Okayama University Scientific Achievement Repository

Onodera, Isenosuke

Eine Methode zur Isolierung der Ameisen-, Essig- und Milchs&auml;ure')

Kondō, Mantarō

Simplified Chinese

Untersuchung der Samen der in Japan vertretenen Brassica-Arten. Ein Beitrag zur genauen Feststellung der Sortenunterschiede.

Harukawa, Chukichi

Yagi, Nobumasa

&Uuml;ber die Lebensweise des Pfirsichtriebbohrers, Laspeyresia molesta Busck. I.

Miyake, Chiaki

The experimental eπor in field trials and the effect 
on this eηor of various methods of sampling. 
By 
Chiaki Miyake. (Nogaku-Tokugiosんi.)
1. Introductory remarks. 
The homogenous growth of crops on a field is impossible， since numerous 
factors can never act in exactly the same manner upon al individuals and， 
they are very complex， some of them being independent others reacting upon 
one another. For the same reason， the mean results of a series of experi-
ments does not always represent the truth. The magnitude of the experi-
mental error in field trials is variable owing to nature of crops， systems of 
their cultivation， irregularities of the soi1 and weather of the season， etc.; 
thereby its magnitude must be culculated by ordinary methods based upon 
the theory of least square， from results of series of these field trials themselves. 
Thus the magnitude is variable but， 1 believe， itis not difficult to de-
termine the general degree of irregularity from even a たw results of series 
of field trials. 
ln general， the value of an experiment depends upon the degree of 
confidence which can be attached for its result. So even the measure of this 
general degree， seems for us to be indespensable for agric1l1tural experimenters， 
as necessary to the interpretation of results of field trials， especialIy to the 
knowledge of the e佐cton this error of various methods of sampling. For 
a few examples of these questions in ]apal1 1 have worked the following 
measurements. 
11. The experimental eηor of field trials on barley. 
ln order to illustrate the magnitude of the experimental error in 
112 
field trials， I have measured the irregularity of yield on the barley which 
was usually cultivated in 1912 on the Experimental Farm of Imperial Col-
lege of Agriculture and Forestry at Morioka. Of course， the crop has been 
su吋ectedto no irregular treatment throughout the field. At the time of 
ripelling in J une， that日eldwas divided into 100 small unit plots of each are a 
Tsubo1l along the furrow. The barley which was growll on these small unit 
plots of a hundred numbers was harvested， air dried， threshed and then 
weighted up separately and carefully il same manner. 
From these results，21 I have obtaind the following numerals by ordinary 
method.31 
(A) Average yield of single ul1it plot.…..・H ・-…..・H ・.667 Momme4l 
(B) Avcrage deviation 01 the yield of unit plots. .・H ・.15.3%
(C) Standard deviation 01 the yield of single unit plot.…18.0% 
(D) Standard dcviatiol1 on the average yield. .…..・H ・. 1.8% 
Next， I have culculated the standard deviation of sllccessive combination 
plots， made up by adding the neighbouring plots together. The last stcp 
was to test the standard deviatioll of other combination plots which was 
made up by adding equi-distant scattered unit plots together. 
These culculating白gureswere represented in the Table 1. 
Table 1.
Size of p!ot.[St. dev. 01 new plot.[ Estimated st. dev. 
(in Tsubo) I (in percentage) I (in percentage) 
18.0 18.0 
3 II.O 10.5 
3 10目8 10.5 
5 9.6 8.1 
8.0 8. ( 
10 7-4 5・7
10 5.9 5・7
1.) Tsubo = 35掛 Sq.ft. 
Combination plot 
that 
(unit plot itself.) 
made up of sucesive 3 unit p)ots. 
" "" scattermg 3 " ". 
" "" suceSlVe 5 " 
" "" scattermg 5 " 
" "" suceSlve 10 " 
" "" scattermg 10 " 
2.) On the details se“Jour. of the sci. Agric. Society， No. 127， p. 20-29， 1913; Tokio 
]apan." 
3・)AIl cu)cu)ation on this a回目ferdto“An introduction to the theory of statistics byG. U. Yule." 
4・)Momrne = 0.1323 Ounce. 
113 
Above secured results enable us to settle fol1owing three important 
points. 
(a) The standard deviation decreases with the size of the plot， but the 
ve10city seems to be slackened gradual1y. 
(b) The standard deviation of “the scatteri暗 lyadding plot" is always 
smaller than that of “the successively adding plot"， under the 
equal area. 
( c)The theory of least square teaches us that the magnitude of the 
standard deviation varies with inverse square root of the measureing 
“weight" which may be represented by the area in this case. If 
the standard deviation of the unit plot (namely 18%) be divided 
by the square root of the area of combination plots， the quotient 
shall be the estimated standard deviation which is expressed in the 
