EXPERIMENTAL DESIGN 215 



paying much attention to the randomization of samples. The same people 

 have had litde need to analyze their data statistically. The reason, of 

 course, is that the differences between populations (a population of con- 

 trols and a population of experimentally-treated organisms) are very 

 large compared to sampling errors and the variance of the populations. 

 This difference is probably no accident because many of these experi- 

 ments were very carefully thought out and steps were taken to make 

 sure that if a difference existed it would be a large one. 



Some simple designs 



The simplest of all experimental designs is the one most commonly 

 used in the experimental laboratory, a simple comparison of two groups 

 of measurements. The following experiment can be used as an example, 

 and it can be seen that the same reasoning could be applied to many 

 different experiments. 



We wish to know whether maleic hydrazide has any effect on the 

 respiration of yeast cells. We set up six manometers with a yeast sus- 

 pension and then add maleic hydrazide to one set of three and an equal 

 concentration of a neutral salt to the other three. We measure the oxy- 

 gen consumption at five minute intervals for thirty minutes. We now 

 have samples from two populations. Each population has a mean (wi 

 and m2) and a variance (cti^ and 0-2^). The means obtained in the three 

 manometers provide a good estimate of the population mean. The only 

 estimate we have of the population variance is the variance of the sample 

 s^. The application of the t test tells us whether the difference between 

 the means is significant and at what level of significance. 



Paired Design: A similar experiment could be performed as a class 

 exercise. Imagine seven groups of students, each performing the experi- 

 ments described above. For simplicity, let each group of students use 

 only one pair of manometers instead of three. The data could be analyzed 

 by lumping together all the figures for untreated cells and all those for 

 cells treated with maleic hydrazide. Whether each group uses one pair 

 of manometers or three, the variance is likely to be somewhat larger 

 than before because of individual differences in technique, in reading 

 manometers, and in timing the readings. It is possible that each group 

 would find a significant difference, but the combined data would indicate 

 no statistical significance. In this case it would be wise to match the re- 

 sults in pairs, with the experimental and control manometers of any one 



