## Advanced Statistics - Biology 6030 |

## Bowling Green State University, Fall 2019 |

Consider the data set: "Trout.txt", it contains a pair of original variables: Pond: [1,2,3] - the particular pond the trout came from; stLength - the standard length of the trout [cm]

As an exercise into the underlying math - **compare ANOVA tables** from:

**one-way ANOVA**of standard length (stLength) of trout as a function of the pond (Pond) used to raise them**linear regression**of length as a function of pond while treating pond as a continuous variable (I agree, this analysis makes little sense with the previous setup. Consider the numbers in "Pond" a measure of the depth of the pond in meters). Easiest way is to use the lm(Y~X) command**second order polynomial regression**of length as a function of pond (as a continuous variable). Easiest way is to use the lm(Y~poly(X,2)) command.

Examine the ANOVA tables and understand how all terms are derived. Are any terms the same across ANOVA and 2nd order regression? Examine the formula for the second order equation, plug in values for x, and examine the resulting y values. Do you recognize these numbers? If so, understand why some ANOVA tables are identical.

**Does eyesize differ among lineages of cichlids?**

- Download the file "CichlidEyesize.txt" at <http://caspar.bgsu.edu/~courses/Stats/Labs/Datasets/CichlidEyeSize.txt>. The first line contains the names of the three variables - Lineage, EyeDiameter in mm and BodyVolume in mm
^{3}. - Examine whether the size of the eye differs among lineages.
- Consider that fish differ in body size, which presumably also impacts eye size.
- Can we distinguish between the effects of body size and lineage? How would you go about answering this question?
- Explain your course of action and your reasoning.

last modified: 2/12/10

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