BIOL 315 – W 2018: Tiny Shark-Hippo Hybrids – Bio-Stats

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Bio-Stats Assignment:

You are interested in how the abundance of sharkapotomuses (tiny shark-hippo hybrids) varies among different lake types in Alberta (prairie potholes, farm ponds, alpine lakes). One scientific hypothesis is that sharkapotomuses will be most abundant in alpine lakes, where the water is least polluted. An alternative scientific hypothesis is based on the fact that sharkapotomuses eat Daphnia (water fleas). This hypothesis says that sharkpotomuses will be most abundant in farm ponds and prairie potholes, as these are nutrient-rich and highly productive, and so support abundant, fast-growing populations of sharkapotomuses. You identify 3 alpine lakes, 6 farm ponds, and 11 prairie pothole lakes, which for purposes of this question can be assumed to be independent of one another and randomly chosen. Within each of your 20 study areas, you count the number of sharapotomuses in a sample of water.

A) Use Bartlett test to test for equal true variance of sharkapotomus density in the three lake types, vs. the alternative that the true variances are not all equal. Report the value of the test statistic, the degrees of freedom, the P value, and the statistical inference. You may assume that all groups have approximately normal distributions.

B) Test for variation in sharkapotomus density among lake types using an ANOVA with a randomization test of the null hypothesis, using 10,000 randomizations. State the null and alternative hypotheses, provide the test statistic (note that that coin uses “max” as its ANOVA test statistic rather than the F statistic; that’s ok) and P value. Illustrate the statistics with an appropriately-labeled boxplot summarizing the distribution of the data for each group. Briefly describe the major features of the boxplot that are relevant to your statistical analysis and interpretation. State the null hypothesis, statistical inference, and your scientific conclusion and its implications. You may assume that all groups have approximately normal distributions.

C) Is there any reason to be concerned about the validity of your randomization test from part

D) Transform the data so as to approximately equalize the variances, using a boxplot to illustrate the transformed distributions. Note that there may be no transformation that makes them perfectly equal; just do the best you can using transformations you’ve been taught. Then repeat the ANOVA from part b, using a conventional ANOVA rather than one based on a randomization test. Report the ANOVA table (SS, df, and MS for each source of variation, along with the F value and P value). Does the transformation change your statistical inference or scientific conclusion from part b?

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Posted on : April 02nd, 2018
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