INSTITUTE OF STATISTTCS
)
A STUDY OF WEATHER FACTORS AFFECTING COTTON YIIlLDS
w.
1
D. Foster
J
'1
1
j
Insti tute of Statistics
Mimeograph Series #37
For Limited Distribution
.<J.
TA'BLE OF CONTENTS
...
Introduction
1
Statement of objectives
2
Description of Ootton-Weather experiment
2
Preliminary statistical tests
4
Selection of predictors
5
Statistical adjustment of data
a
Regression approach
10
Empirical approach
14
Distribution of weather variables
20
Oode for weather data punched on IBM cards
20
21
-
Appendix of Tables and Figures
Table
Table
Table
Table
Table
Table
Table
Table
Table
•
,
f
1:
2:
3:
4:
5::
6:
7s
8:
9:
Figure 1:
Figure 2:
Figure 31
Figure 4&
Figure' 5:
Figure 61
Figure 7:
Figure 8:
Planting plan
Mean yields of cotton
Analyses of variance on yield by stations and by years
Homogeneity tests for error variances
.Analysis of variance combining five stations and years
Regression models, coefficients, tests of significance
'Weather variables, yields and predicted yields
Oomparison of correlations of gro\'1th periods and yield
Code for punch card data
**
*
Graphs computod from Regression 1
Graphs computed from Rogression 2
Graphs cow~uted from Regression 3
Scoring sheet for empirical method
Scatter diagrams for 10-19 weeks
Prediction curve for 10-19 weeks
Scattor diagrams for 6-16 weeks
Prediction curve for 6-16 weeks
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q"
R
FINAL REPORT TO \1EM.'IIER BUREAU
A STUDY OF WEATHER FACTORS AFFECTING COTTOIT YIELDS
.
1/
W~lter
D. Foster
INTRODUCTIOl~
r
The relationship of crop and weather would be studied fex more offectively
if data taken from sources which vary in both time and space could be analysed
by statistical
material.
techni~es
designed for most efficient combination of such
Unfortunately, this statistical problem is. a most complex one.
While
it is not the purpose of this paper to search for such an analysis, the latest
approaches to this problem will bo used in analyzing cotton",,",,1I'eather data which
were obtained from five experiment stations throughout the South and Southwest
over a period of throe years.
The advantages of using multiple sources are at once apparent.
range of woo.thor variables is afforded.
conditions is obtained.
A more representative sample of fiold
The amount of data desired can be
much shorter longth of Ume.
A greater
ac~ired
over a
"'ith careful measurements taken from a uniform
experimental design, practically all variation in yield except that portion due
to weather nne!. soil can be removed and the residual variation. the far greatest
proportion of which is ascribable to weather, is available for statistical
,
treatment_
This method is inherontly more accurate because it is a truer
picture of plant response to climatic variation under actual conditionse
1I Research
Assistant, Department of Sta.tistics, N. C. State College,. August 1940
-2-
OBJEOTIVES
1. To apply the latest statistical methods of combining data taken from
diverse sourcos so that extraneous variations involved in general pooling are
excluded.
2.
To use amended regression technique and to search for new techniques which
will use information already known about the cotton plant in order to refine and
make more accurate the mathematical expressions of the relation between cotton
and weather.
3.
To predict cotton yields from weather cata.
A.
To conpare predictors.
i. :By regress ion.
ii. :By empirical nethods.
13.
To compare tho various periods in gro\rJ'th of plant!t
i.
For independent weather variables.
il. For all weather variables jointly.
From this portion of the investigation,
ll-tl
attempt is made to d.evise an
accurate forecast which will be t1vailable beforo the end. of the growing season.
•
40
To investigate the distribution of weather factors used in this study.
5.
To devise .a punch card code for tho no·st efficient method of recording
the weathor data to be collected from the Soil Weather project.
11
DESCRIPTION OF COTTON EXPERIMENT
In a. complex design repeated i<:lontical1y at five stations throughout the
South and Southwest; four varieties of cotton were grown at two levols of f01"1,lizer treatment.
At each station. there were
~10
plnntine dates per year for a
series of three consecutive yoars.
jJ This experiment is known as the Cotton-Weathor project. Sponsored by the
~
Agricultural Markoting Service.
As will be shown by the preliminar,y tests, thero aro sufficiently largo yield
differences between planting dates and betwoen stations to consider them as
influencod by different woathor conditions.
In this way,
ind~endont
observations
are made available as though the experiment had been continued over a 30 year period
t
~
at one location, except for soil differences.
The five stations cooperating in this experiment nre as follo\'IS:
I
South Carolina.;
Griffin, Goorgia:
Stonoville, Mississippi;
Florance,
Marianna, Arkansas;
and Latlfton, OklaJ.lOma. From geography it is obvious that a large range of climatic
factors wore available during the growing season.
At these stations, the four
varieties of cotton grown were Oklahoma Triunpb,Dixie Triunph, Shafter Ac81a, and
Stonoville, all of which are varieties of
~crican
upland short staple cotton.
Thus far we have controlled five major effects influencing cotton yields;
variety, date of planting, fertilizor treatment, station and year.
added a sixth, blocks.
To those is
The field plan, Table I, wns roplicl1tecl t\-l1co at ovary
station to give an estimate of experimental error.
Furthormore, to prevent carry-
over effects from yoez to year such as soil depletion from affocting yield, fresh,
completely different plots of ground were usod each year.
In this
w~.
a continuity
correlation wns avoided, though possibly at the expense of a slightly larger soil
variation.
However, it was bolieved by the experinentors that this source of
additional variation was negligible.
Of the many measurements tclten during the
to weather will be enumeratod.
~)crioent,
only those pertaining
Tonperatures recorded daily includo the maximum,
ninimum,' and nean. Precipitation
\"iaS
oeasured both by the ''leather :Bureau standard
eight inch rain gauge and by a recording gauge.
fron a standnrd whi to atnometer.
3S" were neasured by tensiometers,
Evaporntion rates wore obtained
Soil noisture nt four levels; Sn, 12".
24",
and
duplicated at each station for greater stability
of index.
Other weathorphenoMena were indicated in tho form of ronarks by the
observers, such as ttwindy~. "heavy rainlJ • trpartly cloudytr. etc.
The administration of the field work was centralized in ordor to
t
M~~O
the
procedure as unif.om as possiblo with every possible care taken to in.troduce
:
no variation other than that which is actually encountered in field conditions.
The advantage of working "'ith data. from an experimental arrangenent such as this
can be seen at once in tho homogeneity of conditions in each sub-class in which
the noasurenents were taken.
Although the soils at the various stations are known
to be dissimilar, the fertility of each was raised to a
of a dressing optinum to each location.
nnxi~l
by the application
By this Means, the effect of tho soil
differences is minimizod except for the water content, an inclex of which is available.
Thus tho contribution of tho soil factor is believod to be small compared
to the weather effects and it is
u.~der
this
assw~tion
that the relation of weather
and cotton yield will bo estimated in this study.
No mention has been rnaf.e thus far of the insect factor which principally
is the boll weevil.
The ordinary precautions of dusting the crop early in the
season against boll weevil
was
followed throughout the three years_ For the first
two years, 1939 and 1940, there was no noticeable effect due to insocts.
Howevor,
in the thircl year, the infestation was particularly heavy at Florence with varying
degrees of attack at other stations.
An estimate of the anount of cotton lost
due to boll weevil was obtained by snop1inG, hence sane adjustment for these
fib~es
can be mnde.
PRELIMINARY STATISTICAL TESTS ON DATA
As we have seen, the data consists of means of yield of seed cotton in pounds
per acre classified. by variety, treatr.lent,. date, year. station and block. A table
- 5 i
of these means is sho~ in Table 2 where it can be seen how wide17 these figures
vary.
In order to investigate the JIlaGAitude of these differences, the first
preliminary test was the ana17sis of variance on 7ield
station for a given year.
fo~
variation within a
For exampl"e, at Stoneville in 1939, the main effects
tested were blocks, varieties, date and treatment with the first order interactions
that are of primary interest, i.e., those showing variation in time.
summarizes these testse
I
Table 3
The customar,y significance levels of 5% and 1% are indi-
cated in deference to the precedonce in the literature, although it is felt that
the significanoe levels in weather and crop weather data should be more on the
order of 1/2% and 1/1CYf, due to the ske\'Tod distributions often encountered in this
ty'pQ of data.
The assumption that differont weather condi tiona were encountered in t he two
dates of planting at a single station was woll substantia.ted according to Table 3.
Furthermoro, looking at the F value for blocks, it is soen that for the most part
thore wore no differences attributable to soil variations within stations.
Nor
can the variety by date interaction be considered significant, that is, to say.
the variotios reaoted similarly among themselves to a given planting date.
