Fish and Wildlife Population Ecology  Dr. Edward O. Garton


Wlf 543 E. O. Garton
1. Objective: Take a sample from the population, measure some characteristic on each of the sampled units, and use this information to estimate (infer) the characteristic in the entire population. 2. Simple random sampling is the most basic sampling procedure to draw the sample. 3. Simple random sampling forms the basis for many of the more complicated sampling procedures. 4. Simple random sampling is easy to describe but is often very difficult to carry out in the field where there is not a complete list of all the members of the population.
DEFINITION: A simple random sample is a sample of size n drawn from a population of size N in such a way that every possible sample of size n has the same chance of being selected. 5. Note that this definition requires that we know the population size N. ASSUMPTIONS FOR SIMPLE RANDOM SAMPLING Simple random sampling is one form of the general set of sampling procedures referred to as probability sampling. Probability sampling procedures must meet 4 criteria (Chochran, 1977:9):
For any sampling procedure of this type we can calculate the frequency distribution of the estimates that it generates if repeatedly applied to the same population and therefore determine bias and variance of the estimator. In general we do not assume that the underlying population follows a normal distribution, but in order to calculate bounds and confidence intervals from single samples it may be useful to assume that the estimates follow a normal distribution. This assumption will be appropriate for large sample sizes but will be problematic for small sample sizes drawn from highly skewed populations. Cochran (1977:42) suggested the "crude rule" for positively skewed distributions that n should be greater than 25G12 where G1 is Fisher's measure of skewness. Alternately Tchebysheff's theorem states that at least 75% of the observations for any probability distribution will be within 2 standard deviations of their mean (Scheaffer et al., 1986:16).
Taking all of this together, we can state the following assumptions for simple random sampling:
DRAWING A SIMPLE RANDOM SAMPLE
4. EXAMPLE: Suppose that we wanted to sample a stream to estimate the mean number of fish per pool. We could travel along the stream from its mouth to its headwaters identifying the pools and assigning each pool a number. Then we could pick n random numbers from a random number table and sample the pools corresponding to those numbers. 5. An alternative way to use random numbers to select samples if you have access to a computer is the following:
ESTIMATING THE POPULATION MEAN
ESTIMATING THE POPULATION TOTAL
