Lecture 14
Topics
Study Sources
The Main Points
- We can quantify the dispersion in a couple of ways:
- The easiest one is the range. This is simply a report of the extremes of the sample sizes, like the shortest and longest of the isopods we measured on Samoa Beach.
- Another way is to use the variation among the samples to calculate a variable called the variance. In its simplest form, this amounts to subtracting the sample mean from each of the samples, squaring the differences, summing the squares and dividing the sum by the number of samples minus one. This yields a statistic called the sample variance. The sqaure root of the variance yields the statistic called the standard deviation. In a symmetrical frequency distribution, 95% of the samples will fall between 1.96 standard deviations on either side of the mean value.
- We can use the variance to help us understand the dispersion pattern of a population by comparing it with the mean. A variance/mean ratio that is close to 1 indicates a random dispersion pattern; a ratio much greater than 1 indicates the population is patchy or clumped; a ratio much less than one indicates an even pattern.
- Each of these dispersion pattern types suggests a different array of questions about the population. Randomness indicates that the habitat in which we have sampled is equally available and hospitable to individuals. Patchy dispersion may be due to unequal quality of the habitat, reproductive activity, unequal dispersion of seeds, etc. An even pattern may, for instance, indicate antagonistic behavior or territoriality among the individuals. In any of these cases, testable hypotheses are abundant once one knows about the dispersion pattern. And the best part, it is relatively easy to gather the data and calculate the variables.
- During the semester we will be going to Samoa Beach to sample intertidal isopods. We will be setting up sampling grids, randomizing our samples and doing these descriptive statistics.