ESM 206B
Lab 3 ANCOVA
Hampton
April 2009
Today’s lab is designed to give you experience with executing analysis of covariance
(ANCOVA) and interpreting ANCOVA results.
The scenario in this simulated data set is: In Study 1, estimates of average
macrophyte stem density were collected from ponds with and without invasive
crayfish; researchers sought to sample ponds as evenly as possible at a range of
nutrient levels, intending to do ANCOVA with nutrient as a covariate.
They hypothesized that a) in the presence of crayfish, macrophyte density would be
lower, b) that macrophytes generally increase along a nutrient gradient, and c) that
macrophyte response to nutrient increases would be mediated by the presence of
crayfish.
Results were tantalizing in this study, and a colleague was eager to replicate the
study in the following year, testing the same hypotheses, with native crayfish in an
area where invasive crayfish had not yet been observed (Study 2).
1. Open fake_crayfish.xls in JMP.
2. Create the ANCOVA model for Study 1. Fit Model -> Phosphorus, Crayfish,
PhosphorusXCrayfish as X variables, Stems as Y -> Run
3. Are results going in the directions consistent with the hypotheses? How are
the residuals? Transform if necessary, and reinterpret results. Does the study
appear to be designed appropriately to detect effects? What is the interaction
term telling you? If you had to explain the meaning of this interaction term to
a journalist, or an uncle who never studied science much, how would you
describe the meaning?
4. Run a new ANCOVA for Study 2 and interpret results as above, answering the
same questions.
5. What are some of the reasons (e.g., environmental or statistical) that results
of the two studies may have differed?
6. Explore the effects of confounding effects, as discussed in lecture. Imagine
now that in Study 2, the native crayfish under consideration are not found in
the lowest nutrient lakes – they are found only at phosphorus levels of 0.06
and higher. Additionally, the researchers could find no lakes at 0.08 and
higher phosphorus concentrations that did NOT have crayfish. You’ll make a
new simulated data set called 2a that reflects this situation.