Further information obtained :from Table 3 shows that in all but two instances
a respectably small ooefficient of variation existed. indicating the homogeneity
of
re~onse
per classification.
The most important in:formation obtained from Table 3 is the general magnitUde
of the error moan square, which is a quantity arising from random variation between
replicationst such as block by treatment, block: by variety. block by variety by
date. etc.
It 1s obVious from tho range of these error terms that pooling among
stations without furthor investigation would be
~ardous.
As an index, :Bartlett's
test for homogeneity of variancos woo applied to these errors by years.
~
Results
of this test arc shown in Table 4 where it is seen that the probabili ti os of
ilU.S.
Bartlett, Su:pplcmont te tho Journal of t he Royal Statisti cal Society, 4:137
(1937) •
11
obtaining such \'lidely varying figures in random sampling from the same population
.
~
are very, very small.
Hence we are warned against casual pooling of errors among
stations within years for any exact test.
The next preliminary test is concerned with investigating the magnitude of
the differences between stations and between years.
.
•
Again, our hypothesis that
different weathor conditions oxisted at the five stations was SUbstantiated by
the significant between stations mean squaro, (Table 5).
As oxpected, the main effects account for the groat bulk of variation with
station, date, and years which carry the climatic factor, appearing considerably
larger than tho other contributors.
As a matter of fact, tho items in
Tabl~&:~
!
.
which El.re due purely to weather and soil comprise 05% of the total variation, i.e.
ignoring treatment and variety.
S3LECTION OF PREDICTORS
Of the various weather elements measured during the experiment, three
.~eem
most comprehensive and indicative of the total influences oxerted by weather during
the growing season.
tion.
These three are soil moisture, mean temperature, and. evapora-
Precipitation was not used since it is obvious that soil moisturo readings
are a much better indication of the moisture available to the plant. Relative
humidity, a function of tel!lJ?erature ane. amount of moisture in the air, was measured
.~
.
at only three points during the
included in an
ind~~
d~
of evaporation.
and appears to offer nothing that is not
Evaporation results from the action and inter-
action of solar radiation, air temperature, wind velocity, and humidity and thus
•
presents in a single figure the influence of a number of atmospheric elements
. which if taken as individual predictors would make regression extremely cumbersomo
and. empirical techniques too bulky.
11
Miller, E. C., 1931.
1J
Further, evaporation has been found
Plant Physiology.
McGraw-o-Hill :Book Company
to be the
-7best single measure of transpiration:
a first
~roximation
to the effect of
transpiration on yield is hereby afforded.
Since soil moisturo was moasured at four levols of depth, it was felt that
•
some way of conbining these roadihgs into one would expedite handling of the data
without serious loss of information.
11
Brown
found that in general the tap root
of the cotton plant extended to 2 1/2 feet while the laterals roached that dopth
and sometimes went deepor.
Although tho maximum c1epth of the roots is about four
I
•
6
feet, the bulk of the roots
seome~
to lie
be~feen
one and two feat.
Fron this
<'
~
it fo11O\'ls that the noisture supply at 12" nnd 24ft is the nost inportnnt ",hila
that of Sit and 36" might be classed together ..
Hence a weighted average of these
.
, .*
deDths was
COliQ.)llt,ed.
0,0
SM5
+ 2SV~2 + 2SM24 + SM36
SM = - - .__._ . -----..
-----av
6
The figure, SMav,was used throughout this stllily
os the,
soil moisture index.
.
It is worthwhile montioning the character of the instrument which was used to
measure soil moisture.
The tensiometer consists of a porous cup located at a
desired depth and connected to the surface oy an air-tight tube.
The cup is filled
with water and tho resulting tension caused oy a thirstjr soil endeavoring to IIdrinlc"
the wa.ter from the cup is neasurecl by mercury column.
the
~reater
t:>
Thus, tho (trier the soil,
tho tension while a saturated soil exerts no tension on the
y cun.
~
Although this instrQuent has been very popular, it has two
..
.'
dr~backs.
First,
its range extends over one atmosphere of tension, while the tension range fran
s aturat eo. soil to an average wilting point is several timos as "groat.
hand, plant growth beyond the range of the tensioneter
11 :Brown,
E.!
H. B., 1938.
Baver, L.
D.,
1940.
Cotton.
ap~roaches
On the other
a 1init rather
J.lcGrnw-E:ill :Book COT:1PatlY
Soil Plvsics.
John \'TileY ancl Sons :Book Co. p. 207.
I
-8quickly.
The second disadvantago is an inherent hysteresis.
For a given amount
of soil noisture, the instrument docs not give tho same renQ.ing when moisturo is
increasing as it docs when noisturo is decreasing, although this differenco is
probably much loss than the sampling variation encountered in field conditions.
Despite these ninor liMitations, the tensiometer
1n~ox
is believed to offer a
roli~blo
of available soil water.
Tho original weather records wore replete with tenpcrature Teadings,offering
daily
nrorinun. nininun,
and Menn.
Whilo it was a tomptation to c..-.ctonC':. tho study
to include investigation of all three, all indications fron the literature and
the cotton experts in the N. C. Experiment Station advised narrowing the field to
the moon temperature, a fD.ctor which conbines the values of both maximun 8>nd
mininUr.1 roadings into ono, though withquostionable efficacy.
STATISTICAL .ADJUSTMENT OF DATA
Conforming for a while to precedence, tho unit of time was chosen as the week
. and the daily weather records wore transformed into weoklyneans, measured from
the date of planting.
This maneuver erased some of the difficulty of data missing
due to instrunent failure, etc.
In comparing tho problom at hand, that of explaining tho variation in cotton
yields
b~'meons
from data
tcl~en
of weather factors, to the problem of estimation of a true yield
fron sources which vary in either tine or space, it is soon that
each is a segment of a
p~rent ~roblcn.
vfhen the data arc collected fron different
.
- ~
centers in tho samo ycar p Cochran assumed a constant response with heterogeneous
variances.
(A constant response with honogonoous vari~~ces/is handled by the
faniliar Dnalysis of variance without acljustment.)
11
His solution shows the rolative
Cochran, W. G. t 1937. Problon Arising in the Annlysis of a Series Of Similar
Exporimonts. Sup. to Jour. of Ro~.Sto.t.Soc. Vol. IV 31.
- 9-
efficiency of woighting ench mean inversely as the observed variance conpnred to
the true variance for vnrying degrees of freedom at onch cent or, provided the
number of cen"iel'E!, k, ::.s :1nfinitoly largo.
Attacking tho
problem, rorter
~O
Mel f~r varying
cOlllJ!utecl the relnt·l.vD GfflC'iencies for stops of k fron 2 to
degrees
0:
11
SaDe
f:rooc'lo!:1 a.t 8C'::h. center.
A furi;ho:':' cnr.rqlic".tion to this problem is added when tho responrws at the
several
the
C911tG:i:S
arc <'!:i.i'f8:ront as well as the variances.
fnvos~lgaticm hoa.1ed
prog~ano
.?J
Th1 s is the nature of
by eaChI'M at presont in a Navy sponsorecl research
Thus far. 1 t has beon loarnocl that tho most effic1.ont opl;"1.up.to of the
true yio11 i('l
t~1e
uIlv!oigh't:ecl nonn in tho case \1r..on tho Vl1,rinnC0
reSl)onses rOJ:1r:.i:1B tho s'ane fron center to center.
0-:: the different
In the altornat;,yo case, when
the varianco of the different responses varies from conteI' to conteI' a system of
partial or seni-weights is the nost effective.
It is planned that the ncixt phase
of the investigation will cover the estimation of true yiold when data are available
not only from different locations but in different years.
It is here tr.at tho t\'J'O problems begin to overlaJ!'
W'hile the crop-weathor
question attenpts to eX]?lain the variation as r.lainly clue to
of the truo yiold is acconplishod after all variation
to tho crop itself has beon removed.
unweighted
accor~inG
~:"eather,
oxc~pt
the estimation
that inherently due
The figures in this cotton stuB.y are best
to the foregoing for use in regression.
To reduce to a
minimum all vari~tion except that due weather, only tho yielcs from tho £toneviilo
\.
2]
variety of CQtto:a wore selected for regression, Stoneville 'being a
l,)ol)ular~
high yielding variety of cotton grown widely throughout the cotton bolt.
Further,
only yiolds from plants given tho high level of fertilizer were considored.
By
this means, the soil differences between stations nre Fdninized sinco each station
iJ
Porter, S. H., 1948. The Relativo Accuracy of \'1eighting Inversely as the
Estimated Variance. Master's Thesis. N. C. State College.
Progress Report, 1948, to Office of Naval Resonrch.
»J
- 10applied as the high lev61 of
fertilize~ that dressing considered optimum
by the
agronomists for the local soil.
