# Determining the relationship between sample size and margin of error

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.

Table 1: Estimate population size and percentage error

Table 1 shows the percentage error for each estimated population size.  Each estimate was obtained using different sample sizes in the recapture:  10, 15, 20, 25 and 30 individuals.  Four trials were considered.   The results in the table suggest a trend of a negative correlation between percentage error and sample size.  Although percentage error does not necessarily decrease with each successive round, there is an overall decrease from round one to found five in all four trials.  However, this relation can be depicted more clearly in graphical form.  A scatter plot will be used to display the data, ...