4.3 Relationship between Sample Size and Margin of Error

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There is a predictable relationship between sample size and margin of error. The numbers found in Table 4.1 help to explain this relationship.

Table 4.1. Calculated Margins of Error for Selected Sample Sizes

Sample Size (n) Margin of Error (M.E.)
200 7.1%
400 5.0%
700 3.8%
1000 3.2%
1200 2.9%
1500 2.6%
2000 2.2%
3000 1.8%
4000 1.6%
5000 1.4%

From this table, one can clearly see that as sample size increases, the margin of error decreases. In order to add additional clarity to this finding, the information from Table 4.1 is also displayed in Figure 4.2.

The graph shows the relationship between sample size and margin of error. Margin of error decreases as the sample size increases.

Figure 4.2 Relationship Between Sample Size and Margin of Error

In Figure 4.2, you again find that as the sample size increases, the margin of error decreases.  However, you should also notice that the amount by which the margin of error decreases is substantial between samples sizes of 200 and 1500.  This implies that the accuracy of the estimate is strongly affected by the size of the sample.  In contrast, the margin of error does not substantially decrease at sample sizes above 1500.  Therefore, pollsters have concluded that it is not worth it to spend additional time and money for samples that contain more than 1500 people.