Stratified Random Sampling

Example

The data set in Table 1 is the number of possums caught in traps in a study area in New Zealand. The area was divided into three strata based on a map of the area. By looking at the map and studying the mapped hill slope and aspect, the researcher divided the study area into three contiguous strata roughly corresponding to hillside easterly aspect, valley floor, and hillside westerly aspect.

The mean for stratum h is calculated as

where nh is the number of units selected from the hth stratum and xih is the value of the ith sample unit in the hth stratum.

The sample mean from stratified sampling is the weighted sum of the stratum means, calculated as

Table 1 Different Strata for Random Sampling
Stratum 1	Stratum 2	Stratum 3
2	2	0
0	4	1
1	2	2
4	0	3
1	2	0
0	0	0
4	4	1
2	0	2
0	6	4
6	1	1

where N is the size of the population and Nh is the size of the hth stratum.

The estimated variance of the sample mean is calculated as

where sh2 is the sample variance for the hth stratum.

In this example, the stratum means were X¯1 = 2.00, X¯2 = 3.50, and X¯3 = 1.40, and N1 = 200 hectares, N2 = 150 hectares, and N3 = 450 hectares. The data show some differences in possum numbers among the strata, with half again as many possums caught in stratum 2 as in stratum 3. The sample variances were s12 = 3.80, s22 = 5.65, and s32 = 1.64. With these stratum statistics, the stratified sample mean and estimated variance of the sample mean are calculated as