;
RJl'4RES SIOU
There are many possiblo ways regression could be applied to this problem.
In order to handle as many predictors as possible, it is first nocessary to assume
a linear relationship betwoen the climatic elements and final yield.
This assucp-
tion is by no means a new one in crop-weather research and seems justified only when
a slight improvement in the analysis by uso of higher dogrees is c07!1J?ared to the
enormous work required in obtaining it.
For instance, in this study there are not
a sufficient number of observations to allow a least squnres fit for second or
higher degreo.
A second assumption is more critical.
It is necessary to sUl:>pose
that the effect of a weather factor at any given period is indepondent of the
effect at another period during the grm"ing season.
Perhaps one of the bes t
\'lDtVS
to investigate the validity of this hypothesis would be to compute various
serial correlations and if they appear to be more than trivial, examine them in
an effort to fine!. a form of regression or statistical technique which would be
more effective in explaining tho crop-weather relntionship.
However. it is believed
that this assumption involves no great error provided tho weather variables do not
deviate from their expected values too greatly.
A second great saving in the number of constants to bo fitted in regression
was effeoted
l!
by R. A. Fisher
to multiple regression.
when he introduoed the use of orthogonal polynomials
This method has been usee!. considerably and descriptions
of the process of fitting nrc abundant.
y
:By the usc of Fisher's method, tho
if
Fisher, R. A. 1924. The Influence of Rainfall on the Yield of \fueat at Rothamsted.
Roy. Soc. Phil. Trans. Sere D. 213, 89-142.
W Davis,
F. E. a."ld Pal1esen, J .E. 1940. Effects of the amount and clistribution of
rainfall and evaporation during the growing season on yields of corn rotd spring
wheat. Jour, Agr. Res. 80:1-33.
Hopkins, J. W. 1935. Weather and 'wheat yield in western Canada. Canada Jour.
Res. ].2&308-334.
'
Davis, F. E. and Harrell, G. D•• 1942. Relation of Weather and its Distribution
to Corn Yields. U.S.D.A. Tech. Bull. a08.
INSTITUTE OF STATfSTJCS
- 11 -
change in yield due to a'unit of the weather factor at a given weck can be computed.
thus sl10wingthe critical stages with regard to a given woather factor during tho
growing season.
While Fisher's Model represents a gront improvoment in the technique for
studying tho crop""'Weather rolationship, it still l'..ssumos thE'.t only ono weather
factor is to bo stuc1.ieC1. at one tine, or if several are usoel, that each is inclopon-
JJ
dent of tho offect of the other.
Hendricks and SCholl
have amended Fishe.r t s
approach by sotting UJ? a model which stuftios the effect of wep-.ther olenents simulselJar~tely.
tnlloously as well as
For oxar:1!)le, in thoir l?aper tOr.JI>orature, procipi-
tatlon, and the joint effect of temperature and precipitetion
~xe
used to account
for variation in corn yield•
. In this study,
are c0r:lIJuted.
re5~ossions
mocelcd both from Fisher and
Hendr~cks~~d Scholl
In a gross wtW, n cOI':1j?nrison of tho t\'lO is provided, although the
nain purpose is to study the effoctiveness of various predictors.
For instance, the
first regression patterned after Fisher has as independont Dreaictors soil moisture.
evaporation and Eean tempern.ture.
second, regression
*
Lot us call this function regrossion rIF 1.
The
2, follows Hendricks and Scholl and includes evaporation,
soil moisture, and the joint effoct of ovaporation and soil moisture.
Regression
:#= 3 expresses yield as a function of !loan tom,pcrqture, soil moisturo, and tho
joint effect of ter:rperature and soil moisture •.
Tho models of those regressions are shO\m in Table 6.
It is noii proposed in
this paper to offer a complete description of tho development of those
te~iniques'
since full details can oe obtained from HendriCks' and SOholl's article if
desired.
,The data for those regressions, as explained before, consist of yield of seed
cotton in Dounds por aero, while the weather olononts have boon averaged ovor
if
Hendricks. \If. A. and Scholl, J. C. 1943. Techniquos in l'ieoouring Joint Relationships. Tech. Bull. 74. Agr. ~~. Sta., N. C. State College.
II'
- 12-
weekly periods. Using the dato of planting.. as the zero or reference point, the
weeks were nunbered 1, 2, 3 etc.
Since there was considerable variation in the
length of records kept by each station cooperating in this
eA~erirnent,
it was
necossar,y to soloct those weeks affording the longest consecutive series when nIl
five stations were considered at once.
For instance, if station A shows weather
records fron weeks 1 to 6 and sta.tion B shows weather recorcl.s froll 1IIeeks 2 to 7,
then weeks 2 to 6 are available for stue1.y for both stations.
In this nanner. nine
consecutive weeks starting with the eighth week after planting a.nd ending with
the l6tbweek wore available.
In terns of the cotton plant, this overall period
includes half of the squaring period, blooning and the setting of young bolls_
The
periods in this stUdy wore based on the actual phenological dates and have
been defined in terns of weeks after planting as follows:
squaring, 6-9 yeeks;
blooning, 10-12 weeks, sotting young bolls, 13-16 weeks, opening of bolls, 17-19
weeks.
These weeks correspond aloost
y
]J
exact~
to those described in the literature.
C. B. Doyle and Brown have indicated that the period of blooming is the most
critical in the life of the plant, while the water requirenents for squaring and
setting bolls are high.
A further stop in handling the data was to compensnte for the boll weevil
dM!l€e.
Though the eA"Porinont as a whole wns relnt!vely free fron this pest,
certain of the yiold figures ore low because of it.
The rate of infestation was
estinated by taking randon s8n11les of the cotton and counting tho nunbor of locks
por boll dostroyed by the weevil.
This rate was expressed as a percontage and
the adjusted yield would be that figure which when decroasod by the rnte of
~estation
jJ Doyle.
Y
becones tho actual recorded yield.
C. :B. 1941.
:Brown, II.
n.,
For instance, at Sto.tion A tho
Yearbook of .Agriculturel Clmate and MDne pp. 348-363.
Loc cit.
- 13 -
rate of infestation is 25% and its rocordodyiolc1. is 1200 lbs./acre.
Then the
adjusted is 1200/.75 or 1600 lbs./acro.Despito the apparent logic of this nathod.
in sone cases it fails to adjust the yield to a credible figure.
for tho lack of a bettor cothod, the above procedure was followed.
Nevortheless.
Later in this
paper. a second nethod of adJustnent will be doscribed though it is not applicable
to regression.
A conparison of the three regressions is best seen in tabular and graphic
fom.
In Table 6 in the appondix where the nodels, rogression coefficients, tests
of significanco, and the nultiple correlation coefficients ore given, it is seon
that the joint relationship of soil nobture lUld evaporation was easily the nost
eRa = .537).
effectivo of tho threo nodels with a correlation of .73,
Further
inspection shows that regression"" 1 is fitted with nine constants instoad of ton,
while regression"" 3 has only five.
In regression
*
1,
predictors because it was so closoly correlated to A.
o
0.
0
\-las
deleted fron the
When such a condition is
present, solution for the regression coefficients is possible by the abbreviated
Doolittle nethod of matrix invorsion only when an oxtrenely largo nunber of digits
is carried throughout the conputation.
Since eight digits were carried in these
calculations, it was deemed norc fCl'..sible to drop the predictor than to attor:rpt
the operation with 12 or nore digits.
*
This problen was compounded in regression
3 where there were so many dependencies in the matrix of normal equations that
its virtual rank was reduced to five.
.
.
From these observations, it imnadiately
predictor is tho least
i~ortant
~ppears
that mean tenperature as a
of the three despite the slight evidence to the
contrary offered by the t-test for the regression coeffioients in regression
*1
in which tho three temporature coefficients present a questionab1Y best showing.
The qu.aclratic terns in regression f
a without
probabilities of being obtained by chance.
,
exception showed the snallest
The fact that the coefficionts for
."
- 14-
ova~orntion
nppoar to be better ostinatod than those for either soil noisture
or the joint effect of evaporation or soil noisture is presented without connent.
Tho first partial derivative of yield in regression # 2, with respect to
evaporation when evaluated for t and arbitrary values of soil noisturc offors a
fMily of curves which shows the effect of
0.
unit of evaporation for c1ifforont
water tension values en the final yiold of Stonevillo cotton at different woeks
in the
~rowing
season.
These are shown in Figura
=I/:
2.
Likewiso, the partial
with respect to soil Moisture leads to another fanily of curves. also shown in
FiRUre
*
2.
Tho labels' and orientation of tho curves n~ be confusing unless one
remenbers that soil water is neasured as tension with the result that a high tension
indicates a low anount of soil water.
The other units are direct; evaporation,
for instance, is low for a low index.
