438 GROWTH OF PLANTS 



measurements made on these samples. A second method is to take great 

 pains to secure homogeneous material by selecting from a large supply a 

 relatively homogeneous portion and discarding the remainder. At the same 

 time much effort may also be expended in the control and regulation of 

 the environment, thus providing uniform conditions in the relatively large 

 spaces often required. Finally, in the last two decades there has been a 

 rapid development in experimental planning and statistical methods. The 

 essence of this approach lies in the division of the experimental material 

 into parts, each relatively homogeneous within itself. As a consequence, 

 the parts now differ substantially among themselves. In the simplest 

 form each part constitutes a complete experiment, there being as many 

 replications as there are parts. It has been found that the marked differ- 

 ences which exist between the parts do not contribute to the experimental 

 error. Subject to appropriate randomization of the comparisons within 

 the parts, statistical techniques exist w'hich provide for a valid estimate 

 of the precision attained. The precision attained by this technique is 

 substantially that which would have been possible if all the material had 

 been as homogeneous as the material within the parts into which the 

 initially heterogeneous supply was divided. This procedure, and more or 

 less complex modifications of it, has been very widely employed in recent 

 years, and it is evident that some understanding of these developments 

 in experimental planning is becoming of increasing importance in many 

 fields of work. 



The papers mentioned in this section, while usually concerned with a 

 specific inquuy, also constitute examples of the application of experimental 

 design and statistical analysis. A field trial ^"^ of fiber pots which could 

 be buried and allowed to disintegrate and possibly give the seedling an 

 added advantage over the usual practice was arranged on a somewhat 

 complex plan. In all, there were 40 different combinations of pot type, 

 pot size, soil, and variety of tomato. Based upon early field technique, 

 considerable difficulties would be expected from employing so many 

 treatments. The use of a split-plot Latin Square arrangement in the field 

 made possible the detection of an effect of pot diameter on the yield of 

 tomatoes which was of the order of 6 per cent. The plants in the most 

 successful type of pot showed a large gain over the plants grown in 

 flats. 



From one point of view, a field trial may be regarded as a sampling 

 process. The field is divided into plots which may be thought of as samples 

 of the field and which it is hoped wall be closely similar except as treatments 

 are deliberately applied. In consequence the same statistical processes are 

 valid in appraising a sampling technique and they provide an approach 

 to determine the number of samples needed for a specified precision. 

 Youden and Mehlich ^°^ tested the efficiency of different spacings in soil 

 sampling and found that, for surveying large areas, intervals as small as 

 10 or even 100 feet between replicate samples were inefficient. For a given 



