Microsoft Office Tutorials and References
In Depth Information
For a more detailed explanation of the ANOVA t-test, see Black ( 2010 ).
Important note:
You are only allowed to perform an ANOVA t-test comparing
the population means of two groups when the F-test produces a
signiﬁcant difference between the population means of all of the
It is improper to do any ANOVA t-test when the value of F is
less than the critical value of F. Whenever F is less than the
critical F, this means that there was no difference between the
population means of the groups and, therefore, that you cannot
test to see if there is a difference between the means of any two
groups
since
this
would
capitalize
on
chance
differences
between
these
two
groups.
For
more
information
on
this
important point, see Gould and Gould ( 2002 )
8.5 End-of-Chapter Practice Problems
1. In a controlled greenhouse experiment, what type of soil conditions are
favorable for the growth of a common ﬂowering species such as Daisy Fleabane
(Erigeron annuus) often found along roadsides? Suppose that you wanted to
conduct a controlled research study to compare the growth of this ﬂower in
three types of soil treatments, speciﬁcally the effects of Nitrogen. Nitrogen is an
essential macro-nutrient necessary for plant development and is commonly
found in fertilizers: (1) Group 1: No nitrogen added to the soil (2) Group 2:
Low amounts of Nitrogen added to the soil, and (3) Group 3: High amounts of
Nitrogen added to the soil. Your measured variable will be milligrams (mg) of
dry biomass of Erigeron annuus. To do this study, you have obtained soil from
one location of land in the state of Colorado and seeds from a distributor. You
have sterilized the soil so that you could place it in 12 containers for each type
of treatment (i.e., 36 containers in all). Suppose, further, that you planted the
same number of seeds of Erigeron annuus in each container and maintained the
containers in a controlled greenhouse under constant conditions for a growing
season. You then clipped and dried all the Erigeron annuus from each treatment
to obtain dry biomass. You then weighed the dry biomass of each treatment and
generated the hypothetical data given in Fig. 8.6 . Note that there are a different
number of containers in each of the three treatments because some of the plants
did not survive the growing season. To test your Excel skills, you have decided
to run an ANOVA test of the data to determine the growing characteristics of
this plant with respect to varying amounts of Nitrogen.
(a) Enter these data on an Excel spreadsheet.
(b) Perform a one-way ANOVA test on these data, and show the resulting
ANOVA table underneath the input data for the three levels of Nitrogen.
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