third column of the Table 1， and which may be right theoretically， 
under the presumption as it is due simply to the error in random 
sampling. 
In comparing this estimated standard deviation with the real 
one in the second column of the Table 1， 1 find that the scattering 
addition method is more favourable than the successive addition me-
thod in point of sampling. 
m. E玄.perimenton the rice crop. 
In autum 1914， 1 carried out a measurement which on the same prin-
ciple as that in the last article， on the rice crop at the δhara Institute of 
Agriculture at Kurashiki near Okayama. 
The crop and field were ordinarily and uniformly treated so that the 
growth of the crop did not seem apparently very irregular， except a たw
square feet at two corners of the field. The rice crop was planted in regu・
lar shape at the rate of 42 stubbles per Tsubo. When the crop was ready 
for harvesting， 1 reaped along the row of it rectilineally; and whenever the 
reaped stubbks amounted 50 in number they were tied in a bundle. Thus， 
1 got 176 bundles by the time al crops in the field were harvested up. 
These bundles were air dried for a few days， threshed， cleaned and 
treated to that the unhulled gl叫nwas weighted up from the first bundle to 
the next and next separately. 
Figure 1 gives the frequency curve for the above secured results.1l 
E・)On the details se“Jour. of the sci. Agric. society， No. 1巧5ι，p即P.4ψ73一48匂9，191巧5;T。休kζd
Japan ". 
114 
Fig. I.
70 
、 ??， 、
?
? ? ?
?
?????。?』
?
?
?
?
150 2∞ 250 3∞ 
Weight of a Bundle (in Grarnrne). 
We may assume that no abnormal causes of variation are at work， 
and we may average our results with confidence. Furthermore， as the case 
of the barley， 1 calculated the average yields and those standard deviations 
on the unit plot and successive and scattering combination p[ots. 
Table I shows these results， and Fig. 11 their plotteo curves. 
Tab!c I. 
Size ofplot. Average yielcl. Mandard Estirnated st. dev. Combination plot deviation. 
(in Tsubo) (in Gramme) (in Percentage) (in Percenlage) that 
2090 10.3 10.3 (unit plot consisted frorn 50 stuhhles.) 
3 6257 6.4 6.0 made up of successive 3 uni t plots. 
3 6257 5-4 6.0 " " "scattering 3 " ". 
10436 5-4 4.6 " " "succeSSlve 5 " ". 
5 10436 4.7 4.6 " " "scattermg 5 " ". 
10 20879 4.0 3.3 " " "succeSSlve 10 " ". 
10 20879 2.9 3.3 " " "scatlering 10 " ". 
17 35495 2.9 2.5 " " "success¥ve 17 " 
17 35495 2.4 2.5 " " "scattering 17 " ". 
Fig. I. 
2 4 6 8 10 Ja 14 16 18 20 
15上 (Areaof a plot in Tsubo.) 
150 250 350 450 550 650 750 850 
Bundle number of a plot. 
Suces ive plot. 
Scatering plot. 
Estimated C:lse. 
This table furnishes the following conclusions， namely; 
a) the standard deviation decreases with the size of the plot; 
115 
b) the standard deviation of “the scattering addition plot" is always 
smaller than that of “the successive addition plot"， on an equal area; 
c) the scattering addition method is always more reasonable and favour-
able than the successive addition method in point of sampling. 
These points are the same as those of barley， except only that the 
standard deviation of the fonner was smaller than that of the latter in nu-
merical magnitude. 
IV. Interpretation of the me闘 urements.
It is to be remarked that， such high heterogenity， as that above men-
tioned， exists upon the yield of crops where the whole field has been uni-
formly treated. Since such heterogenous yield of crops may be expected， 
we have some considerations upon field experimental works and upon the 
interpretation of their results. 
116 
Indeed， we can not conclude from a given experiment that factor A is 
more e佐ctivethan factor B， unless the differences found are greater than 
thos¥! which might be expected from deviation in ・theproductive capacity of 
the plot upon which they were planted. 
As for the magnitude of these experimental errors， several authors 
have tried to obtain some measure， already. Among them， A. D. HaU 
and T. B. WOOd1l report that the probable error on a plot of various crops 
was not far from 土5% of the yield of the plot whose area was from I/2 to 
I/80th. of acre. From the foregoing results， the prob:lble error on a plot 
(area of I/50th. of acre) of barley I may culculated21 as about土3・3per cent， 
and of rice crop as about土I.8per cent. Now comparing these figures with 
those in England， itis obvious that the latter is greater than the former， 
namely about twice. 1 think， the origin of it is the more laborious intensive 
cultivation in our country than in England. 
Ultimately there remains an important question that how referd to the 
probable error in the planning of field experiments and in the interpretation of 
