![]() One method that has been found to be practical and efficient is known as the cumulative square root of the frequency method. Once the number of strata is determined, boundaries between the strata must be selected. Thus, most stratification strategies rely on a relatively small number of strata. Further, additional strata may add to the cost of the study. However, in most practical applications, little improvement is seen beyond H = 6 or so. Theoretically, increasing the number of strata will improve the precision of estimates of population parameters. In order to gain the most from stratification, strata should be selected so that the differences between strata means are as large as possible and so that each stratum is as homogeneous as possible. In other cases, the strata will be defined in such a way as to minimize the variance of estimates of population parameters. ![]() In some cases, the strata will be determined by a desire to examine a particular subpopulation of interest, such as in the study described in the preceding section. How many and what type of strata to define in a stratified random sample will be determined by the goals of the study. Garrett Glasgow, in Encyclopedia of Social Measurement, 2005 The Construction of Strata Chapter 15 will provide further discussion on this topic. In this case we can attempt to take race into account in the analysis after the sample is selected. For example, stratification by race is usually desirable in social surveys but the racial identification is often not available in the sampling frame. When such information is not available, stratification is not possible, but we still can take advantage of stratification by using the poststratification method. The formulation of the strata requires that information on the stratification variables be available for the elements in the sampling frame. The estimates from the stratified sample approach have less variation - that is, have greater precision than the SRS approach in this case. If one person is randomly selected from each stratum, the smallest estimate is 135 pounds (= /2), and the largest estimate is 155 pounds (= /2). As an alternative, we could use a stratified random sample where the strata are formed based on gender. If we use an SRS, the smallest possible estimate is 115 pounds (= /2), and the largest possible estimate is 175 (= /2). We shall form our estimate of the population average weight by taking a sample of size two without replacement. The weights of the females in the population are 110, 120, and 130 pounds, and the weights of the males are 160, 170, and 180 pounds. The population contains six persons: three females and three males. In this example, we wish to estimate the average weight of persons in the population. Let us consider a small example that illustrates this point. Another way of saying this is that the reduction occurs when the variable used to form the strata is related to the variable being measured. This reduction in variability occurs when the units in a stratum are similar, but there is variation across strata. If an SRS had been used, it is likely that too few people in these groups would have been selected to allow any in-depth analysis of these groups.Īnother advantage of stratification is that it can reduce the variability of sample statistics over that of an SRS, thus reducing the sample size required for analysis. For example, in the first National Health and Nutrition Examination Survey (NHANES I), the elderly, persons in poverty areas, and women of childbearing age were oversampled to provide sufficient numbers of these groups for in-depth analysis ( NCHS 1973). In this design, units need not have equal chances of being selected and some strata may be deliberately oversampled. The strata are formed to keep similar units together - for example, a female stratum and a male stratum. In a stratified random sample design, the units in the sampling frame are first divided into groups, called strata, and a separate SRS is taken in each stratum to form the total sample. Stratification is often used in complex sample designs. Mike Hernandez, in Biostatistics (Second Edition), 2007 6.3.5 Stratified Random Sampling ![]()
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