## Advanced Statistics - Biology 6030 |

## Bowling Green State University, Fall 2019 |

You are charged with helping your neighbors answer an important question. They are farming trout in a series of three ponds, each had been stocked at the beginning of the season with a random selection of 1100 fish. Jerry and Darleen would like to know whether the conditions in these ponds are equal or whether some ponds are more favorable to raising trout than others. They just drained the ponds and collected 1000 fish from each pond.

**Exercise 1: ****Descriptive Statistics**

- Consider the data contained in "Trout.txt" located at "http://caspar.bgsu.edu/~courses/Stats/Labs/Datasets/Trout.txt". The file contains a pair of variables: Pond: [1,2,3] - the particular pond the trout came from; stLength - the standard length of 1000 trout from each pond. Obtain a set of descriptives statistics for all fish, regardless of the pond they came from (mean, SD/var)
- Obtain a set of descriptives statistics for each pond separately (mean, SD/var).
- Using only the three pond means, obtain a set of descriptives statistics for these three values (mean, SD/var)

**Exercise 2: Estimate MS (i.e., population variance)
**

- Assuming all trout come from the same underlying distribution, obtain the total Mean Squares from the sample statistics for all trout combined (Exercise 1.1)
- Obtain the total Sum of Squares

- Obtain the model Mean Squares from the sample statistics for the three sample means (Exercise 1.3)
- Obtain the model Sum of Squares
- Obtain the error Mean Squares anyway you like
- Obtain the error Sum of Squares

**Exercise 3: ****Treatment Analysis**

- What analysis would you perform to test for pond differences and why?
- Perform the analysis of your choice and present your conclusions.

**optional Exercise 3: You aim to perform a Power analysis for these
Treatment Effects**

- What are appropriate
**s**and**d**values? - What is the
**power**of this analysis? - What is the
**least significant number of observations**that would be needed to obtain significance in the above analysis?

last modified: 2/10/15

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