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of Florida
Some Factors Contr uting
to Year to Year Var nations in
Florida Orange Pro auction
 .
April, 1964
Agricultural Economics Mimeo
S" Report EC6412
The Dept. of Agricultural Economics
Agricultural Experiment Stations
University of Florida, Gainesville
The Florida Crop and i""
Livestock Reporting Service :
l. .Orlando, Florida
'C .i
.`"
V,' '
,,.. .. .% '. : .': ,
.,:,..,. . r ,* ., )
..s .., ,'" '' 7 ".," .. .'
CONTENTS
INTRODUCTION. ..... .. .... o
INTRODUCTION 0 0 0 0 0 0 0 0 0 0
PurpMethod o o o o o o o o o a o o 0
Method o ......... ...
ANNUAL VARIATIONS IN ORANGE PRODUCTION0 ..........
ANNUAL VARIATIONS IN FACTORS.c .
Tree Numbers o o 0 .
Number of.Fruit Per Tree o o
Size of Fruit o. oo .
Droppage .Rates .o o o o o
RELIABILITY OF ESTIMATES OF FACTORS
Tree Numbers o o o 0 0 0 o o
Number of Fruit Per Tree o o
Size of Fruit .. .
Droppage Rates o 0 0 0
EQUATION FOR ESTIMATING ORANGE
PRODUCTION PRIOR TO HARVEST o o
ESTIMATED COMPONENTS OF CHANGES
IN ANNUAL PRODUCTIONo .co oc
0 0 0 0 0 0 0 0 0 0
00000OO00 O0 o
AVERAGE RELATIVE IMPORTANCE OF THE FACTORSo oo o o .
SUMMARY o o o o .o o o o o o o o o o o
0 0 0 0 0
0 0 0
0 0 0
0 0 0
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SOME FACTORS CONTRIBUTING TO YEARTOYEAR
VARIATIONS IN FLORIDA ORANGE PRODUCTION
Roy Go Stout
INTRODUCTION
Yeartoyear variations in the production of oranges creates a
considerable amount of instability in the various processes involved in
marketing. Such variations also create added problems with respect to
labor, fertilizer, pesticide and other factor supplies.
Processing firms have additional problems in budget allocations in
such areas as sales, advertising and promotion campaigns, At the retail
level freezer space, price leader items and such related problems all
increase due to the uncertainty of the size of each year's orange crop,
Purpose
The purpose of this report is to analyze the influence of selected
factors on the yeartoyear variations that have occurred in the produc
tion of Florida oranges during the last decade
Method
Most of the information used for analysis has been collected'by the
Florida Crop and Livestock Reporting Service in connection with the fore
casting of orange production. The report includes sections on the annual
variations in the following factors: (1) tree numbers; (2) number of
fruit per tree; (3) size of fruit; (4) droppage rates; (5) the reliability
SOME FACTORS CONTRIBUTING TO YEARTOYEAR
VARIATIONS IN FLORIDA ORANGE PRODUCTION
Roy Go Stout
INTRODUCTION
Yeartoyear variations in the production of oranges creates a
considerable amount of instability in the various processes involved in
marketing. Such variations also create added problems with respect to
labor, fertilizer, pesticide and other factor supplies.
Processing firms have additional problems in budget allocations in
such areas as sales, advertising and promotion campaigns, At the retail
level freezer space, price leader items and such related problems all
increase due to the uncertainty of the size of each year's orange crop,
Purpose
The purpose of this report is to analyze the influence of selected
factors on the yeartoyear variations that have occurred in the produc
tion of Florida oranges during the last decade
Method
Most of the information used for analysis has been collected'by the
Florida Crop and Livestock Reporting Service in connection with the fore
casting of orange production. The report includes sections on the annual
variations in the following factors: (1) tree numbers; (2) number of
fruit per tree; (3) size of fruit; (4) droppage rates; (5) the reliability
SOME FACTORS CONTRIBUTING TO YEARTOYEAR
VARIATIONS IN FLORIDA ORANGE PRODUCTION
Roy Go Stout
INTRODUCTION
Yeartoyear variations in the production of oranges creates a
considerable amount of instability in the various processes involved in
marketing. Such variations also create added problems with respect to
labor, fertilizer, pesticide and other factor supplies.