There is another precaution to observe.
Since only a quadratic was fitted to the data, it is best not to extrapelnte these
curvos.
As a natter of fo£t, even near tho borders of the chart, sono of the
curves tond toward tho incredible.
Sioilur Charts
~)Deor
for tho othor two regressions, although it is innediately
apparent that with such largo oonfidenco linits as indicated by the t-tests for the
ooefficients, tho true location and orientation of the curves could easily bo
entiroly different.
SCORn lmHOD
-•
Thus far, it has been seen that rogression has beon ha.nperod by restrictive
assunptions and narc sovorely by the linited nunbor of constants that could be
fitted.
These penalitios nre tho price paid for the advantnges of tests of
significance, the availability of confidence lioits, estination of the contribution
of oach woather factor for a given week on tho final yield and following the wellkno~nl
path of previous investigation.
As was indicated in the prclininary report,
-15a difforent
c~pronch.not
nocessarily now, was intended whoso results were to
be judged by conporison_with the regressions rather
t~an
by statistical tests
of significance.
The basic ideo. in this onpirical 1nvestigc.tionis to !Jut on
0.
quantitative
basis tho lore and experience of those who have worked nany years with cotton.
By assenbling tho nany obsorvations of cotton yielQ$ as affected by various typos
. of weather, a little e~erinento.tion in assigninG values to weather factors
according as they aro dosirable or
undesir~blc
several pE'.tent MVtmtages over regression.
lends to
0.
score nothod which has
The prinary o.c".vantfl.go is tho cOn:Pleto
freodon in the simultaneous use of as many ,weather factors as clesirecl.
regression studies. only two variables could bo
lk~dled
by tho joint relationship
The floxibility innate in this approach offers a choice of
techniquo.
cor.r,parisons and investigations 1;lith
a
In our
nininun of calculation.
The problon of
adjusting for bollwGovil infestation is solved nuch nore offoctively.
is considorably sinplified. both in construction ana in use as
nru~
0.
Conputation
prediction nothod.
The inprovement (>nd expansion of this or sinilar methods londs considerable proniso
towards
:JJ
0.
narc accurate definition of tho
relationship which C. B.
cotton-wo~thcr
Doyle has concluded is not likely through tho usual investigo.tions of l)reciI)i tll.tion
and tcr.tpero.turee
11
Y
Y
Fron Doyle. Ermin. McNnnnra
on~
!I
associo.tes, Hawkins
§./
and associatos. Kraner
and,otherSt generalities about the belioved optinun clinatic roquirenents of the
if
~
Doyle, O. 3. Loc cit.
13ro\'lnt II. :9. Loc cit.
y
McNan.1ra, II. 0., Hooton, D. R., and Porter. D. D. 1940. Difforontial Growth
Ratos in Cotton Varieties and their Responsos to Soasonal Conditions at Greenville,'
Texas. Teoh. Dull. 710 USDA.
sJ Hmo/kins, R. S.t Matlock, R. L•• and Robnrt, C. 1933. Physiological Factors
Affecting tho Fruiting of Ootton with Spocial Reference to 13011 Shedding. Tech. Bull.
46 Univ. of Arizona At,,-iculturo EJq1. Sta.
§/ KrD.T.1or,P. S. 1944. Soil ~10isture in Rolntion to Plant Growth. :Botanical Review
10; 505-556.
- 16cotton plant for eaCh of the periods wore obtained.
period of blooning, the water
very moist soil is bost.
requirenen~
For instance. durine the
is believed to be at a maxinum, i.e., a
Evaporation or transpiration is believed to have little
effect except when the soil is dry.
Tor:r,porature is thoUght to have little effect.
On tho other hand. a dry soil causes excessive shedding of blossons.
The
opti~un
conditions wore set up in a qualitative sonse for this study
purposely without regard, to the weovil nnd the weather conditions for its spread.
Although it is knovTll that the woevil thrives one1 spreads rapidly when soil water
is abundant, relative hunidity high, and tenperature warn, these facts were omitted
from consideration, since the presence of these connitions by no neans guarantees
the presence of the weevil.
A correction for the weevil is shown later.
The construction ofa chart to
assi5~
quantitativa values to certain combina-
tions of weather factors was achioved first by dividing the range of each woather
,e
variable into suitable blocks.
o to
60.
The range of soil moisture tension was found to be
It woo convenient to define 12 blocks,
run..l1iIl{~
0-5, 5-10, 10-15, etc.,
with the convention that a reading of 10 would fall in the 10-15 block.
great deal of experinentation, the nost effective size of block for
was found to be ten degrees
an~
for
eva~orntion
units to 65, and over 65 for tho last
Figure
11=
b1ocl~.
After a
te[~eraturo
ton unit blocks up to 50. then 15
These coordinntes can be seen in
4.
The second step in the construction wns to dofine fivo basic cll',ssifications
into which the various weather conbinations "rould fall.
Those classifications,
excellent, good. fair, poor, and very poor nrc used to charactorize the effect of
weather on final yield according to the writers on this SUbject.
of excellent confers a hie)l score while very
10'1
~oor
The classification
on tho other oxtrone confers a
score; a plant with a hiGh tot!'.l score is eX]?ectocl. to have a high yield.
the assignnont of values to the classifications is soen to become a Droblon in
inteI1Jolation.
Thus
- 17-
Once the nunber of blocks was decicted, the assignment of values to these
blocks was undertaken.
In Figure
vll.lues was taken as 1 to 216.
*
4 where there aro 216 blocks, the range of
f
Then the five classifications were allottecl a
ntmber of blocks to correspond approxiMately with a nornal distribution (although
no use is OMe of this arbitrary (lecision.)
Of tho 216 blocks, "excellent" and
"very poor" euch receivod. 22, lleood" Dnd "poor n eooh received 52, and "fair"
received 60. Because of the iopossibility of ranking every block, that is, to
say of two adjacent blocks near optioUT.1 that one is better than tho other,. oach
classification was further graded into three approxinatoly equal sets, donated
by different colors and each block of tho sane color in the sane aajor classification assigned tho niddlo value of its o"m range.
classification was allotted 22 blocks.
For instance, the "excellent ll
These were further
gr~~ed
colored orange, seven blocks green and soven blocks brmm.
blocks would end with 195.
into eight blocks
Countinp' fran 216, 22
If the orange blocks are to be assigned the highest
values because they represent the best erowing conditions for a given period,
then they would occupy the values 216 down through 209.
Using the middle value of
this range, all tho orange blocks in the "excellent" classification receive the
value 212.
taken.)
(vr.hen a cl10ico between two niddle values occurs, the evon nunber was
Sinilarly, th.o Groen blocks ,..,ere evaluated at 205, the l)rown at 190.
Tho rest of tho schene can be soen on tho na.rgin of Figure
was follmfed for onch of the four
and opening of bolls.
porio~st
~f
4.
This arrnngenent
squariUS, blooning, setting
YOQ~e
bolls,
Since thore was considerable lomray in arranging tho ordor
of the weather conditions fron best to worst, considerable exporinontation was
involvod before the nost successful plan was selected.
of the last three l)lans con bo seen in Table O.
The relative effectiveness
-18.AdJustnent for boll weovil daoage becooes extremely sirtple.
.An estimate of
the rate of infestation is required and can bo obtained by sOl1pling the crop and
reporting, as was done in the Cotton-lleather project, the ratio of
to ,total locks as a percentage.
dDOaged
loeks
.After tho scores for tho weeks have been add()d,
the total score is adjusted by nultiplying it by the percentage of good locks.
Thus. if the total score is 1500 and the rate of infestation is
1.3P.
then the
adjusted score becol!1es 1600 x 00% or 1320. Should other measurable conditions
arise. further adjustnent is nado in a sir:tilar canner.
As an eXD.t1:plo, the steps in obtaining a score will 'be described in detail.
At Florence, South Carolina for the noma! planting in 1939. the soil noisturo
reading for the 10th week was U.l whilo the noan tonperature was 04.3 and .the
evaporation reading
WttS
45.7.
Reforring to Figure 4: and using the chart for
blooning, since the 19th week is dofinotl to belong to blooning, the corroct square
is found in the botton section in
It good"
and is colored green.
thiQ squnre is 167 according to the code on the norgin.
Il'he vOolue for
Likewise, the score for
the 11th week: was found to be 198. Repetition of this process through the growing
season gives a series of scores wbose tota.l is 14"..0.
Since tbere was no weevil
damage reported, no adjustment of this scoro is necessary.
Plotting this score
against the recorded yield of 2366 lbs./acre for tho Stonevillo variety, we obta.in
a point,. labelled for reference a.s 1. (soo Legend, Table 7).
rest of the points comprises a scatter
...
diagr~,
Figure
SA.
