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Show 2 Utah Academy of Sciences, Arts and Letters [Vol. XV, be distributed within the blocks at random to insure a valid test of significance. In this respect, the experiment would be well designed. In putting the experiment into operation under this design, the experi menter would immediately be faced with the problem as to the kind of last irrigation to give those plots which are being studied with particular refer ence to the type of first irrigation. Of course, one might select the normal type of last irrigation for all Oof the first irrigation treatment plots, but in doing so he would make an unwarranted assumption to the effect that the type of last irrigation is entirely unrelated to the type of first irrigation as regards the quality of peas harvested. Likewise, of those plots which are being studied with respect to the effect of period of last irrigation some decision must be made as to the type of first irrigation the plots are' to re ceive. The experimenter might propose to irrigate them all uniformly with the so-called normal first irrigation. In doing so he necessarily assumes that the type of first irrigation is unrelated to the effect of the last irrigation on pea quality. In other words, this type of experimental design offers no oppor tunity to study the interacting effects between the various factors studied in the experiment. In setting up the experiment on the basis of a factional design each of the first irrigation treatments would be studied .in combination with each of the last irrigation treatments. For example, there would be three plots given an early first irrigation, one of which would be given the very early, one the early and one the normal last irrigation. Similarly, there would be three plots given the normal and three the late first irrigation with one of each group of three receiving one of the variations of last irrigation. Nine plots would be required, therefore, for the nine possible combination treatments. If these nine combination treatments were included in one block, it is obvious that there would be no direct replication of any combination treat ment, but it may be readily observed that anyone single treatment is rep licated three times. The early first irrigation would be applied to three plots, and the normal first irrigation would be applied to three plots, and although the three plots receiving the early first irrigation are treated differently with respect to last irrigation, yet as a group they are similar with respect to first irrigation and may be compared directly with the three plots receiving the normal first irrigation. Thus, it may be observed that when the various treatments are considered in groups of three that each treatment is replicated three times. This type of replication has been referred to by Fisher (1) as indirect or hidden replication. Advantages of Factorial Design The first advantage of a factorial design is greater efficiency. In the of the single-factor experiment where 6 treatments were to be studied, 36 plots would be required for 6 replications of each treatment. .In the fa torial experiment, however, where 9 combination treatments are involved, III order to get the total of 6 replications, and hence the same precision offered in the single-factor design, owing to the 3 hidden replicates in each complete set only 2 complete sets of direct replications will be necessary, and the total number of plots will be 18 instead of 36. Thus, with the factorial des_ign, the same precision is obtained with only half as many plots. It IS ObVIOUS that this means efficiency and economy in the use of land, labor and all other things involved in the operation of the experiment. The second advantage of the factorial experiment is greater compre In addition to furnishing information concerning the e!Iects hensiveness. of the two single factors, time of first and last irrigation, the epenmet under the factorial design will furnish information concerning' the rune p.OSSl ble interactions, and this with the same precision applicable to the smgle case ''If ,," --: ... . . 6< ".:''' .... .. ..... o-•• - .... . . iIIt -"t. a" . .' . .. .. " . . " ... flo ,,'*' .. ). •• ( " 1)1" e ." '\ a c '!. \ '" .. \. '" l. t. e> c t l. \. fJ, .. I. 'l. C.. c to • tilt. c ",'" '", .1< '\ t:. l. 'c 1:1",'- (: «. t 1,. c ..... , . t: : ... :., |
