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Chapter 16: One-Way Analysis of Variance
Using the
P
-value Approach to a One-way ANOVA
Hypothesis Test
:
: Not all the population means are equal
P-
value = 0.0000 (obtained from
Figure 6-17
)
.:
For a given significance level of 0.01, reject the null hypothesis if the
computed
P
-value of 0.0000 is less than the significance level of 0.01.
Conclusion
: Since 0.0000 < 0.01, reject
. That is, at the 1% significance
level, there is a significant difference between the mean heat loss through the
bricks for the four different non-toxic chemical mixes.
The conclusion is the same for the
P
-value approach as with the classical
approach.
Since the null hypothesis was rejected and we concluded that there is a
significant difference between the average heat loss for the respective
populations of non-toxic mixes, then the question is which of the means are
different from the others? We can use
multiple comparisons
to help
answer this question.
Multiple Comparisons
One way to visualize which population means are significantly different
from the others, one can compute the confidence intervals using the sample
information. The workbook output in
Figure 16-17
shows plots of the 99
percent confidence intervals. Observe that the confidence intervals for the
average percentage of heat loss for mix1, mix2 and mix 4 all overlap. This
would indicate that there is not a significant difference between these
averages. On the other hand, the confidence interval for the average
percentage of heat loss for mix 3 does not overlap with any of the other
confidence intervals. This would indicate that the average percentage of
heat loss for mix 3 is significantly different from the average percentage of
heat loss for mix 1, mix 2, and mix 4. In particular, since the confidence
interval for the average percentage of heat loss for mix 3 is to the right of the