Tho plot of the
Curiosity inmedia.toly
required the a.pplication of the scoring nethod to the yields of the other throe
varieties with weeks 10-19 tnken as the scoring interval.
These rosults are e.lso
shown in Figure 6, where it is Oopparont that tho two high yielding varieties,
Oklahoma. TriUE1ph and Stonoville. have alnost identical scatters \'rhilo tbo two
lowor yielding variotios, Acala Mel DixioTriUtlpb are very similar.
A cubio was
- 19 fittod by len.st squ.o.res to the averaged yields of Ol<lohona and Stoneville nnd
nodificd near the end points where the characteristics of a polynonial fit are
net true to actual trend.
~e
lewer nean yields are satisfied with a linear fit.
Thus, FiGUre 6 becones a prediction chart based on a scorinG interval of 10-19
weaks for varieties of cotton sinilar to
t~~es
studied here_
llowever, it is desirod to offer a forecasting tool which is available earlier
in the season.
Dy takinG
~lvant~~e
of the flexibility of the scoring nothod t it
is easy to obtain a direct conparison of any conbination of periods of growth and
to learn if a scoring nethod which torninates before the tine of harvest is any
less accurate and if so, by how nuch.
the four
peri~ds
and
3y totaling tho scores ever any throe of
a linear fit, the corresponding correlations were
ass~ing
cODputed and conpared in Table
o.
Thon, if tho onission of given period reduces
the correlation by nore than any other onission, it is concluded that the period
~
onitted has the greatest effect on yield and is the nost critical fran the standpoint of clinatic factors.
~y
a simple
ra~ng
test, Table 0, the blooning period
was easily the nost iMportant to final yield, followed by the periods of
bolls, opening and squaring.
According to scoring
~othod
settin~
# 1 which is the one
adopted in this study, thero is vory little difference whethor the scoring
is taken as 6-16 \"{ecks or 10-19 weeks..
intol~al
Than by observing the scatter cUagraos in
Figure # 7 anet 0, where the some schooe has been followed as described above for
Figuro 5 and 6, a forecasting
di~0ron
is present which makes a forecast available
three weeks before the first of the cotton is
roa~~
to be ginned.
Apparontly it is
a Characteristic of the scoring dingran which consistently suggests a cubic fit
for the 10-19 week scoring interval and a linear fit for the 6-16 week interval.
In order to obtain sufficient yield data to evaluate all of theso periods
e
when nine weeks of data were availv.ble for regression. a snall Mount of
extrapolation of certain woather values was necessary.
In hearly all of those
-20 extrapolations, concomitant moasurements existed in sufficient detnil to offord
a very intelligont euess.
As a further justification, the range of values in the
in1iviiual blocks is largo onough to absorb considerable variation from the true
value.
of an
..
Even a gross error wouli probably result in no more tlk'Ul the substitution
~~acent
block for tho correct one, with an undotectnble result in the final
correlo.tion.
While the scoring nethod presented is for from elegant, it has certainly
held its own in conporison with the other approaches hero.
A systonntic experi-
mentation in the construction of these or similar charts by agronomic exports
would undoubtedly lead to nore accurate predictions than offered here.
FREQ,mlNCY DISTRInUTION OF WEATE:Ea F.A.ClIIaB.S
In the search for a stable pattern of frequencies of occurronco, the three
weather factors, evaporation, soil moisturo and mean temperature were eaCh divided
into small classes of five, three and two units respectively suCh that there were
~fuether
at least 20 classes in the range of values for ea.ch factor.
the values
enumera.ted were daily or weekly, the histograms were obviously inconsistent both
for .individual stations and for pooled observations, although it was noted that
mean temperature tended to
ShO~l
the least skewness of the three.· Sinco theso
frequency patterns are best investigated when extensivo do.to. are available; the
.,
effort in this direction was PUXDosely curtailed.
CODE FOR PUNCI! <lARDS
A prelimina1"'J code is given in Table 9 for recording on 113M punch carets the
large quantitios of weather data which are being accumulatod by tho Southern
Cooporativo Group.
At the prosent time, this codo is being revised by its authort
.,
- 21J~ T.· \Takcloy, to inprovo the index of tcnporo.turo D.l1c1. sunlight \'lhile other
changes are probable.
SUMMARY
Measurements of soil moisture.
eoployed to
stuc~
evaporation~
and monn temperature have been
the relationship of weather to final yield of cotton in an
identical experiment conducted in 1939. 1940 and 1941 at five experimental stations
Widely scatterod
throUt~hout
the cotton belt.
The preliminary tests have shown that differences in yields botwoen stations
and bet\1een years were by no !!leans attributable to chance variation.
These'tests
also proved that tho differences betweon a normal and a late planting elate at the
same location were statistically sibnificant.
lienee, from the control of other
variables in the experiJ!1ent, it is argued that the differences in yield are due
to weather and soil, other miscellaneous factors contributing practically nothing.
Further, the variation causee'. by soil differences is minimized by the al'plicnti.on
of fertilizer optimum for each location, leaving weather as the only major
influence affecting final yield.
The clamage from boll weevil \'las !!leasured and. tho
yields were adjusted accordingly.
Linear regression in the form developed by R. A. Fishor lmel amended. by l·r. A.
Hendricks was
ap~lied
to these data in preference to any other type of regression.
since it is felt that these models offer tho latest ana most comprehonsive
..
approach.
Three regressions, each with ton constants to bo fitted, were
using various conbinations of woather variablos.
co~)utcdt
Tho greatest amount of variation
was explainod by using evaporation. soil moisture and tho Joint effect of evaporation and soil noisture.
A second combination,
toaporature taken independontly. was less
ev~)orationt
offective~
soil noisturo and nean
while the third, soil noisturo,
meM tonporature and the joint effect of soil moisture anel moan terrporature \'{as
-~-
found to contain fivo internol ~ependoncies which reduced the nunber of paroootors
to five.
It was concluded that mean temperature was the least effective of the
three weather factors, eithor singly
o~
in combination.
Applied to cotton datuJ tho regressions used in this study were felt to be
insufficient, sinco the data pemitted n maxinun of only ten predictors.
Cotton
is 1010wn to be extremely sensitive to wonthor~ a fact which roquires a nore complete
description of tho clinntic factors than apparontly afforded by the
studies presented here.
r~gression
In an effort to r.mnufncture a dovice which approximated
the joint effect of all three weather variables simultaneously, it was necessary
to abandon regression and endure the loss of the associated tests of si{,n£icance.
Drawing upon the experience of cotton
experts~
a score method was devised
whiCh allotted a high score for the combination of weather factors considered eood
and a low score for undesirable weather.
In terms of final results, the score
method was considerably more accurate in predicting cotton yields than any of the
regressions. nue to the fleXibility of the score method, a forecast of final
yield could be made available at the end of the 16th week from planting without
loss of accuracy.
Purely as a prodiction tool, the score method or similar
schemes appear to be considerably nore effective than regression and certainly fur
easier to construct.
Tho penalties for these advantages are the inability to
place confidence limits on estimates and the loss of tests of significance_
An attempt was nade to find a recurring pattern in distribution of the
weather elements moasured.
Nothing definite was discovered in several methods of
constructing frequency diagrams_
Further, should any distribution have been
offered, its validity would be open to serious question duo to tho relative
paucity of observations.
e
Table 1:
Sanplc
l?lantint"~
• •
e
••
e
PIon Fron Cotton Weather Exporinent
Plots 103 feet, 0 l/Z inches - 1/30 nere. 4-row plots, lfidth of row - 3 feet, 6 inches
SUbblock:
0109
a
:3ordor Cotton
b
V4 D1 TZ
0209
VzDZTl
Dixie Triunph lZ
Late Planting Date
Hif"..h Fortilizer
Itow Fertilizer
OZ10
VI DI T2
0110
V3DI TZ
Okla. Triunph Z9 - 44
~toneville 2:B
Nornal Planting Date
lNornal Plantin{~ Date
Low Fertilizer
[,ow Fertilizer
kllll
V4DZT1
OZll
V3DZT2
.Acala (Shafter)
Stoneville 4a
~ate Planting Date
Late Planting Date
IIUch Fertilizor
Low Fertilizor
021Z
V4 DzTZ
VaD2T2
l;J 0112
Acala
(Shaftor)
!Dixie Triunph 12
~
l;j Late Planting Date
Late PlantiIl{; Date
~ Low Fertilizer
LO\-1 Fertilizer
0113
V1D2T2
0213
VID2~
Okla. Triumph 29Okla. Triunph 29 - 44
Late PlantiIl[; Date
Late Planting Date
Hir-:ch Fertilizer
!Low Fertilizer
0214
V4D].Tl
0114
VzD1Tl
kala (Shafter)
Din e TriUlll'ph 12
Noma! Planting Date
Norna! Planting Date
Hl,g:h Fertilizer
Bip'..h Fertilizer
OZ15
V3D1Tl
0115
V3D2Tl
Stoneville 2.D
Stonevillo 2J3
Nornal Planting Date
Late Planting Date
IIicll Fertilizer
Hicll Fertilizer
OZ16
V2DIT2
0116
V DlT
Dixie TriumPh 12
Okla. Tri unph 2~ Nornal Planting Date
Nomal P100ting Date
Low Fertilizer
·IIiah Ferti1i~er
EORDER
r.t~.tN l3J.JOOK I
~nla (Shci'ter)
~omal Planting Date
i-
!
