Clinical Trials

❘❙❚■ Chapter 17 | Types of Data and Normal DistributionCategorical variables are most conveniently summarized and presented in termsof percentages and compared by treatment groups. For quantitative variableswe can do more than this, as we have other measures with which to summarizethe data (summary measures). From the observed data, we can calculate thelocation (or central tendency) that summarizes where the center of thedistribution lies and we can also summarize the spread, range, or variation of thedistribution, and describe how widely the values are spread above and below thecentral value.There are three measures commonly used to describe the location or ‘center’of a distribution of a quantitative variable:• mean: the mean can be calculated by summing all the values ofobservations and dividing by the total number of observations• median: the median is the value that divides the distribution intoequal numbers of observations. The median can be more appropriatefor distributions that are skewed, such as physical fitness. When thedistribution is symmetrical, the median equals the mean• mode: the mode is the value that occurs most frequently, ie, the mosttypical value. There may be more than one mode if two values areequally frequentThe main differences between these measures of location are:• the mean is sensitive to outliers, but the median and mode are not• the mean and median are not affected by small changes in the data,while the mode may beSo which one should be presented? Generally, for skewed distributions(ie, asymmetrical distributions with extreme values) the median is a bettermeasure of central location than the mean, though ideally it is worth presentingboth. For statistical analysis and inference, the mean is more commonly used,although if the data are considerably skewed then statistical techniques based onmedians should be employed.Percentiles are also sometimes used to describe a variable distribution, givingproportions of the data that should fall above and below a given value. The pthpercentile is a value such that at most p% of the measurements are less than thisvalue and at most (100 – p)% are greater. The 50th percentile is the median.The most frequently used percentiles are the 25th, 50th, and 75th.172