The details for determining sample size, based on the desired width of the CI, in a single-group cross-sectional study are given in Chapter 3. Thus equation (3.4) gives the sample size necessary when estimating a mean and equation (3.6) for estimating a proportion or prevalence. It is worth emphasising that sample-size calculations do not provide 'exact' answers to the study size required as they are based on anticipated values of the parameters concerned. As we have indicated in Chapter 3, their objective is to provide a 'ball-park' figure for what the study size might be, whether 10s, 100s or 1000s. Thus investigators will usually examine a whole range of options to investigate the feasibility of the design they propose.
In many situations, the description of the single group of a cross-sectional study may contain within-group comparisons. For example, in patients with schizophrenia, differences in mean latency of the auditory P300 between males and females may be examined. However, these comparisons are secondary to the main objective which is to describe the group as a whole. In a truly comparative study, two or more groups of subjects are identified and the examination of differences between them is the primary objective of the study. Thus Weir, Fiaschi and Machin (1998) wished to compare patients with schizophrenia with those having major depressive illness. This comparison provides the major research question and any secondary variable, such as the gender of the patients, may then be used as a covariate to see if taking this into account modifies the observed differences between groups with respect to the measures taken.
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