!4
j
f
...~...
,
~
-It
~
c
d
0309
V4Dl TZ
.!cala (Shafter)
Ncrnal Planting Date
Low Fertilizer
0310
V~ZTl
Stoneville 213
~atc Planting Date
[IiF..h Fertilizer
0311
V1DZT2
Okla. TriUI:lph 29 - 44
Late Planting Date
LOl'l 1J'ertilizer
0312
V3D1T2
Stoneville 2B
~iornal Planting Dato
!Low Fertilizer
0313
V2D2 T2
lDixi e TriUI:lph 12
Late PlantinR Date
!'Low Fertilizer
0314
VIDITl
Okla. Triuoph 29 -44
~Toronl Planting Date
Iil?h Fertilizer
P315
V4D2Tl
Acala (Shafter)
!Late Planting Date
fli.d1 Fertilizer
0316
VzD1Tl
Pixie Tritlr.lph 12
lornal Planting Date
!il"h Fertilizer
OOTTON
MAIU
··\1
i
0409
V4 DZT2
Acala (Shafter)
Late Planting Date
lLow Fertilizer
0410
V :> T
~ala (Shafter) 4 1 1
~omal Plonting D~te
IIIil?h Fertilizer
0411
V1D
Okla. Triunph 29 Nornal Planting Dato
Low Fertilizer
0412
V3D2T2
Stonevillo 2B
Late Pllint:1:I'l.g Date
ILmof Fertilizer
0413
V;lJ T
;Dixie TriUDph 12 1 2
Nomol Planting Date
Low Fertilizer
0414
V3D1Tl
Stoneville 2D
Nornal Planting Date
ni~ Fertilizer
VlDtp
0415
Okla. Triurlph 29 Late Planting Date
~Iip."h Fertilizer
0416
V;aD2Tl
[Dixie Triunph 12
Lato PlantiI4:~ Dato
llip."h Fertilizer
:I3LOOK II
1a
:4l
l:.:J
~
~
~
I
fl>-
•
Table 2:
Tabla of Mean Yields ofsf7ed Cotton (lbs./acre) for Planting Dates,
Varieties and Treatment 1 for all Stations and Years.
Sto.tion :Treat-:
& Year :ment
Normal P1ant'f' Dato:.
VI
V2
3
V4
SoC. '39: 1
2052
2374
2Q54
2366
.. 2 :: 1572
1641 1630
1540
Meon • 1012 2000
2002. 1197
,
.
•
•
140: 1
... 1560 1722 1716 1540
2
964
1410 1575 1455
: Mean • 1262
1566 1646 1502
·
0
0
..
0
0
0
·
·
0
.
14H
·
•
..•
0-
e-
o
1
2
• 1040
0-
e-
: Mean 0•
"
0
Ga.
139:
:
1
2
601
064
·•• 1137
.•
0
1002
..• Moan : 1070
•
140: 1
• 1239
2
1030
•• Moon •• 1130
••
1100
'41: 1
.... 2 . 097
.; Mean : 1030
0-
·
•
0
·
·
·
.
579
506 •
502
012
505
690
914
703
040
1110
1134
1122
1230
1233
1232
1146
1110
1120
1203
975
1009
1227
1572
1400
1330
1000
1173
914720
021
745
572
650
962
730
050
: 2206
1
.. 2 : 1090
• Mean : 2052
•
••
140: 1
: 2130
• 2
:. 1974
: Mean : 2052
0
·
..•
.
0
0
"iJ
.•
0
0
·••
.•
•
.
0
·
:
0
o
..
Late ~lMti, Date
VI
2
3
V4
2192
2250
2170 1952
1726 1519
1524
1570
1007 1001 1940 1736
·
·
...
··•·
·•
··.
·..••
2227
21442106
2515
2327
2421
1716
1514
1615
1020
1944
1002
2344
2302
2323
1410
15L10
1479
.
·
2172
2137
2154
2370
2161
2270
2294
2100
2237
..·
·
..
..••
I,taon
00-
2176
1591
1004
..
..
0
·
0
1150
1120
1139
1430
1116
1277
1611
1533
1572
1450
1347
1402
255
267
261
110
100
109
172
105
130
194
62
120
765
097
031
663
043
753
049
792
020
550
591
1122
1056
1009
1041
1003
1062
002
050
070
904
699
042
922
706
054
476
450
642
459
467
550
514
420
471
1650
1754
1706
1424
1640
1536
1077
1502
1690
1002
1175
1120
1301
1240
1314
1127
1177
1152
1492
1423
1450
616
720
660
1701
1603
1652
1299
1103
1201
0041232
1050
1630
1391
1510
0
0
..
..•
1526
1315
1420
0
6~1:
·
·•
·•
•
•
0
0
0-
·.•
0
·.
·
·•
·
512
396
454
940
946
943
1130
1036
1003
794
633
714
0
0-
141: 1
2476
•• 1901
-: 2
: MeaJl : 2220
.•
..
0
0
0
0
0
0-
0
Miss.'39:
•
0
0
0
0
•
0
•.
1030
1745
1793
1538
15.1,2
.
1540
..•
172<,1
0
••
••
••
1054~
i7n9
Troo.tment 1 is "high fortilizo.t1on" for the station in question. Treo.tnen'b;:> :ts
"low fertilization lt for tho station in question. Tho·~e levels are cone1stent e:C::l0p'b
for Lawton. Oklahoma, where (lOll between rows) and (20" betweon rm"s) were 'hIle
treatnents.
.1,;,
-]-
Table 2: (Oontinued)
Station :Treat-; Normal Planting Date
: mont : VI
V2
V3
V4
& Year
.
•
Ark. '39: 1
.
• 2
"
·• 1614
:
:
: Mean :
...
•..
'40: 1
:
.... 2 :
: Moan :
..
.
•
:
'41: 1
.... 2 :
: Mean ...
...
...
1
.
Okla. 39: 1
..
• 2
1370
1492
1524
1381
1"152
2433
1903
2200
1040
1764
1006
2415
2469
2442
1063
1660
1766
2097
1603
1090
1567
l542
1560
1992
1545
1760
1900
1824
1902
176
196
105
166
162
164
175
176
176
144
196
170
755
070
012
052
040
046
939
022
000
052
007
030
• 1014
•. 970
: 996
753
007
700
073
1035
954
924
915
920
·
·
·..
: Mean •
·.
'40:
1
•.. 2
Meon
••
'41: 1
..• 2
: Moan
..
..••
1735
1871
1003
1406
1622
1504
..
•
•
.•
·
·
Lato Planting Date
V4
V2
VI
V3
....
••
••
....
~!oan
•
.•
1527
1497
1512
•
..•
1960
1771
1066
2013
1767
1090
1752
1413 ...
1502 ...
1599
70
122
100
120
106
117
76
76
76
...
136
....
010
795
002
700
696
702
725
714
720
610
594
606
•.
...
255
171
213
231
204
210
405
294
350
:
624
..•
540
390
465
••
599
612
..·..
··...
..
·.
.
···
.
.•..
·..
1295
1436
1366
1634
1753
1694
1451
1200
1366
2070
1974
2022
1404
1570
1491
2002
1617
1850
1566
lll6
1341
1096
1713
1004
1400
1302
1395
142
114
120
1470
1364
1421
•..
..
·.
...
.·
•.
•..
1047
1~123
144
140
702
767
Y174
Treatment one is "high fertilization~ for tho station- in question. Treatnent two
is ttlow fertilization ll for the stD-tion in question. These 1ave1s D-re ccnsisten~
excopt for Lawton, Okla., whore lOll bet\;reon rows and 20 11 bet\'loon rows tfore -the
treatments.
i7
1
;""
Table 3:
~ses of Varlan~for Yield of Seod Cotton (pounds per acre) by
Stations and Yoars
,.
•
·•
tTabulated F
F Ratio
·:d.f.l·• 1939 .Actual
..• 1940 •.. 1941 ... .05 ... .01
••
•..
•
•..
·
Florence, S. C.