Processing firms have additional problems in budget allocations in
such areas as sales, advertising and promotion campaigns, At the retail
level freezer space, price leader items and such related problems all
increase due to the uncertainty of the size of each year's orange crop,
Purpose
The purpose of this report is to analyze the influence of selected
factors on the yeartoyear variations that have occurred in the produc
tion of Florida oranges during the last decade
Method
Most of the information used for analysis has been collected'by the
Florida Crop and Livestock Reporting Service in connection with the fore
casting of orange production. The report includes sections on the annual
variations in the following factors: (1) tree numbers; (2) number of
fruit per tree; (3) size of fruit; (4) droppage rates; (5) the reliability
of the estimates of the preceding factors, since they have been estima
ted from a sample; and finally (6) the yeartoyear changes in each fac
tor related to actual production, Specific methodology regarding the
accumulation of estimates of each factor are discussed in detail in the
pertinent sections
ANNUAL VARIATIONS IN ORANGE PRODUCTION
A simple regression analysis of trends in orange production since
1950' indicates that the average annual increase in early and midseason
oranges has been 460,000 boxes; the figure for Valencias is 670,000 boxes
Asshown in Figure 1, considerable variation about this average trend line
occurred, thereby indicating that a considerable portion of the yearto
year variations in orange production occurred during the period 195051
to 196263. The 36.8 million box early and midseason production in
195051 was the lowest during the period; it rose to a high of 52o3
million in 196162 and declined, following .the December, 1962 freeze,
to 43.5 million for the 196263 season and 24o4 million for 196364,
Valencia production during the past 12 years has been more variable
from year to year than early and midseason varieties Output in
195051 was 30.5 million with a high in 196162 of 56o5 million.
The change in production from the preceding year in million boxes
and in percentages is shown in Table lo
The average absolute change in actual .production for the 12 year
period was 3o7 million boxes for early and midseason and 808 million
boxes for Valenciaso Early and midseason orange production showed an
average absolute percentage change for the 12 year period of 802 percent,
Actual
Production
Early and
Midseason
Valencias
Trend Line
Y = 43,20 + ,46X
/
S\ /
Trend Line Actual
Y = 3218 + 067X Production
195253 195455 195657 195859 196061
195253 195455 195657 195859 196061
196263
196263
Figure 1,Florida Orange Production Trend and Annual Variation,
Source: Florida Agricultural Statistics Citrus Summary, 1963 Issue,
Florida Crop and Livesto Reporting Service
65 
60 
55
50
35 
30
25
20
195051
0 1
This compared with an absolute percentage change of 2208 percent for Va
lencias, The big changes generally occurred as a result of disasters
such as freezes and hurricanes
Although a hurricane in September, 1960 brought about substantial
damage to the citrus industry, it does not completely explain the large
actual increase of 20.8 million boxes (58,3 percent) in Valencia produc
tion the following year of 196162.
Ye
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
Abso
Ave
Table l,Florida Orange Production
ar Early & Midseason
Million Boxes Percent
.52 7,0 19.0
53 lo5 3o4
54 507 13,5
55 1,5 3,1
>56 ,8 lo6
57 2,9 6,0
58 o4 08
!59 7,o 13,9
>60 1.0 2,3
161 1,9 4.2
.62 5,3 11,3
63 9.8 18,7
>lute
rage 3.7 8,2
Change from Preceding Year.
Valencias
Million Boxes
4,3
4,9
11o2
4,7
3,1
o8
8o9
9,1
3,6
6,8
20o8
27,5
8.8
ANNUAL VARIATIONS IN FACTORS
Variations in yeartoyear changes in the factors considered to
contribute directly to the size of the orange crop are presented in this
section, It is recognized that basic factors such as soil types, root
stocks, disease, insect population, and weather affect these factors,
However, these basic influences are not considered herein,
Percent
14, 1
14,1
37.5
11,4
8,5
2,0
23,0
30,5
9,3
16.0
58,3
48,7
22,8
~
Tree Numbers
Routine agricultural censuses and surveys requesting information
from owners and managers, have not resulted in accurate estimates of
tree numbers. This is due to many factors such as absentee ownership,
large acreages, periodic replanting, and mixing of varieties. Conse
quently complete enumerations of all citrus groves by counting .the trees
in the groves has been conducted at different times in the past, I/
The total tree census surveys of 1934 and 1957 have been the basis for
preparing annual estimates of tree numbers by adjusting these figures
with information on nursery stock movements. In 1960 a continuing
survey procedure was adopted to maintain a more accurate and current
estimate of tree numbers. 2/
Very few changes have occurred in early and midseason tree numbers
as compared to the large increases in Valencia trees (Figures 2 and 3).
