A drug company reports that taking their new drug Dammitol results in half the number of heart attacks compared to those not taking the drug. Fifty percentage less sounds pretty good. However, if a population of 100 is what is being studied and normally there are only 2 heart attacks in that population, a 50% decrease in heart attacks is not as impressive. It means that the number of heart attacks has only decreased by one out of the 100 people studied, or 1%. A 50% decrease in heart attacks is the relative decrease. A 1% decrease in heart attacks is the absolute decrease. The drug company reported the relative, rather than the absolute, decrease in heart attacks, thereby making the results look better.
The same company also reports that there is only a 1% increase in the side effect of splitting headache from Dammitol compared with a placebo. However, if two people get the side effect on the drug, and only one gets it on placebo, this means a relative 100% rise in side effects on taking the drug. The drug company would not report a 100% increase in splitting headache, but phrase the results differently, namely that the drug causes only a 1% increase in the headache, from 1% off the drug to 2% on the drug, the absolute increase.
The problem is that drug companies sometimes report only relative results when it comes to making the drug look effective, but absolute results when referring to the side effects. It is important to distinguish whether the results are relative or absolute. When unclear, it is best to look at the raw data of number of patients rather than just the percentages.
For further information see Clinical Biostatistics and Epidemiology Made Ridiculously Simple, by A. Weaver and S. Goldberg, Medmaster.