Database Reference
In-Depth Information
The output also includes the (112,611), (862), the
F
-test statistic (130.6), and
the
p
-value (< 2e-16). The
F
-test statistic is much greater than 1 with a
p
-value
much less than 1. Thus, the null hypothesis that the means are equal should be
rejected.
However, the result does not show whether
offer1
is different from
offer2
,
which requires additional tests. The
TukeyHSD()
function implements Tukey's
Honest Significant Difference (HSD) on all pair-wise tests for difference of means.
TukeyHSD(model)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = purchase_amt ˜ offers, data = offertest)
$offers
diff lwr upr p adj
offer1-nopromo 40.961437 33.4638483 48.45903 0.0000000
offer2-nopromo 48.120286 40.5189446 55.72163 0.0000000
offer2-offer1 7.158849 -0.4315769 14.74928 0.0692895
The result includes
p
-values of pair-wise comparisons of the three offer options.
The
p
-values for
offer1-nopromo
and
offer-nopromo
are equal to 0, smaller
than the significance level 0.05. This suggests that both
offer1
and
offer2
are
significantly different from
nopromo
. A
p
-value of 0.0692895 for
offer2
against
offer1
is greater than the significance level 0.05. This suggests that
offer2
is
not
significantly different from
offer1
.
Because only the influence of one factor (offers) was executed, the presented
ANOVA is known as one-way ANOVA. If the goal is to analyze two factors, such
as offers and day of week, that would be a two-way ANOVA [16]. If the goal is to
model more than one outcome variable, then multivariate ANOVA (or MANOVA)
could be used.
