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

group in your study.

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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