Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Figure 4. Histogram and fitted normal distribution curve for systolic blood pressures (SBPs) from 4,000 subjects.0.150.03Fraction0.100.05Density0.020.01080 100 120 140 160 180SBP (mm Hg)080 100 120 140 160 180SBP (mm Hg)The normal distributionIn medical research, most quantitative variables have a range of values that occurwith the highest frequency at a mean value and less frequently further away fromthis mean value, yielding a symmetric, bell-shaped frequency distribution. This isknown as a normal distribution. The assumption of a normal distribution for outcomevariables is a key prerequisite for various statistical analysis methods and models.What is a normal distribution?Quantitative (continuous) variables are those whose values can, in theory, takeany numerical value within a given range. Consider the SBP measurements of4,000 subjects participating in a health survey. Figure 4 shows the frequencydistribution of these SBPs. In the left-hand histogram, the height of each verticalbar shows the proportion (or fraction) of subjects whose SBP corresponded to avalue within the 5 mm Hg intervals plotted on the basal axis. If the heights of allthe bars in the histogram are summed then they will total 1, because all theobserved values are represented in the histogram.In the right-hand image, we have rescaled the histogram by dividing the height ofeach vertical bar by the width of the bar (5 mm Hg), generating a density histogram.In this histogram, the sum of the areas within all the bars equals 1. Indeed, if acurve is superimposed joining the midpoints of each of the bars then it forms a bellshape (solid curve in the left panel of Figure 4) and is very close to an underlying‘normal distribution’ (solid curve in the right panel of Figure 4).175