The trend line in Figure 2 shows that the average annual increase in
early and.midseason varieties was 42,000 trees. The trend line in Fig
ure 3 shows an average increase in Valencia tree numbers of 467,000
trees per year,
Bearing Valencia tree numbers exceeded early and midseason varie
ties in the 196061 season. The following year (196162) Valencia pro
duction exceeded early and midseason production for the first time,
Nonbearing tree numbers have followed similar patterns (Figure a),
1/ A complete citrus tree census was completed in 1934 and 1957,
2/ Roy G. Stout and J, W. Todd, "Continuing Survey for Estimating Citrus
Tree Numbers" Mimeographed paper, Agricultural Economics Department,
Florida Agricultural Experiment Stations.
15.0
14.5 
14.0
13.5
13,0
O0
o 12.5
STrend Line
S12.0 Y = 12.473 + .042X
11.5
11.0
10.5
0 I I *I I I
195051 195253 195455 195657 195859 196061 196263
Figure 2,Reported Number of Bearing Early and Midseason Trees,
Source: Florida Crop and Livestock Reporting Service, Annual Citrus
Summary, 195051 to 196263,
16,0
15,0
14.0
13.0
c)
S12.0
o I.0
9,
44
0
o 11.0
4
10.0
9.0
8.0
7.0
0
I 9I I I 19
195051 195253 195455 195657 195859
196061 196263
Figure 3.Reported Number of Bearing Valencia Trees.
Source: Florida Crop and Livestock Reporting Service, Annual Citrus
Summary, 195051 to 196263o
Y = 7.958 + ,467X
9,0 
8.0
7,0 
6#0 
E Early and /
5.0
44 Midseason /
3.0 .
^^ IValencia
1,0 
0 
195051 195253 195455 195657 195859 196061 196263
Figure 4,Reported Number of NonBearing Early and Midseason and
Valencia Trees.
Source: Florida Crop and Livestock Reporting Service, Annual Citrus
Summary, 195051 to 196263.
From 195152 until 195859 Valencia nonbearing trees outnumbered early
and midseason by an average of around 300,000 trees, Since 195960
early and midseason types have been larger by about the same amount,
Number of Fruit Per Tree
A method utilizing a technique of branch sampling, was developed
by Jessen and applied to Florida citrus by Kelly for estimating the
average number of fruit per tree. 3/ In this method a sample of trees
throughout the citrus area is selected; within each sample tree a sample
branch which is about 1/10 the cross sectional area as that of the trunk
is selected, A random samplingprocess in which the probability of se
lection of each branch is proportional to its cross sectional area is
used to select the sample branch, All fruit on this branch is counted;
this count is multiplied by the reciprocal of the probability of selec
tion to give an estimate of the number of fruit on the tree, Starting
with the 195657 season, a survey has been conducted annually by the
Florida Crop and Livestock Reporting Service to determine the average
number of fruit per tree as of September 1. These results are used in
making the October 1 citrus crop forecast.
The seven year (195657 through 196263) average number of fruit
per tree for the early and midseason types was 1,21.0, The annual
3/ R, J. Jessen, "Determining the Fruit Count on a Tree by Randomized
Branch Sampling" Biometrics, Volo 11, No, I (March, 1955) ppo 99109o
Bo Wo Kelly, "Objective Methods for Forecasting Florida Citrus Pro
duction" Estodistica, Journal of the InterAmerican Statistical
Institute, Marchi .19 58e .
estimates varied from a low of 1,005 in 195960 to a high of.1,380 in
195758, The same seven year average for Valencias was 893 with a high
of 1,056 in 195758 and a low of 740 in 195859,
The 196364 average number of fruit.per tree was not included in
the above averages, due to the heavy freeze of 1962, They were 492 for
early and midseason and 541 for Valencias0
The total.quantity of fruit on a tree is .related to the area of
bearing surface of.the tree, A positive relationship between number of
fruit.per tree and.the area of bearing surface is suggested by the data
shown in Figure 5. Following the high counts in September, 1957, the
freeze of.that December reduced.bearing surface to the extent that the
counts the following year were greatly reduced After the reduced count
following the freeze, average counts per tree showed an average annual
increase of 66 fruit for early and midseason and 43 fruit for Valenciaso
The freeze of December, 1962 reduced .bearing surface to the extent that
the average number of fruit per tree in September, 1963 was less than
half of the year before for early and midseason oranges and about 60
percent for Valencias,
Size of Fruit
Information on size of fruit as of September 1 and monthly there
after until harvest time and monthly droppage rates are obtained by the
field.men of the Florida Crop and Livestock Reporting Service for pre
paring and.making monthly revisions of the citrus forecastso4/ The
4/ Description of the sample and additional information can.be found in
Roy G. Stout, Size of Fruit and Droppage Rates Influence Total Citrus
Production, Florda Agricultural Experiment Stations Agricultural
Economics Mimeo Report 622, July, 1961c
Early and
Midseason
Average
1400 
1300 
1200 
1100
1000
900
800
700
600 
500 
0
195657
195859
196061
Figure 5,Average Number of Fruit Per Tree as of September 1, Early