6.79t"
..• 5.5
5.91"-:
t
3.3
2.06
3
·
·: 3
3.3 · 5.5
4.5 ..• 0.9
·.·• 11 ·••• 1.29 •• 2.00 ••
4.6 ·
• 0.9
,.
3.3
1.30
3 :
6.60"*
• 5.6
·
·
*
•
:
5.6
..
3.62*":
1.30
3.3
3 ·
1.04
•
•
·
,.
•
10.ao-lI:
0.9
4.6
1
oft
-#
.
:
:
· ••
·
·
:Error M.S.
•· 14 :10903.406: 6510.696: 3179.531:
:Coef.. of Var .. (%) :
5.3 ,.• 12.4 ·,.
5.5
·•
,.
..
.
...•
.
..
•
·
·
·
·
· 3 2.00 .· 1.31
Griffin, Ga.
::Blocks
#= .· 3.3 • 5.6
·
:Vorioties
3.55
3 ·
·· 3.09 3.3 .• 5.6
7.95"':
0.30"': 4.6 0.9
:Dates
110.05 ·
1
* 3.27
: 1
4.5 •• 0.9
:Trcatments
1/: · 1.40 ••
•
5.6
2.90
:V x D
1.00
3
1/=
· 3.3
·
·
,.
:
5.6
:V x T
1.27
3.3
3 ·
1,.
· 1.36
.
0.00
:D x T
1
:fir • 4.6 D 3
'*
.
:Error M.S.
• 14 :10179.402:59394.214:63397.562:
·
·
22.5
10.7
35.6
:Coef. of Var. (%) :
··
•
•.
..
:
...
· 1.62 ,.•
.• 3.3 ·.. 50S
Stoneville, Miss. :Dlocks
4.00":
3
41,01--\
2.50
:Varieties
3
•• 3.3 •• ·.·.0
""
·
109.46Jl'lf': 4.6 •
:Datos
1
•
7.20*":
2.09 •• 4.6 ·
:Trontmcnts
• 1 ·
•
·
·
2.91
:V x D
3.3 6,5
3 c
••
*
,.
.
{I:
Lh43*:
:V x T
1.33
3.3
3 :
:n x T
·· 1 0.64....: * · 1.41 • 4.6 ··•
* ...·•
:Error M.S.
14 ,. 9630.430:23053.054:53365.464:·
·
5.5 :
:Coof. of Var. (%) :
9.0 • 12.9
Station
•..
Source
•..
:J31ocks
:Varioties
:Dates
:Troatments
:V x D
:V x T
:D x T
2
1
6.51~':
5.0ga~
21.7;at'~
073.01~1l:
250.93~
29.1~
33.45"'~
.'
t
e
71.40"~
254.17'H~
~
214.1~
.~
;':-$9
iJ,=,9
6.13~
6'>0
00.9
,.
~
.
,.
if
~
In each analysis of variance, the second order interaction V x D x T with tH')
degrees of freedom has been omitted. This term has no valid moaning for this 8 (;".dy,
nor is it a true error term.
Casos in which error M. S• greater than tho M. S. being tested.
Significant at 1% level.
....*
*
Significant at ~ loval.
-D-
Table 4:
Test of honogoneity of orrot variancos for yield of sGed cotton
stations by years.
bG~fOOn
5 Stations
•
X
•
2
2
reater X
.03
1939
10.07
1940
60.62
.«.0001
1941
30.26
.«.0001
4 Stations, Lawton omitted
n. er
.45
1939
1940
16.02
1941
<means
"Less than".
4;ieons "Much less tlum" •
...
.
",.2
.A
<'0001
;-:-~
-E-
Table 5:
Analysis of V£l.l'io.nce for Yield of Sood Cotton (pounds por aero) Conbining
Fivo Stations for Throe Yoars.
Sourco
•
c't.f.
Moon Squaro
Sta.tions
Yoars
SxY
Raps in Stations and Yoars
4
2
0
15
25,650.902:1'*
Datos
Variotios
Troatoonts
DxV
DxT
VxT
DxS
DxY
DxSxY
VxS
VxY
VxSxY
T x S
TxY
TxSxY
DxVxS
DxVxY
DxVxSxY
IlxTxS
DxTxY
DxTxSxY
VxTxS
VxTxY
Vx!i'xSxY
]locks in Reps in Stations and Years
Pooled Error
1
3
1
3
1
3
4
2
0
12
6
14,744,133*111,051,302.....
l,OOO,776**153, 922 rr
70,001 *"
67,-150*
1, 140t663*~
650,400Mf291,074'**
235, 310*"""
12
6
24
30
240
Total
479
*~
Significant at 1% level.
"*N.S.
Significant at 5% lovol.
Statistically non-significant.
24
3,270,060~*
"$
.
5 0 006,294'**"
132,734
*
457t-120~""
102,366*-*
4
302,l14~jI-
2
17,465 N.S.
160..030 fo""
35,152**'
12,710 N.S.
0
12
6
24
4
2
0
134f444*~
30,754 N.S.
7,972 N.S.
11,740 N.S.
22,460 N.S.
7,102 N.S.
26,005 "t~
23,055
13,304
--
fable 6:
fable Showing Regression Models, Coefftc1cnt!h fests of Signiflcnnco,
and Multiplo Corrolation Coofficients..
=
Code:
!
weekly r.tean tenpero.turo
E'= wgekly moan ovaporation
Rggrossion 1:
Model: Y
Y
= AI:J+
•
=F(T,E,SM)
8M
t
R = .67
=weekly nean soil moisture
=week fron planting dnte
R2
= .44
~T ... ~ETt + ~'lt2. + boEE + blEEt + bg::Et 2 + cotSM + OX!:SMt
+o~Mt
2
Coefficients
.541
Probability of a larger t •
5.701
T test for above ooeffioients:
•44
.33
.50
.50
RWGlsion 2:
Y = F(E,SM.E-SM)
Model: Y = .AtJ ... aoEE + 6.J.!:Et +
:it
=
.73
a~Et2 + botSM +
.50
.40
.50
-.566
.50
2
R = .54
bIt SMt +
b~SMt2
+ ooI:ESM ...
~I:ESMt
... o~ESMt2
Ooefficionts
3,751.34 19.690 ..9.414 --4..375 23.310
-2.254 -4.334
-.060
.159
!f test for above coefficients: ProbabiU ty of a larger t •
•19
.24
.13
.10
.20
.50
.16
.22
.27
RwudoQ ~:
Model: Y
= Ao
Y
=F(f,SM,T-SM)
+ acEf + ~!:Tt ...
B == ..43
¥Tt2
.151
.12
R3 =: .10
+ botsM ... b1ESMt ... baESMt2 + coE1'8M + O:L!:!I.'SMt
. +~TSMt2
Ooefficients
~
Ao
1,003.33
.004
.
~
~
~
~
...223
1.720
.097
f test tor abovo coefficients: Probo.bilit7 of a. larger t
.50
.30
.39
~
°2
.....066
.16
e
Table 7:
I
1
2
4
5
6
7
~T
730
731
715
709
716
710
o 702
9 710
13 740
15 715
16 724
17 740
10 741
19 732
20 733
21 702
23 717
I 24 714
• 25 771
26 756
'I 27 726
, Legond:
".,
.
i
e
•
e
Cotton Yields and Weekly Tomperature, Evapora.tion, and Soil Water Variab1os.
~Tt ~Tt2 ~E
1":Et ~Et2 ~_S!!~SM~u ~~!"ft2 ~~.!!_~~Mt ~ESMt2 !:TSM ~TSMt tTS~!~_'!'L_
4004 266 -107 1625 100 - 2
492
3299 -1030
13690 06073 - 114
39849 1979
4070 245 -177 1762 110 - 50
795
3335 -3504
23410
9495 -4205
64300 1451
4606 269 -122 1772 206- 45
064
6562 -3069
25907 16616 "'3696
67030 1613
4702 230 -162 1912
42 - 10
350
1237 -1469
12660
3309 -1134
20543 1300
4691 185
60 1193
52
70
432
1164
1013
9239
4155
5535
33790 1207
4697 257 ... 56 1577 242
274 1609
6555
5551
42740 19136 21620 132042 1740
4651 213 -130 1490 316
160 1075
7070 - 350
43705 24569 11196 144114 1606
4620 240
55 1690 175
305 1435
5370
0956
42193 14150 25091 113240 1590
4920 245 - 70 1744 107
259 1410
40695006
37713 15401 21054 117132 1917
4755 103 - 20 1163
09 ... 46
770
1702 - 701
13602
6974 -. 19
6031:3 ·.1760
4603 172
45 1002 156
250 1294
2963
5602
25770 12463"20506 102520 1741
4913 230 -150 1795 194
99 1154
4000
104
31071 16015
0426
94940 1960
4090 196
66 1340 219 ... 62 1349 4670
4
20550 10022 -5204 110353 1760
4075 205
36 1906 351
369 2060 11242 13251
72057 20374 29019 165052 1044
4936 320
156 2433 443
190 2776 16490 15506 117757 36052 1S473 220294 1766
4506 197
44 1316 102 250 1250 4205
6464
29803 14230 '19035
94631' 1305
4721 202
45 1203 273
248 1576
5419
6307
37240 21673 18677 144103 1761
4741 226
70 1640 307
175 1041
7946
7052
54345 24290 12461 143937 l306
-24 5160 025 -269 5020 375 190 2265 3~102 8005 214060 32020 16049 194343 570
-36 4994 009
116 5691 440
34 2930 39742
0945 270039 36959
1065 243504 -233
7 4699 523
91 3253 292
241 1060 17031 15650 107261 23560 19105 147230
945
4/: 1 F10ronco, '39, Normal *16 Stoneville, '40, Late
lil Ill' Evaporation
2
II
II
Late
17
II
t 41 Norna!
