THE MEASUREMENT OF RESULTS 23 



and, where such plots are distributed throughout a series of 

 experimental plots, it is sometimes found advisable, instead of 

 taking the average of the results from them, to draw a smoothed 

 curve through these results, and to compare those of the 

 experimental plots with readings taken at corresponding points 

 of this curve. 



The proper expression of results in horticultural experiments 

 presents several special difficulties. It is well, of course, to repre- 

 sent the values in the check plots as 100, and then the differences 

 exhibited in the other plots will be percentage differences ; but 

 ordinary percentages may be quite misleading. Owing to the 

 smallness of the number of trees in each plot, or to differences in 

 behaviour with different varieties, etc., the results of similar 

 experiments often show considerable variation, and may even 

 be in opposite directions, and to take a mean of positive and 

 negative percentage differences is open to error : thus, if we have 

 double the normal growth in one case, and half the normal growth 

 in another, it is clear that, on the average, the trees show no diver- 

 gence from the normal ; but, expressed as percentages, there is an 

 increase of 100 per cent, on the normal ( + 100) in the first case, 

 and a decrease of 50 per cent. ( 50) in the second, the mean of 

 the two being -f 25. To obviate this source of error, which is 

 serious only when large percentage differences have to be dealt 

 with, what may conveniently be termed " proportionate percent- 

 ages " have sometimes been used; these are obtained by always 

 dividing the smaller quantity into the larger, and then putting 

 the sign + or to the result, according as the experimental plot 

 has given larger or smaller values than the check plot; thus, 

 in the above instance we get 



Proportionate percentage. 

 Check. Expt. Total value. Difference. 



A ... IOO 2OO TOO (2OO -f- IQO) = 2OO + IOO 



B . loo 50 loo (100 H- 50) = 200 - loo 



Mean o 



The only objection to this method of dealing with results is that 

 negative values greater than 100 per cent, are sometimes ob- 

 tained, which have the appearance of being impossible. 



Though the above is an exaggerated instance of discrepancy, 

 it is in the nature of horticultural experiments that the results in 

 some cases may be in the opposite direction to those in the 

 majority. It must be remembered, however, that such discre- 

 pancies do not invalidate the conclusion drawn from the means 

 of the results, any more than the measurement of the distance of 



