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Analysis of anthropometric variables
Use of statistics for predictive purposes
Brief conclusions and recommendations
C. G. N. Mascie-Taylor
University of Cambridge, Department of Biological Anthropology, Downing Street, Cambridge CB2 3DZ, UK
This paper provides a detailed
account, with examples, of the types of statistical analyses which can be carried out on
cross-sectional anthropometric data. For continuous characters the analyses described
cover t-tests, one-way analysis of variance, more complex analysis of variance with
covariates; testing for curvilinearity; regression analysis and multiple regression
analysis. For discrete characters the analyses include chi-square, odds ratios,
sensitivity and specificity, logistic regression and discriminant analyses.
The research exercise proceeds from a planning stage, to design, data collection, processing and analysis, presentation, interpretation and publication of results. In many of these stages statistics plays an important role. Although this chapter is concerned mainly with cross-sectional analytical issues it is worth noting that a poorly designed study with an inappropriate sample size and sampling framework makes a mockery of any statistical tests which might be applied.
There are two main types of study design, observational and clinical trial. In the observational design the researcher aims to obtain data from a number of individuals and then draw inferences about the total population from which the individuals were drawn. For this extrapolation from individuals to population to be valid it is essential that the individuals are representative of the population, i.e. they constitute a random sample.
A number of sampling strategies are available (e.g. stratified, quota, cluster) and some studies use a combination of strategies. For instance researchers investigating variation in adult stature may stratify by location (urban or rural), use a cluster design (by picking a fixed number of villages and urban zones) and select by quota (measuring 200 adults in each cluster).
In the clinical trial, of which the randomized control trial is the strongest design, people are allocated randomly to two or more groups. With two groups the design would consist of experimental and control groups. The experimental group receives the new treatment whereas the control gets either conventional therapy, a placebo or nothing. The randomization ensures that the two groups are identical except for differences that may arise by chance.
A common question asked is 'how large a sample do I need?'. The answer depends on the sample design and whether the data are qualitative or quantitative. In both cases the researcher has to take into account two types of error. A type I (alpha, a) error occurs whenever a null hypothesis (Ho) which is true is incorrectly rejected (researchers usually set the alpha error at the 5% level).
If the null hypothesis is not
rejected, there is a chance that it is false and should be rejected. This type of error is
called a type II (beta, b) error. The power of the test is the
probability of correctly rejecting Ho given Ho is false. A number of books and articles
(e.g. Mascie-Taylor, 1993; Lemeshow et al., 1990) have recently been published
which deal with this topic in more detail.
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