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# Determining the relationship between sample size and margin of error

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Introduction

Determining the Relationship between Sample Size and Margin of Error 10 November 2008 PURPOSE To determine the effect of sample size on the amount of error in a population estimate obtained by capture, mark and recapture techniques. HYPOTHESIS When comparing two different samples from the same population, the null hypothesis is used. The null hypothesis expects that there is no difference between samples of different sizes. DATA PROCESSING AND COLLECTION The estimated population size was calculated using the Lincoln Index: For all rounds (in all trials) the number of individuals initially caught and markers was 20. In each round, the number of individuals recaptured as well as recaptured and marked differed. Sample population estimate calculation (for trial 1, round 1): Sample 1 (individuals initially caught) = 20 Sample 2 (individuals recaptured) = 10 Individuals recaptured and marked = 1 The actual population size was obtained by counting all members of the population in the sample area. The margin of error between the estimated population size and the actually population was determined by using the formula for percentage error: Sample percentage error calculation (for trial 1, round 1): These calculations have been used to produce Table 1. ...read more.

Middle

The curves of best fit for all four trials have a similar shape; initially the percentage error is high, but as sample size increases the error decreases. However, the data for each trial does not clearly follow the curve of best fit, which raises doubt on the accuracy of the trend suggested by the curve of best fit. Though to determine a curve that is more representative of a general trend, an average percentage error in population estimate for each sample size (for all four trials) must be taken. Sample calculation for average percentage error in population estimate for sample size of 10: Table 2: Average percentage error in population estimate (all four trials): Recapture Sample Size 10 15 20 25 30 Average percentage error in population estimate (%) 33.3 16.6 27.8 18.8 6.3 The averaged values in table 2 take into account all three trials and now can be graphed as a single set of points on a scatter plot. Figure 2: Average relationship between sample size and percentage error in population estimate The curve of best fit for the average data is similar in shape to the curves in figure 1. ...read more.

Conclusion

Other inaccuracies could have occurred because the sample sizes were relatively small. The first sample of 20 individuals in the initial capture (constant for all rounds in the experiment) could have been greater and for the second sample (the recapture sample which varied in each round), a greater number of sample sizes should have been considered to determine how far the trend continues. Lastly, since this experiment was carried out using beans in a container, the shape of the container prevented that sampling from being truly random. The beans on the bottom of the container were covered by many other beans and were rarely chosen in the sampling. To correct this, all the beans could have been laid out on a flat surface, where they would randomly be selected. Although natural human error would still exist, this method would be more representative of a sampling in a terrestrial ecosystem. Therefore, to improve this experiment more trials should be considered, a greater number of samples should be taken and the selection of individuals should take on a flat surface where each individual has an equal chance of being selected. 1 "Sample Size Calculator." 2004. Raosoft. 1 Nov 2008 <http://www.ezsurvey.com/samplesize.html>. ?? ?? ?? ?? 2 ...read more.

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