Application Guide

ANOVA (ANOVA)
Computes a one-way analysis of variance for comparing the means of 2 to 20
populations. The ANOVA procedure for comparing these means involves analysis of the
variation in the sample data. The null hypothesis H
0
:m
1
=m
2
=...=m
k
is tested against the
alternative H
a
: not all m
1
...m
k
are equal.
The ANOVA test is a method of determining if there is a significant difference
between the groups as compared to the difference occurring within each group.
This test is useful in determining if the variation of data from sample-to-sample shows
a statistically significant influence of some factor other than the variation within the
data sets themselves. For example, a box buyer for a shipping firm wants to evaluate
three different box manufacturers. He obtains sample boxes from all three suppliers.
ANOVA can help him determine if the differences between each sample group are
significant as compared to the differences within each sample group.
ANOVA 2-Way (ANOVA2way)
Computes a two-way analysis of variance for comparing the means of two to 20
populations. A summary of results is stored in the stat.results variable.
The two-way ANOVA analysis of variance examines the effects of two independent
variables and helps to determine if these interact with respect to the dependent
variable. (In other words, if the two independent variables do interact, their combined
effect can be greater than or less than the impact of either independent variable
additively.)
This test is useful in evaluating differences similar to the ANOVA analysis but with the
addition of another potential influence. To continue with the ANOVA box example, the
two-way ANOVA might examine the influence of box material on the differences seen.
Selecting an Alternative Hypothesis (ƒ < >)
Most of the inferential stat editors for the hypothesis tests prompt you to select one of
three alternative hypotheses.
• The first is a ƒ alternative hypothesis, such as mƒm0 for the zTest.
• The second is a < alternative hypothesis, such as m1<m2 for the 2-SampletTest.
• The third is a > alternative hypothesis, such as p1>p2 for the 2-PropzTest.
To select an alternative hypothesis, move the cursor to the appropriate alternative, and
then press Enter.
Selecting the Pooled Option
Pooled (2-SampletTest and 2-SampletInterval only) specifies whether the variances
are to be pooled for the calculation.
• Select No if you do not want the variances pooled. Population variances can be
unequal.
• Select Yes if you want the variances pooled. Population variances are assumed to
be equal.
Lists&Spreadsheet Application 341