their results. In regard to this question Halla nd Wood (loc. cit.) have fully 
eXplained it in their works， so here 1 shall make no further statement. 
V. On the sampling method of estimation of the total yield 
of rice crop in a :fi.eld. 
Jn some cases， itshall be required to estimate the total yield of crop 
in a field by means of pa凶alharvesting. In ]apan such sampling methods 
are called Tsubogari or Tszt'Jogari-ho， and frequently they take place in 
rice fieJds. However the Tsubogari with such purpose are objected to 
by many agriculturists， since it brings a great error in its results， even 
although it be carried out s】dllfllllyand carefully. But in fact， itleaves ln-
known what magnitude of error attaches to the usual method， and what 
system is preferable in these various methods. To solve these qu巴stion，1 
carried out the following experiments. 
Sω託金le.fields. 
In the Experimental Farm of the δhara Institute of Agriculture， for 
sample fields， I chose six rice白elds，the area of each of them being within 
one Tan3) or 50・ Eachsample field was treated in the most u5ual way， and 
E・)See “F目ldtrials and their interpretation，" by A. D. Hall， and E. J. Russel， and “The 
interpretation of experimental results，" by T. B. Wood. On the supplement (No・7)to the J ourn. 
Board of Agr. Great Britain. Nov. 191. 
2.) 1(50 acre = 24 Tsubo. 
7・4¥/10
Probable eror on the ba巾y=土0・6745xマ万一=土3.3
4・0ν10
Probable eror on the rice crop =土0.6745x一てつ-ー =土1.8
v 24 
3・)Tan is ahout th. of acre. 
117 
therin 42 stubbles of the plant in each Tsubo were planted regularly in 
square shapes. In each of the six field， 1 tried partial harvesting by foIIow-
ing白vemethods in same ways. 
Sω況がringmetltods. 
1st method. Usual method in ]apan. 
Let us select the most moderately grown part， at sight， in the field; 
and from this part take up 50 stubbles in a square shape. Then we may 
consider the yield of these 50 stubbles of rice plant to be representative of 
the whole area. Since the moderately grown part is not limited to one 
place only， so from another two similarly grown parts 1 reaped up 50 stub. 
bles each. The first 1 wiI cal1 IA plot， the second IB and the third IC. 
Furthermore the plot ID was made t1p by getting together the results 
of plots IA， IB and rC. 
2nd method. 
The most representatively grown part in the 自己ldwas selected， and it 
was limited to 10 Tsubo marked with two rop~s ， each 12 and 30 feet long， 
to make a rectangle. And then， from those along the two oposite shorter 
sides of that reci:angle and its middlc line， 30 ordinary stubbles of rke 
plants were harvested together. 
3rd method. Scattering method. 
By this mcthod， from every ten scattered places that appear moderately 
grown ten ordinary stubbles are cut together， and then the total numbers 
of sample stubbles amount to one hundred. 
4th method. Diagonal method. 
In the first place， let us find out the principal four corners in the fidd， 
and stretch to ropes b巴tweeneach two opposite corners diagonally. Next 
1 reaped the nearest stubble to the diagonal rope， in each row of plants， 
and 1 gathered them in two diagonal groups. Any one of these groups 1 
called the 4A， and the otlzer the 4B and the sum of these two the 4C. 
5th method. Dr. Inagaki's method. 
By this method， we first estimate roughly the total number of stubbles 
in the field and assume the estimated numbers divided by a hundred， then 
we may know the stubble number N in each of hundred divisions. 
11 the next place， counting the total number of plants rectIinearly from 
the first row to the second and so on， we come at number N; then we 
take aり onestubble from the first division， as the first reaped stubble. The 
first reaped stubble being so determined the stubble which fals on the Nth 
from the first shall be cut off as the s巴cond.
In the same way， the third， the fouth......and ultimately to about the 
hundi'edth stubble should be harvested scattered at equal distance. 
Result. 
In these ways， 1 had sixty plots as a whole and these results may be 
mention as follows: 
118 
Table II. 
Number of the Yield of grain. The yielrl. 
Sample lield. Sampling method. cuttmg (in Momme) (in Percentage) Stubbles. 
E4 IA. 50 643 106.6 
E4 IB. 50 685 13.6 
E4 IC. 50 666 110.5 
E4 ID. 150 1994 110.3 
E4 2. 30 462 127・7
E4 3・ 100 1182 98.0 
E4 4A. 117 1328 94.0 
E4 4B. 110 1194 90.0 
E4 4C. 227 2522 92.1 
E4 92 1063 95.8 
E5 IA. 50 513 94・3
E5 IB. 50 543 9.8 
E5 IC. 50 556 102.2 
E5 ID. 150 1612 98.7 
E5 2. 30 323 98.9 
E5 3. 100 1113 102.3 
E5 4A. 57 598 96.4 
E5 4B. 45 510 104.1 
E5 4C. 102 1108 9.8 
E5 96 1046 100.1 
E6 IA. 50 541 102.4 
E6 IB. 50 547 103.6 
E6 IC. 50 461 87.2 
E6 ID. 150 1549 97.8 
