28 SCIENTIST 



have in our hands a new drug which is said to be helpful 

 in reducing the mortality rate. Since very few drugs cure 

 all patients and many patients get well anyway, how can 

 we be sure that the drug helps? What we do is to set up 

 two different groups of patients, say 50 in each, selected 

 alternately as the patients come into the hospital. The drug 

 is given to one group but not to the other. Ten patients 

 die in the "control" group and eight in the one that re- 

 ceived the drug. Offhand it looks as though the drug has 

 a shghtly favorable effect. At this point we ask ourselves 

 what the probabihty is that the reduction in deaths oc- 

 curred by chance. In other words, how likely is it that the 

 reduction could be accounted for as the result of the normal 

 variation in the severity of the disease and of unidentified 

 differences in the way the two groups were selected? Our 

 equations tell us that indeed the difference can be explained 

 in this way and that the drug is in all probabihty ineffective. 



If only three people died in the treated group, our 

 calculation shows that this could have happened only 4 

 in 100 times as a result of chance so the odds are 96 to 

 4 that the drug "really works." The probabilities that dif- 

 ferent scientists find convincing vary somewhat but it is now 

 fairly standard practice to "believe in" a relationship that 

 might have been due to chance as often as 5 times out of 

 100. 



The converse of this proposition is that most scientists 

 are fully prepared to tolerate the probabihty that what 

 they learn about the past will in one case out of 20 be a 

 poor guide to what will happen in the future. 



I am only too clearly aware that this discussion of the 

 roots of scientific knowledge is not easy to follow and may 

 strike many readers as irrelevant and boring. It seemed to 

 me necessary to provide at least a skeleton outline, how- 

 ever, since there is still much misunderstanding about 



