QSci 482 Lab Activity Topic 2

A benthic ecologist is studying the pattern of gap formation in intertidal mussel beds. Unfortunately, he has been unable to find a previous paper listing the average number of gaps formed in a coast area of a given size. He assumes that since gaps are formed fairly infrequently and randomly they will follow a Poisson distribution. He also knows that he can estimate the parameter for his distribution by finding the average in his sample, but that by estimating this parameter from his data, rather than using a constant from elsewhere (previous research, foraging theory, etc.), he will lose a degree of freedom (df). [NOTE: in HW1 #2, the value for mu, the hypothesized population mean, is given, so you do not have to subtract a degree of freedom there. However in this lab problem, since we have to estimate the average first and then use it in computing probabilities, we “pay” for this bit of statistical information by subtracting one df.] He has the following data from counting the number of gaps in each of 60 plots. Help determine if his data follows a Poisson distribution at the a = 0.10 level of significance.

Number of gaps Number of plots

0 8

1 13

2 20

3 11

4 6

5 2

State H_o and H_a biologically and statistically.

List test assumptions.

Calculate the average number of gaps per plot. (This is your best estimate of m.)

Find the probabilities associated with seeing given numbers of gaps in single plots. (That is, what’s the probability of seeing a plot with no gaps, with one gap, with two, etc.?) Recall that

and that the total probability of all the categories (including the possibility that there are more than 5 gaps in a plot!) must add up to 1.

Use the probabilities you found to calculate the expected frequencies, and then find your overall test statistic.

What’s your critical value? What do you conclude (include the p-value)?