424 Statistical Methods
Thus about 72% of the total variation in foam volume can be attributed to
differences in cola brand, cola type, and the interaction between cola brand and
type. Only about 28% of the total variation can be attributed to random causes.Summary
To summarize the results from the plots and the analysis of variance, we
conclude the following:- There is no reason to reject the hypothesis that foam volume is the same
regardless of cola type (diet or regular). - There is a signifi cant difference among the four cola brands (Coke, Pepsi,
Shasta, and generic) with respect to foam volume. Coke has the highest
volume of foam, Pepsi has the lowest, and the other two brands fall in
the middle. - There is no signifi cant interaction between cola type and cola brand. In
other words, we don’t reject the null hypothesis that the difference in
foam volume between diet and regular is the same for all four brands.
You can save and close the Cola ANOVA workbook now.Exercises
- Defi ne the following terms:
a. Error sum of squares
b. Within-groups sum of squares
c. Between-groups sum of squares
d. Mean square error- Which value in the ANOVA table gives
an estimate of s^2 , the variance of the
error term in the means model? - If the between-groups mean square
error 5 7, 000 and the within-groups
mean square 52 , 000 , what is the value
of the F ratio? If the degrees of freedom
for the between-groups and within-
groups are 4 and 14, respectively, what
is the p value of the F ratio?
4. What is the Bonferroni correction factor
and when should you use it?
5. Use Excel to calculate the p value for the
following:
a. F 5 2.5; numerator df 5 10;
denominator df 520
b. F 5 3.0; numerator df 5 10;
denominator df 520
c. F 5 3.5; numerator df 5 10;
denominator df 520
d. F 5 4.0; numerator df 5 10;
denominator df 520
e. F 5 4.5; numerator df 5 10;
denominator df 520
6. You’re performing a two-way ANOVA
on an education study to evaluate a new