E6 2. 30 314 99.1 
E6 3. 100 1091 103.3 
E6 4A. 牛J 454 97.7 
E6 4B. 40 426 100.8 
E6 4C. 84 880 99.2 
E6 87 930 101.2 
119 
Number of the Yield of grain. The yield. Sample五eld. Sampling method. cuting 
Stubles. (in Momme) (in Percentage) 
W2 IA. 50 633 99.8 
W2 IB. 50 662 104.4 
W2 IC. 50 692 109.1 
W2 ID. 150 1987 104・4
W2 2. 30 462 121.4 
W2 3. 100 1191 93.9 
W2 4A. 61 768 99.3 
. W2 4B . 60 781 102.6 
W2 4C. 121 1549 I∞.9 
1九12 5. 105 1232 92.5 
W3 IA. 50 447 97.3 
W3 IB. 50 430 93.6 
W3 IC. 50 426 92-7 
W3 ID. 150 1303 94.5 
W3 2. 30 222 80.5 
W3 3. 100 936 101.8 
W3 4A. 59 583 107.5 
W3 4B. 58 549 103.0 
W3 4C. 117 II32 105.3 
もN'3 102 993 105・9
W5 IA. 50 451 102.03 
W5 lB. 50 438 99.1 
W5 IC. 50 438 99・I
W5 lD. 150 1327 100.1 
W5 2. 30 252 95.0 
W5 3. 100 877 99.2 
W5 4A. 75 660 99・5
W5 4B. 26 222 96.6 
W5 4C. 101 882 98.8 
W5 94 862 103.7 
From this table 1 grouped separately the similar plots of sampling， and 
culculate their average yields and standard errors of each method. 
Table IV shows these results. 
120 
Table IV. 
Sampling method. Average yield in I S山山roron Standard eror on percentage. one plot. the average. 
lA 100.4 士 3・95 土1.61
IB 102.3 土 6.14 土2.51
IC 100.0 土 8.30 土3・39
lD 101.0 土 5.10 土2.08
2 103.8 土16.05 土6.55
3 99.7 土 3.19 土1.30
。4A 99.1 土 4.20 土1.72
4B 99.5 土 4.89 土2.00
4C 99.3 土 3.87 土I.58
5 99・9 土 4・55 + 1.86 
From this table we can summarise the following facts. 
(1) The yields of those methods in which moderately grown parts were 
taken， as the first and second method， always se巴m to us to show 
too much yield. This may be explained from the fact that what 
we recognize， at a glance， to be moderate or representative in a 
group， isfrequently better or larger than the true mean. 
We experimenters must be more careful in this point! 
(2) Th巴 near巴stresulting plot to the average yield (namely 100%) is 
that of the first method， but the farthest is that of the second. How-
ever the value of the method should not be determined by results of 
the yield only， rather it is due to the error attached to it. From 
this point of view， itwill be better to prefer the third or fourth， 
and next the fifth method. The second method seems to be a bad 
one. 
(3) The absoh巾 magnitudeof errors attached to the various methods 
are as foregoing， but for the degree of accuracy there must be taken 
into account the number of plants， taken as a sample. 
The number of cut stubbles， as in table II shown， w巴red旧ト
rent according to those methods and errors of methods may vary 
with inverse square root of the nurnber of those sarnpled plants. 
Accordingly， next， 1 will test how these standard errors are affect-
ed by the number of plants sampled， that is to say， which method 
was more precisely related to the number20f plants sampled. Now 
let 11 be the totaI sampled number of any method and a be its real 
standard error. And suppose 300 stubbles were takcn equaIly in 
each method， so the estimated standard errorωshall be culculated 
through the equation， namcly 
ω=σX • / _n_. 
'v 300 
Table V shows these culculated results. 
121 
Table V. 
n σ 自』
Sampling method. 
Tolal sampled number. Real standerd eror. Estimated standerderror. 
rA 3∞ 土1.61 土r.61
IB 300 :!:2.51 土2.51
IC 300 :!:3・39 :!: 3.39 
ID 900 :!: 2.08 :!:3.60 
2 180 土6.55 :!: 5.07 
3 600 土1.30 土1.84
4A 413 土1.72 土2.01
4B 339 土2.00 土2.13
4C 752 土1.58 土2.50
576 :!: 1.86 土2.58
From this table we may conclude that， the most preferable method is 
the 3rd or the 4th. The first method is worse than the 3rd or the 4th， since 
magnitudes of the standard error varied with the plot as IA， IB and IC; 
and the 日仕his too troublesome for practical purposes. 
VI. Sammary. 
(1) To test the yield hetcroge凶yof crop in a field 1 tried dividing the 
neld into small plots and secured the deviation of yields on these small 
1>lots. According to these results， the probable deviation of the single plot 
whose area was one-fiftieth of an acre， was about土2per cent in terms of 
the yield. 
(2) lt is to be remarked that the result of a field experiment， which takes 
place in such area per plot， has about :! 2 per cent as the experunental error. 
(3) ln order to estimate the total yield of a field crop by means of partial 
narvesting， there should be held various methods of sampling. 
ln those， however， we may take the diagonal or the scattering method， 
favourably. 
(4) The single plot of any field experiment， inorder that the experimental 
.error does not increase should possess a tolerably large area. 
And further， every experimental plot has not single， simplYi but it is 
<livided into several small plots and these small plots should be distributed 
{)ver the field scatteringly. 


