Clinical Trials

❘❙❚■ Chapter 17 | Types of Data and Normal DistributionFigure 5. Normal distributions for simulated systolic blood pressure (SBP), with different standarddeviations (SDs) and means.0.0200.0200.0150.015Density0.010Density0.0100.0050.005050 100 150 200 150050 100 150 200 250 300SBP (mm Hg)SBP (mm Hg)–––– SD = 20 –––– SD = 30 –––– Mean = 150 –––– Mean = 200The normal distribution is the most important distribution in statistics. It is alsoknown as the Gaussian distribution after the German mathematician Karl FriedrichGauss who first gave the distribution its full description [3].Properties of the (theoretical) normal distributionThe normal distribution is completely defined by two parameters: the mean (μ) orcenter point at which the curve peaks, and the standard deviation (σ) or a measureof the spread of each tail, expressed statistically as N(μ,σ 2 ). The value of thenormal curve N(μ,σ 2 ) is:( )1 – [x – μ] 2f(x) = expσ √2π 2σ 2σ > 0, –∞ < μ < ∞ , –∞ < x < ∞Figure 5 gives examples of normal distributions for simulated SBP data. As μchanges, the normal distribution curve moves along the x-axis; as σ changes, thespread is closer or further away from μ. Distributions with different standarddeviations have different spreads (left panel), whereas distributions with differentmeans have different locations (right panel). However, whatever the shape of thedistribution, the area under each curve is equal to 1, often expressed as 100%.176