Fish and Wildlife Population Ecology  - Dr. Edward O. Garton

Probability Proportional to Size

Problem Set 3.

Wlf 543

A powerful technique for sampling uses unequal probabilities of sampling for different units based on the size of those units.  This approach uses sampling with replacement which is also unusual.  This exercise demonstrates the application of this approach, PPS or probability proportional to size, sampling to the same data on snorkel and electro-fishing samples of fish as used in Problem 2.  Use the same data in Table 1 for this exercise.

1. Draw a new random sample with probabilities proportional to size (PPS sample) of the data in Table 1. . Use the snorkel count data as your indicator of size. Select 5 pools and use the electro-fishing data to estimate mean fish per pool, its variance, and 95% bound. How many fish would this indicate occupy the stream? How good is the estimate?

2. Draw a PPS sample of 10 pools and use it to estimate mean fish per pool, its variance, and 95% bound. How many fish would this indicate occupy the stream? How good is the estimate?

3. Did the non-uniform sampling probabilities improve the estimates compared to uniform probabilities under simple random sampling? Why? (Hint: Is there any relationship between the snorkel count and the electro-fishing count?)