Anthropometry for Persons with Disabilities

Sampling Strategies

Sampling involves the process of selecting a group of individuals thought to be representative of an entire population. To put it another way, the small number of individuals in a given sample must reflect a significant amount of the variability extant in the entire population. Accurate sampling is critical to the creation of a database that can be applied successfully to the purposes for which it is intended. As has been noted, the variability of the target population in this country is very great.

There are a number of sources of information on the size of various U.S. populations with disabilities, including the National Health Interview Survey (NHIS), as well as publications of various associations representing specific disabilities but these reports do not give the kind of breakdowns that would be useful in developing a sampling plan. A review of the literature leads inevitably to the conclusion reached by J.A. Sanford (1996), "There appears to be no single data source that directly assesses the prevalence of mobility impairments in the U.S. population."

Ordinarily in sampling for anthropometric surveys, a multi-dimensional matrix is drawn up to make sure that all critical sources of anthropometric variability are accounted for in the eventual sample. In the Army's most recent anthropometric survey, for example, (Gordon et al., 1989), the matrix included sex, race and age. This is because these three demographic parameters account for much of the anthropometric variability in a non-disabled population. While the matrix approach is useful for the population of interest here, the same three parameters are not particularly effective. This is because the type of disability has much more to do with eventual body size and shape differences than does race. Age and sex are still important in describing a population of people with disabilities, so those parameters remain. Indeed, sex is generally important enough that, for anthropometric purposes, designers do well to consider males and females separately, rather than combining them into an appropriately representative population.

Age is a continuous variable, along which anthropometric dimensions change continuously. What this means is that unlike sex, where one is either a male or female, a 35-year-old may not be anthropometrically different from a 36-year-old. Yet, individuals in their 30's are anthropometrically distinct from individuals in their 60's. As a result, when using age in a sampling plan, some arbitrary divisions are needed. For the pilot study, we recommend dividing the population roughly into quartiles. Such divisions might be, for example: 18‒25, 26‒38, 39‒50, and 51and over. There would be anthropometric distinction between the groups, but the distinctions are not so fine as to defy practical significance. To find the exact dividing points for age, one would research the age distribution of the population of wheelchair users, and place approximately 25% of the age distribution in each sampling unit. If such data are not available, then one would use the breakdown of the U.S. Census figures by age.

Dividing the wheelchair population into significant groups is also problematic. One approach is that suggested by Kumar (1997) in Table 2. When developing this into a sampling strategy for a pilot study, one would select the most frequent 4 or 5 conditions, and group the rest into a category "Other". For a full-scale survey, with a more complex sampling strategy, and a larger overall sample size, one would be able to use more specific categories, and reduce the number in the "Other" group. Following this scenario, a sampling matrix might look like the one shown in Table 3. This is based on a total sample of approximately 250 subjects of a single sex. The figure would be repeated for the other sex, for a total of 500 subjects.

TABLE 2

Frequency of Medical and Physical Conditions Necessitating Wheelchair Use

TABLE 3

Hypothetical Sampling Matrix

Kumar's distribution is based on data which were gathered in the U.K. In the literature search undertaken to compile the annotated bibliography, we did not discover similar information for the U.S. Such information is critical if medical condition is to be used as a sampling parameter. It may be the case that another organization will carry out a questionnaire survey yielding appropriate information about: 1) the level and type of mobility aid used; 2) medical causes for using a mobility aid; and 3) other related demographic information. (A sample questionnaire has been developed.) If such a survey is done before planning for the pilot study is complete, then the resulting questionnaire data could be used. If another agency or researcher does not conduct such a survey, then we would recommend the questionnaire survey step prior to the beginning of the pilot anthropometric study.

Dividing the population of people who use wheelchairs into reasonable sampling units can be done in a number of ways. The key is to select a demographic parameter that has anthropometric significance, and then be sure the sampling matrix reflects the proportions of the population in each of the categories.