and Midseason and Valenciaso
Valencias Average
196263
ten year average size of early and midseason varieties was 9.47 cubic
inches on October 1 and 1150 cubic inches on January 1 (Figure 6)
January measurements are used as harvest size since growth has nearly
been completed, and a large percentage of the fruit is still on the
trees By February 1 a much larger share of the crop has been harvested,
Since the sample is made up of commercial groves the sample.of fruit is
no longer available for measurements when the grove is picked Conse
quently, February 1 sizes are calculated from a smaller sample size
than January 1 sizes
The variation from year to year is substantial both in the October
and the January average sizes of early and midseason types The coef
ficient of variation of the annual averages about the 10 year average
was 11.5 percent for the October sizes and 8ol percent for the January 1
sizes This means that, approximately one year in three, the average
size will deviate more than 115 percent in October and 81l percent in
January from the 10 year average size, If a year with low sizes follows
a year with high sizes, or vice versa, the yeartoyear change can be in
the.order of 20 percent. For example, the 195556 October size was 10o64
cubic inches and the following year the size was 8.54, The 195556 size
was 112 percent of the 10 year average, while the following year it was
90 percent of the 10 year average  a difference of 22 percent, The
difference between 195859 and 195960 for October 1 sizes was 29 percent
Another worthy note in Figure 6 is the trend towards smaller sizes
as harvest time approaches A definite and significant trend effect in
the harvest size over the 10 year period was noted, Since this trend
is not present in the October size data, it is somewhat difficult to
13
13
January 1
Trend
12 \Y = 12o087 1o07X
LO Average
S\\ Average
w 9
Figure 6Early and Midseason Average Volume Per Fruit for October
and January 1o
4
and January 1,
explain. One possible explanation related to changes in harvesting
patterns, That is, with the utilization of fruit for chilled juices
and salads on the increase, emphasis for this use may be concentrating
on large sizes and earlier harvesting. Changes in cultural.practices
may somehow also be a factor in the trend to smaller sizes
The 10 year average October size for Valencias was 8.59 cubic
inches on January 1 and 12o82 cubic inches on April 1 (Figure 7). The
April 1 size has been used as the base harvest comparison for Valencias
for the same reasons presented for the January 1 size for early and
midseason types.
The yeartoyear variations for Valencias are quite similar to the
behavior for early and midseason types. Coefficients of variation cal
culated in .the.same manner were almost identical for both Valencias and
early and.midseason types0 It was .111 percent for October sizes (11,5
for early and midseasons) and 8.6 percent for harvest sizes (8.1 per
cent for early and midseason). Again, interpretation of this coeffi
cient says that, one year in three, the deviations from the 10 year
average could be larger than 11 and 8.6 percent, respectively, for
October and April sizes.
The trend effect is evident in the harvest size but not in the
October size as was true for early and midseason0 The trend is sharper
downward for Valencias, .153 cubic inches per year as compared with ,107
for early and midseason types,
Droppage Rates
A very important factor in determining the realized size of the
April 1
Average
Trend
Y = 13o657 .153X
October 1
/A
195859
195859
196061
Figure 7,Valencia Average Volume Per Fruit for October 1 and April 1,
/
Average
195455
195657
196263
  ~ ^~~ 1111 
I
V
U
V;V
citrus crop after the fruit has set on the tree is the amount of drop
page that occurs before harvest, The survey establishing an estimate
of the average number of fruit per tree is scheduled to provide infor
mation as of September o1 A survey is maintained to estimate droppage
from.this date forward in order that an estimate of the number of fruit
per tree at harvest is obtained. 5/ The Valencia season from September 1
is nearly twice as long as the early and midseason season, This is a
big reason for Valencia droppage being approximately twice the early
and midseason droppage rate (Figure 8). The early and midseason
droppage had an eight year average of 15.9 percent as compared with an
eight year average of 32.9 percent for Valencias, The yeartoyear
variations.in the Valencia droppage, however, is much greater than for
the early and midseason droppage. This larger variation in Valencia
droppage appears to be influenced by weather conditions. If temperature,
rainfall and.humidity are favorable, Valencia droppage is extremely
light, as in the 196162 season, High droppage has occurred in years
of high moisture and humidity, as in 196061,as well as those of freez
ing temperatures, as in 196263o
RELIABILITY OF ESTIMATES OF FACTORS
Statistical analysis has been conducted on the factor estimates to
determine expected ranges in the estimates, These reliability estimates
apply only to the factors estimated on a statewide basis.
