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Post-stratified estimation: with-in strata and total sample size recommendations

Formally Refereed
Authors: James A. Westfall, Paul L. Patterson, John W. Coulston
Year: 2011
Type: Miscellaneous Publication
Station: Rocky Mountain Research Station
Source: Canadian Journal of Forest Research. 41: 1130-1139.


Post-stratification is used to reduce the variance of estimates of the mean. Because the stratification is not fixed in advance, within-strata sample sizes can be quite small. The survey statistics literature provides some guidance on minimum within-strata sample sizes; however, the recommendations and justifications are inconsistent and apply broadly for many different population structures. The impacts of minimum within-strata and total sample sizes on estimates of means and standard errors were examined for two forest inventory variables: proportion forestland and cubic net volume. Estimates of the means seem unbiased across a range of minimum within-strata sample sizes. A ratio that described the decrease in variability with increasing sample size allowed for assessment of minimum within-strata sample requirements to obtain stable estimates of means. This metric indicated that the minimum within-strata sample size should be at least 10. Estimates of standard errors were found to be biased at small total sample sizes. To obtain a bias of less than 3%, the required minimum total sample size was 25 for proportion forestland and 75 for cubic net volume. The results presented allow analysts to determine within-stratum and total sample size requirements corresponding to their criteria for acceptable levels of bias and variability.


post-stratification, within-strata sample, estimates


Westfall, James A.; Patterson, Paul L.; Coulston, John W. 2011. Post-stratified estimation: with-in strata and total sample size recommendations. Canadian Journal of Forest Research. 41: 1130-1139.