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

Simple Random Sampling

Wlf 543

E. O. Garton

 

Snorkel counts are used widely in the Northwest to get an index to trout population sizes. In an attempt to evaluate this technique a complete survey of all the pools on Deer Creek was completed in 1989 by snorkeling and then the survey was repeated by electro-fishing in June. Use the data presented in Table 1 to carry out the analyses described below:

1. Calculate the average no. of fish per pool as sampled by electro-fishing in the entire stream.

2. Draw a random sample of 5 pools and calculate the mean fish per pool, its variance, 95% bound, and confidence interval. How many fish would this indicate occupy the stream? How good is the estimate?

3. Draw a random sample of 10 pools and calculate the mean fish per pool, its variance, 95% bound, and confidence interval. How many fish would this indicate occupy the stream? How good is the estimate?

4. How many pools would you need to sample to obtain an estimate with 95% bound which is within 5% of the true value.

5.  Write your results on the board for mean fish per pool from your random sample if 5 and of 10 pools.  How well did your variance and confidence intervals do for each sample size in describing the results of all the class members sampling?  Did your variance and confidence interval describe the results for the members of the class?  Does this support a frequentist perspective or a Bayesian perspective, neither or both?

The goal here is to learn the use of spreadsheets to perform common calculations for finite population studies.  Feel free to use Excel or QuatroPro or whichever spreadsheet program you use regularly.  Try using the built-in formulas to calculate any of the statistics that are available within the program such as mean (called AVERAGE) and variance but note that some provide the population variance rather than the sample variance (using n rather than n-1 in the divisor).  You can then use these preliminary steps to calculate the appropriate final results including the finite population correction, etc.  There are Excel and Quatropro spreadsheets with the raw data already entered on the S: drive under Wlf543/SAMPLE.  Look for the files called RANDSAMP.

 

Table 1. Total fish counted in Deer Creek, June 1989.

Pool	Electro- fishing Count	Snorkel Count
1	135	78
2	27	13
3	46	27
4	13	8
5	3	2
6	96	51
7	4	6
8	17	12
9	6	5
10	2	3
11	66	39
12	14	10
13	31	18
14	9	1
15	2	1
16	23	18
17	4	0
18	6	5
19	17	22
20	11	6
21	6	3
22	188	97
23	63	38