We have used the number 500 in our hypothetical sampling plan. This was selected to show how a sampling matrix could be developed. Let us now look more specifically at how many individuals should be measured, either in a pilot study or in a larger nationwide survey. In the extreme case, one could measure every wheelchair user, or every person in the U.S. with any kind of disability, and thus know exactly the anthropometric characteristics of that population. Such an approach is obviously prohibitively expensive, and not necessary. At the other extreme, one could measure a single wheelchair user, and assume his or her dimensions to be representative of the group as a whole. At a certain level, a single person could represent the whole group, in the sense that a single person could demonstrate that people using wheelchairs do not have an arm reach of 10 feet. This approach would estimate the population at a very low level of precision. It would also represent the population at a low level of confidence, in the sense that having measured only one, how could we be sure that there are no other individuals with a reach of 6 feet? Increasing our sample from one to some other number, would increase our confidence (since we would feel better about having more than one subject), and possibly increase our precision as well (since we would have more than one, and could observe that several individuals had a reach of less than 10 feet). These two concepts, precision and confidence, have been incorporated into a formula that allows statistical estimations of a sample size. For a specified level of precision at a specified confidence level, we know in advance how many subjects need to be measured. The formula is:

n = (Z · S_x)² / C²

Where: Z is the Z-score associated with a particular confidence level, S_x is the standard deviation of the dimension in question, and C is the desired precision

There are no hard and fast ways to determine an acceptable level of precision, just as there are no fixed ways of determining an acceptable confidence level. Statistical confidence has often been set at 95%, but this has more to do with tradition than any practical consideration. Indeed, 80% may be sufficient for many applications, and less than 80% might be sufficient for a pilot study. Similarly, precision is often targeted at 1½ % of the mean, but this figure is not sacred. Given that each of these parameters is flexible, it is sometimes useful to start with a sample size that is practically achievable, and then calculate back to find what levels of precision and confidence are associated with that n.

The other issue in calculating sample size, or the confidence and precision associated with a sample size, is the selection of a dimension. Note that in the formula, the S_x is the standard deviation associated with a particular dimension. Generally, in searching for a worst case (largest n) solution, a dimension with a high standard deviation is chosen. Typically, this is a circumference with a high correlation with weight (e.g., waist or hip). In the case of dimensions needed for ADAAG applications, circumferences are inappropriate. Here, the worst case dimension, of those needed for this application, would likely be one of the reaches. If the resulting n is unacceptably high (in view of budget considerations, for example) one could select a somewhat less variable dimension (one with a lower SD) which would sacrifice some degree of confidence and precision in favor of lower costs. With regard to the proposed survey, one might, for example, have 1½% precision for body breadth and settle for 2½% precision in the reaches.

The assumption in this approach is that we know what the standard deviation is. In studies of non-disabled individuals it is a simple matter to choose the standard deviation for a particular dimension from a similar population, or from an earlier study of the same population. These do not vary that much, and a good approximation is all that is needed for the formula to be effective. In the case of a population of wheelchair users, however, there is no such reliable resource for which to pluck SD's for given dimensions. A standard deviation from one of the published studies could be used, but all of these are from small or specialized samples that do not represent the entire U.S. population with the full range of disabilities. In the final analysis, however, we would have little choice, since those surveys are all that we have. We would use these values with caution, however, recognizing that they may be inadequate representations of the actual values.

Based on our experiences with anthropometric data collection, we believe that for a pilot study an n of 500 would be adequate. We think that it would show that the techniques are valid, and give a reasonably precise estimate of the mean values for the dimensions in the population, at a reasonable confidence level. A sample larger than 500 would just add to the expenses and the logistic difficulties. As it is, 500 will present some challenges in subject acquisition, but we believe that subject acquisition is potentially such a problem for a full-scale survey, that it is important in a pilot study to explore the magnitude of the problem. A sample smaller than 500 would be easier to collect, of course, but given the large variability in the population, a smaller n might not provide enough precision to form a useful interim database.

The sampling approach described above is a stratified random sample. This is not the only legitimate sampling method available. In Sampling and Data Gathering Strategies for Future USAF Anthropometry, Churchill and McConville (1976) describe simpler sampling strategies that can be perfectly reliable for limited purposes. One such is called a U-shaped sample: "When analysis of a design problem makes it clear that a design which accommodates both small and large men will of necessity accommodate those in between, it makes sense to sample only small and large men. This may be particularly true for arm-reach envelope studies (italics ours), for example, where the sample size is severely restricted because of the considerable time required to obtain the data from each subject. In this case, useful results more than compensate for the difficulties of selecting subjects and obtaining information." The authors suggest also the use of W-shaped samples that add subjects representative of medium sized individuals. In the case of the pilot study described here one might select subjects from the following arm-length categories:

Since arm length correlates very well with other linear measurements of the body, such as sitting height, this W-shaped sample is likely to work for the accessibility measurements as well. The choice of a sampling strategy is one of many determinations to be made by the investigator during the planning phase of the proposed survey.