T =:s. Tenperaturo
3
I'
t40 Romal
10
n
"Late
SM=s Soil Moisture Tension
4
"
..
Lato
19 Marianna,
139 Noma].
t ~ Weok from planting date
5
If
'41 Normal
20
II
If
Lato
Y1=! Preaictod yio1a regression 11
6
If
II
Lato
21
II
f40 Nornal
Yz=
n
If
If
*2
7 Griffin
f39 Normal
22
ff
It
Late
Yz=
"
n
II
sf/:3
o II
1f
Late
23
,1f
'41 J:TorrnaJ.
Y Act.ual Yiold Stonevillo cotton
9
If
'40 Normal 24
If
1r
Late
Stand.ard Error Estino.tion:
10
II
"Lo.te
25 Lawton
'39 N'orr.m3.
Regression 4f= 1
753.9
11
II
'41 Normal ' 2 6 "
Jr
Late
Rogro3sion :f/: 2
710.2
12
If
If
Late
27
"
f40 Normal
Regrvssion
3
015.1
13 Stonevillo 139 Nonm1
20
n
"Lato
14
n
II
Late
29
"
'41 liormal
22
-11
- 9
47
10
7
-39
70
27
53
36
19
-10
-29
3
15
-29
-43
<
=
1,
"
"
...
J.
Ya
Y3
2322 2375
2027 1330
1220 1442
1516 1606
1467 1739
1794 1500
1090 1376
990 1702
1664 1621
1763--'1303
1671 1671
1921 1499
706 1146
2079 1627
1036 909
1504 1750
1739 1497
1510 1401
65 1179
92 624
1037 1475
Y
2366
2170
1611
012
172
l230
049
1227
2515
2344
1492
2370
OOJ;:
1735 r
1634 Ci'l
2415 I
1992
201:5
175
128
939
~=i
~
o
.'Tf
~
<'Il
:::!
()
til
-H-
Table 0:
Oooparison of Various Oombinations of Growth Poriods by Throe Scoring
Methods.
=Squaring
SD = Setting Young Dolls
Oode:
S
J3
= Dlooming
o=
Opening
Scoring Mothods
Period Omitted
S
13
s:n
o
None
1
.059
.750
.017
.050
.029
3
.765
.731
.470
.666
.752
.765
.776
.714
~715
.723
Tho table shows linear correlations botween yield
and score using Stoneville variety, n = 19.
Rank of each combination according to least corrolation; i.e.,
greatest loss by omission..
S
n
sn
0
."
1
2
3
Av. Rnnk
4
1
2
3
3.5
4:
1
3
2
3..0
1
2.3
1
2
3 ..5
2.0
... I ...
Table 9:
Code for Punch Card Data
Soil-Woather Project
Southern Cooperative Group
Thore is to be a card punched for each day's wea.ther record at eMh station for
the entire growing season. It has boon suggestod that tho weather record be commenced two weeks proceding planting. .All theso variables will not be censured
daily, but thoro should be provision for recording thorn on the cord when they arc
taken.
I.
II.
Identification:
Sta.tion
Yoar
Month
Date
Columns
1
2-3
4-5
6-7
Climate:
Maxir:run temp.
UinimUtl temp.
Uean temp.
Re1ative hunidity,
%
II
Precipitation (measure to hundredtbs)
Intensity (~tt/unit time)
Pyrhe1ioneter
0 a.m.
12 noon
~ 100
4 peD.
I
5
Photo-tubo integrator: '10m.
I
5
(differonce)
10
Wind (nph. a.t 2 p eO.)
24-hr. wind tlovement
III.
0-10
11-13
14-16
17-10
19-22
23-25
26-20
29-31
32-34
35-37
30-39
40-41
Soil
Temperature (2" depth; continuous record; range 0-1500 ]'.)
Mo.xir.ruD
MinitlUm
Temperature (all depth; same as above)
MaxiIllUn
Minimum
~
•
42-44
45-47
40-50
51-53
Moistur.e (transforc to lItension" in em. of H20; range 100 -
:M
100,COO
1t
54-57
50-61
14" depth
62-65
fiOOOOff for II no rain'!; punch 1t99991t if it rained but tho anount was not
(missing data).
ltao lt for no measureable wind; punch "9911 if the reading was not taken
data).
.
lt9999lt for missing data.
4
depth]
ott depth
jJ
Punch
recorded
~ Punch
TIDissing
~ Punch
(~ 100)
FIGURE 1
GRAPHS COMPUTED FROM REGRESSION =#: 1
20
15
EFFECT OF A DEGREE OF
T:EMPEBATURE ON COTTON
YIELDS AT A GIVEN WEEK
DURING GROWING SEASON
~;
·10
5
0
•5
(l)
k
0
C\l
---~•
0
~
,(l)
- 5
u.l
..
....
>t
....Q
EfFECT OF A UNIT OF
EVAPORATION ON COTTON
YIELDS A!f A GIVEN WEEK
DURING GROWING SEASON
-10
Q)
!II)
j
0
5
o
-
EFFECT OF A UNIT OF
SOIL W.ATE!l TENSION
ON COTTON YIELDS M
.A GIVEN WEmK DURING
GROWING SEASON
5
8
9
10
11
12
13
Weeks from Planting Date
14
15
16 .
Figure
120
r/l:2:
EFFECT OF .A UNIT OF EVAPORATION ON COTTON YIELD .AT DIFFERENT
LEVELS OF ~OIL WATER TENSION FOR EACH WEEK DURING GROWING SEASON
e <I>
~
U
~§
• 'M
C7.1o+>
.c co
./
60
o-IF-l
-0
'O~
rlil!
<l>1'il
~li-f
I:l 0
.
0--------
'M +3
'M
fog
mCD
•
~s::
00
o+>F-t
~~
-60
5
Squaring
7
8
Blooming
9
10
11
Setting Bolls
12
13
14
15
16
17
WEEKS FROM PLANTING DATE
100
1m
80
~
~
.......
•
...
~§
-.,.;
60
60
ro~
~t
~~
40
.,.;-+.:t
'M
el
CDS
!CD
..c:IS::
0--
20
00
.p~
.~£
-60
EI1'FECTS OF .A UNIT OF SOIL l/ATER TENSION OF COTTON YIELD .AT DIFFERENT
LEVELS OF EVAPORATION FOR EACH WEEK DURING THE GRO\VING SEASON
F1gu.re
r/f:3.
GRAPHS COl-!PUTED FROM REGRESSION *3
o
5
15
-20
mTECT OF A DEGiRE::ll OF TEMPERATURE ON COTTON YIEtJ) A'l DIFFER
L....TorVELS OF SOIL WATm TENSION FOR \
EACH WEEK DURING THE cm.otlING
S:JJASON
-40
I Squaring
7
8
9
. BloQming..
!
Setting :Bolls '
11
~
~
M
lli
~
WEDK.S FROM PLAtWING DATE
ro
35
55
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-60
EFFECT OF A UNIT OF SOIL lfJdlm TENSION
ON COTTON YIELD .AT DIFFERENT LEVELS OF
TEMI?:rm.A.TUBE FOR E.l>.OH l'lEEK :IDURING THE
GROWING SEASON.
-so
850
Weeks 6-9
S'VARING
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SOIL MOISTURE TENSION
10
Figure 14. Oont'd.
:BLOOMING
65
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en
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Figure
14:
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OPENING
.llJ' eeks 16-19
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SOIL MOISTURE TENSION
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9
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Yield·ln-1001bs..!A.::re
C. OKLAHONlA TRIUMPH
05
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OKLAHOMA TRIUMPH Yield in 100 Ibs./acre
3
C,
~.
27
d
3
6
D.. J,.CALA
9
1:2
18
21
Yield in 100 lbs .. /acre
15
24
27
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tA