SNAPS 1999 Standard Errors for Selected Sample Sizes

This page is designed to assist the coordinators on how to set the target size for campus samples or target size for strata that are to be over-sampled.

Unity

100.0%

100.0%

100.0%

100.0%

100.0%

100.0%

100.0%

p

50.0%

40.0%

30.0%

20.0%

10.0%

5.0%

1.0%

q

50.0%

60.0%

70.0%

80.0%

90.0%

95.0%

99.0%

n

 

 

 

 

 

 

 

100

5.0%

4.9%

4.6%

4.0%

3.0%

2.2%

1.0%

120

4.6%

4.5%

4.2%

3.7%

2.7%

2.0%

0.9%

200

3.5%

3.5%

3.2%

2.8%

2.1%

1.5%

0.7%

750

1.8%

1.8%

1.7%

1.5%

1.1%

0.8%

0.4%

950

1.6%

1.6%

1.5%

1.3%

1.0%

0.7%

0.3%

1,000

1.5%

1.5%

1.4%

1.2%

0.9%

0.7%

0.3%

1,200

1.4%

1.4%

1.3%

1.2%

0.9%

0.6%

0.3%

2,400

1.0%

1.0%

0.9%

0.8%

0.6%

0.4%

0.2%

5,000

0.7%

0.7%

0.6%

0.6%

0.4%

0.3%

0.1%

12,500

0.4%

0.4%

0.4%

0.4%

0.3%

0.2%

0.1%

15,000

0.4%

0.4%

0.4%

0.3%

0.2%

0.2%

0.1%

20,000

0.4%

0.3%

0.3%

0.3%

0.2%

0.2%

0.1%

The above table displays the standard errors associated with proportions from samples of varying sizes. The computational formula of the standard error for proportions is:

Here the quantity p is equal to the proportion of one outcome, the quantity q is equal to 1-p, and the quantity n is equal to the size of the sample that generated the two proportions. The table illustrates the law of large numbers: if repeated random samples of size n are drawn from any population, then as n becomes larger the standard errors for the mean (p) decrease (i.e., the quantity p approaches normality). The table also shows that standard errors are highest when the quantities p and q are equal in size (i.e., p = q = 0.5 ).

The recommended target for campus sample size is 1,200. At the 50/50 split the standard error is 1.4%. At the 95-percent confidence interval, the margin of error about the quantity p is just under + 3% (i.e. 1.96*1.44=0.282). If a campus wants to over-sample small strata, the recommended target for any stratum is between 120-200 students. At the 95-percent confidence interval, the margin of error about the quantity p would be between ± 9% and ± 7% at the 50/50 split.