5/ The sample size and design is described in the publication referred
to in footnote 4,
Average
50
40 
20
10 
0
0
0
Early and Midseason
195657
195657
195859
196061
Figure 80Average Percent of Fruit on Trees
Dropped Off Prior to Harvest.
196263
as of September 1 that
Average
_ __
Tree Numbers
Statistical analysis of the current continuing survey for estinsa
',l; tree numbers has been completed for.the 1961.and 1962 season. The
sampling errors for estimates of all citrus, all .orange and.all grape
fruit tree numbers by counties and for the state were estimated for each
of the two years 6/ The procedure utilized was one in which the 1962
estimate included data collected from the 1961 sample This then gives
nearly a doubling of the sample size for 1962; .consequently, a reduced
zpling error was obtained ,or 1962 over 1961o
In the tree number estimate for 1963 it was planned to.utilize sam
pie data for all three years, but the freeze .of December, 1962 disrupted
these plans0 In order to reestablish.tree number data after the freeze,
an accelerated program was installed,, Additional .crews were hired on a
shorttime basis and :he 1961 sample was resurveyed in addition to con
tinuing and completing the regular sample for 1963. Consequently, the
1.963 estimates released recently were.based on two samples as was the
1962 estimate, 7/ Because of greater variability in grove tree counts
created by the freeze, the sampling error for this 1963 estimate is
probably somewhat: 1~:. .' than that shown for the 1962 estimated
Sampling errors were estimated at the .95 percent probability level
(Table 2), which means we can assert with a confidence of o95 that the
6/ Sampling error as used in this report is .defined as the ratio of
the confidence interval divided by the mean and multiplied by 100
to express it .as a percentage
7/ Florida Crop and Livestock Reporting Services Florida .Citrus. Inven
tory of Comimercial. Citrus TL '.S in Florida Oraido 'flrida i
April 22,Y9T
Table 2 Estimated Number of Orange Trees and Relative Sampling
Errors by Counties, 1961 and 1962
Number of Trees (000) Sampling Error a/ (Percent)
County
1961 1962 1961 1962
Alachua 22 28 23.3 22.3
Brevard 893 1054 21.1 26.2
Broward 209 243 59 6 21.2
Charlotte 44 92 17.6 47,9
Citrus 114 130 117,4 58.0
Clay 1 
Collier 1 62 74,4
Dade 22 20 47,8 46.2
DeSoto 562 758 12,1 29.1
Duval 4 4 25,5
Flagler 5 10 
Glades 28 
Hardee 2247 2353 31.3 9,3
Hendry 78 131 36.8
Hernando 785 758 29.8 15.6
Highlands 1635 1619 16 7 10.1
Hillsboro 3427 3331 20.7 16.9
Indian River 525 687 16.3 17,4
Lake 6608 7338 18.6 9.7
Lee 94 102 18,4 25 6
Manatee 483 721 14.1 17.5
Marion 1344 1080 19,6 32.7
Martin 270 510 47 2 41.1
Okeechobee 20 35 31.2
Orange 4047 4014 22 9 6.4
Osceola 1109 1222 11.8 5,7
Palm Beach 67 74 11,2 7.2
Pasco 2002 2442 17.2 10,5
Pinellas 448 401 55.2 43 9
Polk 6983 7085 7.1 8 6
Putnam 356 338 18.1 14 7
Sarasota 109 112 17.4 18 4
Seminole 1169 1252 27.4 38 8
Sumter 236 235 35.5 13,3
St. Johns 17 16 
St. Lucie 1190 1436 18.0 14 0
Volusia 820 830 26.9 20 6
State 37945 40552 4 9 3 6
a/ At .95 probability level.
true numbers will be within the range of the estimated number plus or
minus the percentage of .sampling error. For example,.for Lake County,
the estimated.number of all.orange.trees in 1962 was 7,338,000 trees;
the sampling error was 9.7 percent. This means that, with an .expected
confidence of 95 chances .out of 100, the true number of orange trees
in Lake County in 1962 was 7,338.,000 trees plus or minus 9.7 percent
(711,179 trees) or a confidence .range of 6,626,821 to 8,049,179 number
of trees. Many of.the counties have fairly large sampling errors but
the estimates are considered .sufficiently accurate.bases for many
intelligent.decisions and.the state estimates are considered very
reliable
The samplingerror for the state estimate of all orange .trees was
36 .percent.at the .95 percent probability level, This gives a confi
dence interval of 39,092,128 to 42,011,872 trees for 1962. The esti
mated number of trees is, of course, the.midpoint.of.this range, or
40,552,000 trees, for that year.
