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Using Anova or Ancova to analyse the growth of Northern Pike

Growth of Northern Pike in two lakes
The problem

Northern Pike are voracious piscivores found naturally in the majority of lakes of southern Québec and Ontario. However, in some small lakes there are no pikes unless they have been introduced by man. Such introductions are often favored by fishermen, although we now realize that these introductions can endanger some species of minnows. In any case, it is believed that when pike is introduced in a small lake without piscivores, it benefits from the large initial availability of preys and grows more rapidly where recently introduced compared to other lakes where piscivores have been present for long periods.
The data

In 2005 pikes were caught in two lakes (0 and 1) of Gatineau Park. Lake 0 has had piscivores since times immemorial. In lake 1, no pikes were found until 1990 and pikes were introduced in 1991. The file brochet.Rdata contains the age (in years) and the length (longueur, in mm) of each fish caught.
The task

Analyze the data to determine
1) if the growth of pike differs in a lake where it is recently introduced
In your answer, you should provide:
? An explicit statement of all null and alternate hypotheses (are they one or two-tailed?);
? A rationale for your choice of statistical procedure(s) to test the null hypotheses specified in (1)
? An explicit statement of the statistical conclusion and its biological interpretation.
? A brief discussion of the confidence you have in your conclusions, and an accompanying rationale/justification (Note: a discussion of power may be appropriate here.)
? A brief discussion of the extent to which the provided data and/or your chosen method of analysis are appropriate and/or sufficient to test the biological hypothesis.

2) if the average growth rate of pike in these two lakes differ from what is observed in Wisconsin (72mm/yr)
3) what would be the sample size required to to have 80% power to detect a difference in growth rate of 3mm between lakes.

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Solution Summary

In 2005 pikes were caught in two lakes (0 and 1) of Gatineau Park. Lake 0 has had piscivores since times immemorial. In lake 1, no pikes were found until 1990 and pikes were introduced in 1991. The file brochet.Rdata contains the age (in years) and the length (longueur, in mm) of each fish caught. Data analysis and subsequent guide on how to develop the essay requested. We use anova and ancova to analyze the relationship between growth, lakes and pike length. A step-by-step guide on developing the essay is provided.

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