216 EXPERIMENTAL DESIGN 



experiment compared to each other. The statistical treatment becomes 

 shghtly more complex because there is reason to expect some interaction 

 between pairs of manometers. One group of students might pipette the 

 yeast cells generously, for example, so all their results would be higher 

 than average. 



It is necessary to account for this covariance, as the interaction is 

 called, but this can be done by a shortened method. For the sake of 

 analysis we hypothesize that the two population means are equal, that 

 maleic hydrazide has no effect. In the manometers of each of the seven 

 groups there is a difference between manometer 1 (without maleic 

 hydrazide) and manometer 2 (with maleic hydrazide). The seven dif- 

 ferences make up a sample from a possible population of differences. Ac- 

 cording to the hypothesis, the mean of these differences is zero. Table 

 16-1 shows some numerical results which will make the analysis easier 

 to follow. 



Table 16-1. Results of a Paired Experiment 



The seven differences have a mean of 5.1 as opposed to a hypothetical 

 mean difference of zero. We can apply the t test to find out if the ob- 

 served difference could occur by chance. In order to compute i, we must 

 find the standard error of the mean (s/\/w). The standard deviation is 

 calculated from the table as 



='V^?^=- 



The difference between the two means xi and X2 is the same as the mean 

 difference Xd, and 



• . = ^=.4.7 



s/vw 



