204 STATISTICAL TREATMENTS 



served effects result from the experimental treatment, as opposed to pure 

 chance. 



Let us imagine an experiment as an example. We have observed that 

 in vitro a chemical compound C combines with one of the enzymes in- 

 volved in cellular respiration, but C is not a normal metabolic material. 

 We can form the hypothesis that if C is introduced to living cells it 

 should inhibit the normal respiration. The experiment involves a com- 

 parison of the activity of cells in the presence and in the absence of C. 

 Now, the normal cells will vary, and one sample of cells might be quite 

 different from another sample even if all the untreated cells are part of 

 the same population. Suppose that the cells treated with C respire some- 

 what more slowly than the average of normal cells. The difference might 

 result from the treatment, but it is also possible that the difference is the 

 result of chance, that is, that even a sample of untreated cells could give 

 a rate this much lower than average. A statistical analysis reveals the like- 

 lihood or probability that a difference this large or larger could result 

 from chance. 



If the mean and variance of the population are known, the test of 

 significance becomes relatively easy. The area under the normal curve, 

 or any portion of the total area, can be calculated. If we calculate the 

 area included between a point lo" l)elow the mean and the point lo- 

 above the mean, about 68 per cent of the area under the curve is in- 

 cluded. This means that 68 per cent of the variates lie between these 

 limits (see Fig. 15-2). Between —2cr and +2o-, about 95 per cent of the 

 cases are included, and 99+ per cent lie between ±3o-. Other calcula- 

 tions can be made as well. For example, we could find a pair of lines, 

 one on each side of the mean, that \A'Ould include 50 per cent of the 

 cases. 



Our experiment provided us with a figure for the rate of respiration 

 in cells treated with compound C. If we know the mean and variance of 

 the respiratory rates in normal cells, we can calculate the probability 

 that the observed results are different. In theory, it is impossible to know 

 the mean and variance of the population, but, if we have made measure- 

 ments on a large number of samples, we can have a very good estimate 

 of the parameters of the population. If the rate observed in treated cells 

 is 4.5or below the mean for untreated cells, then the probability that this 

 sample belongs to the population of untreated cells is very small indeed. 

 If the rate is only lo- below the population mean, it would be dangerous 

 to conclude that the treatment has had an effect because 32 per cent 



