Читать книгу Medical Statistics - David Machin - Страница 41

In the randomised controlled trial that investigated the effectiveness of salicylic acid plasters compared with usual scalpel debridement for treatment of foot corns (Farndon et al. 2013), the baseline size of the index corn (at its widest diameter in mm) was measured by an independent podiatrist (foot specialist) who was not involved in the subsequent treatment of the patients. Consider the following 16 baseline corn sizes in mm, listed in ascending order, selected randomly from the 200 patients, with valid baseline corn size data, in the trial.

Thus, the mean = 58/16 = 3.625 mm or 3.6 mm. It is usual to quote one more decimal place for the mean than the data recorded.

The major advantage of the mean is that it uses all the data values and is, in a statistical sense, therefore efficient. The mean also characterises some important statistical distributions to be discussed in Chapter 4. The main disadvantage of the mean is that it is vulnerable to what are known as outliers. Outliers are single observations that, if excluded from the calculations, have noticeable influence on the results. For example, if we had entered ‘100 mm’ instead of ‘10 mm’, for the 16th patient, in the calculation of the mean, we would find the mean changed from 3.6 to 9.3 mm. It does not necessarily follow, however, that outliers should be excluded from the final data summary, or that they result from an erroneous measurement.

If the data are binary, that is nominal and are coded 0 or 1, then is the proportion of individuals with value 1, and this can also be expressed as a percentage. In the foot corn plaster trial, the corn had healed or resolved by a three‐month follow‐up in 52 out of 189 patients. If whether the corn was healed at a three‐month post‐randomisation follow‐up is coded as a ‘1’ for ‘yes, healed’, and a ‘0’ for ‘no, not healed’, then the mean of this variable is 0.257 or 25.7%.