Number of Fruit Per Tree
Statistical .analysis of the limb .count survey for 1956 was com
pleted by Kelly prior to selection of .the .basic .sample of groves that
has.been used since the fall.of.19570 8/ The estimated number of
trees for a required sample .size with four trees per grove to provide
a sampling error of the average number of fruit per tree.at 2 percent
as calculated by .Kelly is shown .in Table .3. The components considered
8/ Kelly, Bruce Wo, "Objective.Methods for Forecasting Florida Citrus
Production", Stadistica Journal of the InterAmerican Statistical
Institute, .March,1 1958 ..
in the analysis of.variance were: (1) area,.(2) age group within area,
(3) grove within age.group and (4) tree within grove. Analysis for
the years.196162 through 196364 is presently being conducted but due
to errors in IBM computer.program preparation it has not.been completed.
Preliminary indications are that the sampling error may be.slightly
higher than the expected.2 percent.
Table 3oNumber.of .Sample Trees, Average Fruit.Per.Tree and Required
Sample Size for.Sampling Error.of 2 Percent for
September.Limb Count.Survey
Early and
Midseason Valencias All Orange
Number of 196162 1144 1280 2424
Sample Trees 196263 1244 1332 2576
196364 1252 1348 2600
Average Number of 196162 1183 1009 1091
Fruit Per Tree 196263 1363 911 1129
196364 492 541 517
Number of Trees
Required for a
Sampling Error
of 2% with 4
Trees Per Grove
2076
1852
1996
The freeze of.1962 .undoubtedlycontributed to this increased sampling
error because.large .numbers of sample trees .had small numbers or no
fruit per tree This .gives.large .deviations from the .average, thereby
making large variances,
Size of Fruit
Analysis of the rate of growth and harvest size.survey reveals a
very high degree of precision (Table 4)o Approximately.3800 oranges of
each.type (early and .midseason .and .Valencias) .were .measured in the
monthly survey at harvest time The percentage sampling error was very
close to 1 percent. For example, for early and midseason oranges in
196162, the average size was 10o95 cubic inches with a sampling error
of 1.0 percent This means that the true value was expected to be be
tween 10.95 t o01 (10o95) or 10,84 to U1106 with a level of probability
of ,95.
Table 40Number of Fruit Measured, Average Size and Relative
Sampling Error, Florida Oranges
Early and Midseason Valencias
No. Average Size Sampling .Noo Average Size Sampling
Year Fruit Per Fruit a/ Error c/ Fruit Per Fruit b/ Error c/
(cubic inches) (percent) (cubic inches) (percent)
196162 3960 10,95 o10 3940 1165 0o8
196263 4020 10o62 08 3740 10,80 08
196364 3880 12o02 l11 3920 13o50 1o0
a/ January 1 average size.
b/ April 1 average size
c/ At 095 probability level.
Droppage Rates
Statistical analysis of the annual,droppage .rates since the 195960
season is shown in Table 5o The sampling error for early and midseason
droppage varied from 1l7 to 2o4 percent,.whereas the Valencias ranged
from a sampling error of.2,3 percent'in 196162 to a 7.0 percent for
196364, The interval for the 196061 season was 11,2 to 15,6 percent
droppage for early and midseason and 22o7 to 28o5 percent droppage for
Valencias,
Table 5 Number of Sample Trees, Estimated Droppage Percentage
and Sampling Error, Florida Oranges
No, Percent a/ Percent b/
Tye Trees Year rop Samlin Error
Early & Midseason 184 195960 12 5 2.0
210 196061 13o4 2o2
300 196162 10o4 lo9
282 196263 164 2o4
226 196364 11o8 lo7
Valencias 142 195960 20 9 5o3
192 196061 2506 309
368 196162 19o9 2o3
182 196263 4408 6,9
336 196364 17o9 7o0
a/ Early and Midseason, droppage is from October 1 to January 1;
Valencia droppage is from October 1 to .April 1, this is less than
the total droppage.for the season
b/ At o95 probability level; Soeo = lo96 sR divided by R, multiplied
by 100o
S2 1 =X2 + R2y2 2RXY ; Y = number of fruit
R n(nl) y
on sample limb on October 1, X = number of dropped fruit, R = Ey
EY
EQUATION FOR ESTIMATING ORANGE .PRODUCTION PRIOR TO HARVEST
Each year on October 10 and monthly thereafter until the end of the
harvesting season, estimates of total orange production are made based
largely on the values of. (1) tree numbers, (2) number of fruit per
tree, (3) projected harvest size.of fruit, and (4) projected droppage
rates These factors can beput together in different ways and it has
been found that, during the years in which these objective data have
been used in forecasting, the following equation has been most accurate;
T C 1D S
(1) P = ., . , p
Tt C 1Di S t
t1 t1 t1 t1
Where t subscript = current year
t1 subscript = previous or base year
P = production
T = number of trees
C = average number of fruit per tree on September 1
D = droppage rate from September 1 until harvest
S = average size of fruit at harvest time
The use of this ratio of change of known factors effecting .production to
estimate the change from the previous or base year, allows for the influ
ence of other factors not in the equation at a constant prc r.i:  effect.