The experimental error in field trials and the effect on this error of various methods of sampling.

Kondo, M.

Untersuchungen &uuml;ber das Volumgewicht des enth&uuml;lsten Reiskornes (Gemmai.)

Osugi, S.

Uetsuki, T.

Untersuchungen &uuml;ber die Azidit&auml;t des Sauer-Mineralboden.I.

Onodera, I.

Untersuchungen &uuml;ber die Besch&auml;digung der Pflanzen durch S&auml;uren und &uuml;ber die Reizwirkungen der S&auml;uren auf Pflanzen.

Okayama University Hospital

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Eine Methode zur Isolierung der Ameisen-, Essig- und Milchsäure')

Untersuchung der Samen der in Japan vertretenen Brassica-Arten. Ein Beitrag zur genauen Feststellung der Sortenunterschiede.

Über die Lebensweise des Pfirsichtriebbohrers, Laspeyresia molesta Busck. I.

The experimental error in field trials and the effect on this error of various methods of sampling.

Untersuchungen über das Volumgewicht des enthülsten Reiskornes (Gemmai.)

Untersuchungen über die Azidität des Sauer-Mineralboden.I.

Untersuchungen über die Beschädigung der Pflanzen durch Säuren und über die Reizwirkungen der Säuren auf Pflanzen.

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