 3-way interaction effect, no further assumptions can be made based on these predicted values.

Graph 5. Low fit conditions - influence of environmental involvement on PBE.

When calculating the predicted values for the high fit conditions (hypotheses 3a and 3d), I proposed that: “When the environmental involvement is low and the fit is high, the green line extension will lead to a more positive brand evaluation, in comparison with the existing line” and “When the environmental involvement is high and the fit is high, the green line extension will lead to a more positive brand evaluation, in comparison with the existing line”.

As seen in graph 4, in the low environmental involvement condition, the green brand extension led to a slightly higher parent brand evaluation (y = 4.13) than the existing line (y = 3.99), which is in line with hypothesis 3a. In the high environmental involvement condition, the green brand extension led to a higher parent brand evaluation (y = 4.56) as well, in comparison with the existing line (y = 4.19), which is also in line with hypothesis 3d. Again, no further assumptions can be made based on these predicted values due to the insignificant three-way interaction effect.

Graph 6. High fit conditions - influence of environmental involvement on PBE.