Thomas J. Albin

An empirical description of the dispersion of 5th and 95th percentiles in worldwide anthropometric data applied to estimating accommodation with unknown correlation values

BACKGROUND Anthropometric data are assumed to have a Gaussian (Normal) distribution, but if non-Gaussian, accommodation estimates are affected. When data are limited, users may choose to combine anthropometric elements by Combining Percentiles (CP) (adding or subtracting), despite known adverse effects. OBJECTIVE This study examined whether global anthropometric data are Gaussian distributed. It compared the Median Correlation Method (MCM) of combining anthropometric elements with unknown correlations to CP to determine if MCM provides better estimates of percentile values and accommodation. METHOD Percentile values of 604 male and female anthropometric data drawn from seven countries worldwide were expressed as standard scores. The standard scores were tested to determine if they were consistent with a Gaussian distribution. Empirical multipliers for determining percentile values were developed.In a test case, five anthropometric elements descriptive of seating were combined in addition and subtraction models. Percentile values were estimated for each model by CP, MCM with Gaussian distributed data, or MCM with empirically distributed data. RESULTS The 5th and 95th percentile values of a dataset of global anthropometric data are shown to be asymmetrically distributed. MCM with empirical multipliers gave more accurate estimates of 5th and 95th percentiles values. CONCLUSIONS Anthropometric data are not Gaussian distributed. The MCM method is more accurate than adding or subtracting percentiles.

A method to improve the accuracy of pair-wise combinations of anthropometric elements when only limited data are available

BACKGROUND Designers and ergonomists occasionally must produce anthropometric models of workstations with only summary percentile data available regarding the intended users. Until now the only option available was adding or subtracting percentiles of the anthropometric elements, e.g. heights and widths, used in the model, despite the known resultant errors in the estimate of the percent of users accommodated. This paper introduces a new method, the Median Correlation Method (MCM) that reduces the error. OBJECTIVE Compare the relative accuracy of MCM to combining percentiles for anthropometric models comprised of all possible pairs of five anthropometric elements. Describe the mathematical basis of the greater accuracy of MCM. METHODS MCM is described. 95th percentile accommodation percentiles are calculated for the sums and differences of all combinations of five anthropometric elements by combining percentiles and using MCM. The resulting estimates are compared with empirical values of the 95th percentiles, and the relative errors are reported. RESULTS The MCM method is shown to be significantly more accurate than adding percentiles. MCM is demonstrated to have a mathematical advantage estimating accommodation relative to adding or subtracting percentiles. CONCLUSIONS The MCM method should be used in preference to adding or subtracting percentiles when limited data prevent more sophisticated anthropometric models.

Stepwise estimation of accommodation in multivariate anthropometric models using percentiles and an average correlation value

ABSTRACT We estimated accommodation on multiple variables using a stepwise combination of pairs of data (percentile values), where each combined pair became an input for the succeeding step. The method is based on calculation of the covariance of intersecting sets using an average correlation value. Two different set-based definitions of accommodation are discussed, intersection, where all values are concurrently less than or equal to their respective percentile values, and union, where the sum of all measurements is less than or equal to the sum of the percentile values. Accommodation was estimated for 280 different combinations of anthropometric data formed by adding 2 to 15 variables and for 40 different combinations of 2, 5, 10 and 15 variables where one variable was subtracted from the others, a total of 320 different models. The estimates were compared with observed values; the average differences for both types of accommodation ranged between 2.2 and −6.5 per cent.

Combining Very Limited Anthropometric Data A Simple Method With Less Error Than Adding or Subtracting Percentiles

Occasionally an ergonomist or designer is asked to develop an anthropometric model that will accommodate a desired proportion of an anticipated user population, but with only very limited anthropometric data, such as a summary table of percentiles, available. Despite the known problems of adding or subtracting percentiles, that may be the only option available to him or her. This paper introduces a technique that reduces the error associated with adding percentiles, although it does not eliminate it. Two examples are given.

Design with limited anthropometric data: A method of interpreting sums of percentiles in anthropometric design

Occasionally practitioners must work with single dimensions defined as combinations (sums or differences) of percentile values, but lack information (e.g. variances) to estimate the accommodation achieved. This paper describes methods to predict accommodation proportions for such combinations of percentile values, e.g. two 90th percentile values. Kreifeldt and Nah z-score multipliers were used to estimate the proportions accommodated by combinations of percentile values of 2-15 variables; two simplified versions required less information about variance and/or correlation. The estimates were compared to actual observed proportions; for combinations of 2-15 percentile values the average absolute differences ranged between 0.5 and 1.5 percentage points. The multipliers were also used to estimate adjusted percentile values, that, when combined, estimate a desired proportion of the combined measurements. For combinations of two and three adjusted variables, the average absolute difference between predicted and observed proportions ranged between 0.5 and 3.0 percentage points.

A method superior to adding percentiles when only limited anthropometric data such as percentile tables are available for design models.

PURPOSE Designers and ergonomists may occasionally be limited to using tables of percentiles of anthropometric data to model users. Design models that add or subtract percentiles produce unreliable estimates of the proportion of users accommodated, in part because they assume a perfect correlation between variables. Percentile data do not allow the use of more reliable modeling methods such as Principle Component Analysis. A better method is needed. RESULTS A new method for modeling with limited data is described. It uses measures of central tendency (median or mean) of the range of possible correlation values to estimate the combined variance is shown to reduce error compared to combining percentiles. Second, use of the Chebyshev inequality allows the designer to more reliably estimate the percent accommodation when the distributions of the underlying anthropometric data are unknown than does combining percentiles. CONCLUSION This paper describes a modeling method that is more accurate than combining percentiles when only limited data are available.

Evaluating the Efficiency of Checklists Used to Assess Risk of Musculoskeletal Disorders

Checklists are commonly used to identify jobs considered at-risk for musculoskeletal disorders and to prioritize the identified jobs with regard to remediation. Often an objective criterion for determining the checklist score that indicates a job is at-risk is not known. A poorly drawn criterion score may cause a checklist to perform less effectively at identifying at-risk jobs than guessing. This paper describes a method to objectively determine a minimum score necessary to correctly identify at-risk jobs that is better than randomly guessing. The method incorporates prevalence into the determination of the probability that a positive checklist score truly indicates an at-risk job.