Factors such as dooryard production and misclassification of some trees
by type would be adjusted for by a constant percentage when using the
ratio to make the estimate. As an example, assume the following basic
data:
Trees 1,0 Minus Avg, Vol.
Season (000) Fruit/Tree Droppae Rate Per Fruit Production
cubic inches mil. boxes
Base: 11,259 1,221 o8515 10,95 52,0
Current: 11,416 494 .8400 12,00
S11,416 494 ,8400 1200
P = o 52 0
11,259 1,221 .8515 10,95
P = 1,014 x ,4046 x .9865 x 1.095 x 52,0 = 23,1
In making the revisions in months following the October estimate,
the tree numbers and fruit per tree remain the same but changes may be
made in the size of fruit and percent droppage in following months
since these are projected to harvest,
.ESTIMATED COMPONENTS OF CHANGES IN ANNUAL PRODUCTION
The production changes from year to year associated with each fac
tor can be evaluated in the framework of the estimating equation, If
we add another variable called other factors and insert values for Pt
and P we can then solve for the raiio of the factors,
tl
t t 1D S Ot
(2) Pt lDt 0 *P
S. ...PS ti
t1 Ct1 1Dtl St t1
Where Ot and Ot1 are the total effectsof all other factors not
mentioned in equation (1).
If we divide both sides of (2) by P t and then the terms within
the brackets we have Pt
Stl
0t ..
(3) T T C 1D S
t1 C t1 lDtl St
The ratio of each factor to the preceding year for production and the
factors of tree numbers, fruit numbers, fruit size, and droppage were
computed and then equation (3) was used to determine the residual ef
fect in other factors. These ratios were multiplied by 100 to put into
percentage form, then .each was subtracted from 100 in order to show a
percentage change from the preceding year. This percentage change is
shown in Tables 6 and 7.
The yeartoyear variations in tree numbers for early and mid
season oranges, as shown in Figure 2, were somewhat erratic so that
only a trend factor in tree numbers was used until the 196263 season
for Table 6, This trend factor was a .3 percent increase each year,
26
Table 60Percent Change in Factors and Production.from Preceding Year
and Average Change for Early and Midseason Oranges,
195758 to 196364 Season
Frut Fui
Fruit
Year Tree Noso Noo
195758 + 03 +13o3
195859 + o3 20o4
195960 + o3 8.6
196061 + 03 +21o5
196162 + o3 3ol
196263 + o3 +15o2
196364** 113 58o2
Absolute
Average lo9 20o0
SIn 196364 actual change used
reduced to nonbearing status
* Change from 196162.
Trend in*
Fruit
Size
+ 206
 4.6
+1908
21l1
+ 609
 3o0
+ 908
97
due to
in the
Fruit
Drop
607
+ 406
48
48
0
+ 2,2
10,7
o14
4,3
the large
freeze
Production
08
13o9
+ 2,3
+ 402
+llo3
18o7
54o4
92
number of trees
15ol
Table 70Percent Change in Factors and Production from Preceding Year
and Average Change for Valencia Oranges, 195758 to 196364 Season
Fruit Fruit Fruit
Year Tree Noso No_ Size DrE Other Production
195758 + 40O +13ol 4o9 26o4 605 2300
195859 + o3 29.9 +10o2 +2603 +3304 +3005
195960 + 7,4 706 + 6.9 12o0 + 05 + 903
196061 + .li + 1ol 12o4 11.3 + 5o8 16o0
196162 +12o7 +25,3 602 +21o4 lo6 +5803
196263 13o4 907 7.3 33,6 + 606 48o7
196364* 112 46o4 +16,7 + 500 + 9,6 41o6
Absolute
Average
19o0
902 19o4
9ol
3205
Other
 808
+ 8ol
 2o2
+ 8o4
+ 408
18o8
+13o6
* Change from 196162 year The June 10, 1964 estimate is used for
the Valencia production for the 196364 season,
Consequently, part of the other factors' influence is tree numbers
Figure 3 showed fairly stable increases in Valencia tree nurmbers from
year to year, therefore, total tree numbers were used to calculate the
changes in Valencias shown in Table 7,
The smallest percentage change from the preceding year for fruit
numbers per tree for early and midseason oranges was 3,1 percent in
196162, whereas 196364 showed a 58,2 percent decrease from the 196162
season (because of the December, 1962 freeze the 196364 ~sascn was re
lated to the 196162 season). The :a : decrease is 1. : 2~ due to :the
reduced bearing surface resulting from the Decrmber, 1962 fireze Th
smallest change for Valencia average number of fruit per tree from the
preceding or base year was 1,1 percent in 1960f61 and the largest,
46.4 percent in 196364 (Table 7).
