**Homework 6**

This homework is based on the
following experiment (data are taken from *The
SAS System for Linear Models*):

A balanced factorial experiment
consists of all possible combinations of levels of two or more factors. Factorial experiments are used to
investigate not only overall differences between levels of each factor (main
effects), but also how levels of one factor affect the response variable across
levels of another factor (interactions).
Consider the following example.
Suppose that 3 seed growth promoting methods (METHOD) are applied to
seeds from each of five varieties (VARIETY) of turf grass. Six pots are planted with seed from each
METHODxVARIETY combination. The
resulting 90 pots are randomly placed in a uniform growth chamber and the dry
matter yields (YIELD) are measured after clipping at the end of 4 weeks.

1.
This
experiment uses a factorial treatment design.
What are the 2 factors being studied in this experiment and how many
levels does each factor have? How many
total treatment-level combinations are being considered? How many times has each treatment-level
combination been replicated? Based on
the information that you’ve been given here, is the experimental design a
completely randomized design or a randomized complete block design?

2.
Construct
a 2-way table of treatment means and generate plots of the treatment
means. Is there any evidence of
interaction? Explain.

3.
Run the
2-way analysis of variance for these data.
First, conduct a hypothesis test to determine whether there is a
significant interaction between the 2 factors.
State the hypotheses, report the F-statistic and p-value for the test,
and state your conclusion. Is it
appropriate to also test and discuss the main effects? Why or why not?