AVERAGE RELATIVE IMPORTANCE OF THE FACTORS
Precise methods of analysis to accurately allocate the yeartoyear
changes to each of the factors discussed are not available, One pcssi
'ble approach was published several y:: ..g by Sewall Wright, 9/ It
was used recently by Swanson and West in estimating which factors are
more important in net returns in cattle feeding, 10/ This procedure
measures the influence of each of several independent variables upon a
dependent variable based on the property that the sum of the coefficients
9/ Sewall Wright, "Correlation and Causation" Journl of AriL"'url
Research 20: 557575, 1921.
10/ E, R, Swanson, "Statistical An.,r .' of Feeder Cattle Returns"
Journal of Farm Economics Vol, 45, No. 1, February, 1263,
R2
is equal to the coefficient of multiple correlation, R2.
The crop forecasting equation in the ratio form in (2) is multi
plicative instead of additive. In order to make the factor effects
additive the equation must be converted into logarithms With only
seven observations in Tables 6 and 7 the number of variables was re
duced to three; fruit number per tree, fruit size, and fruit drop.
Equation (2) was converted to logarithms and least squares analysis
completed. This allowed only three degrees of freedom for error and
only one factor showed significance in each type. For early and mid
season the number of fruit per tree was calculated as accounting for
most of the yeartoyear changes while the droppage was the important
factor in Valencias.
Because of only seven years of observation it was decided to dis
count this analysis and use the average absolute changes as shown in
Tables 6 and 7 and to approximate the importance of each factor by
converting to an index and assuming additivity.
The absolute average shown at the bottom of Tables 6 and,7 is the
simple average of the percentage changes, ignoring the direction or
sign of change. Thus, on the average, the yeartoyear change in
trends in early and midseason tree numbers averaged 1.9 percent. The
average absolute annual change from the preceding year for Valencia
tree numbers was 7.1 percent,
The absolute average annual change in fruit numbers per tree was
20.0 percent for early and midseason and 19.0 percent for Valencias.
Changes in fruit sizes were similar by types; the figures were 907 per
cent for early and midseason and 9.2 percent for Valenciaso
The absolute average annual change in droppage influence was
greater for Valencias  19.4 percent, as compared with 4.3 percent
for early and midseason types. All other factors or a residual ef
fect averaged 9.2 percent for early and midseason and 9,1 percent for
Valencias.
The changes in production from the preceding year averaged 15,1
percent for early and midseason and 32.5 percent for Valencias.
In order to relate these changes to each factor and to the changes
in production, the average changes were summed and each divided by the
sum, that is:
X.
xi
(4) Ci =  x 100
X
Where Xi = average change for each factor in Tables 6 and 7
C = percent of total average change due to Xi factor
For example, the percentage of the change in production of early and
20.0
midseason oranges due to fruit numbers is  x 100 = 44.1 and for
45l
4.3
fruit drop '3 x 100 = 9.5,
45.1
Equation (2) is a multiplicative model .and equation (4) is addi
tive, therefore, this is only an approximation of the true value of
the component parts. These approximations as computed by equation (4)
are shown in Figures 9 and 10. For Valencias, the average annual
change in production is due to a 30.4 percent change in drop, a 29,8
percent in fruit number per tree, a 14.4 percent change in sizes and
a 25.4 percent change in tree numbers and other factors, For the ear
ly and midseason types 44.3 percent of the change is due to changes
in fruit numbers per tree and 9.5 percent change in drop. The two
Figure 9.Relative Importance of Factors Affecting Average Annual
Change in .Valencia Orange Production
Figure 10oRelative Importance of Factors Affecting Average Annual
Change in Early and Midseason .Orange Production
most important factors in Valencia change in production is number per
tree and droppage and for early and midseason types the two most im
portant factors are number per tree and fruit size,
SUMMARY
This report contains an analysis of the influence of selected fac
tors on the yeartoyear variations in Florida orange production during
the last decade, The factors considered were those used in the fore
casting formula used by the Florida Crop and Livestock Reporting Service
in preparing estimates of the citrus crop.
It was estimated that the absolute average annual change in pro
duction was 15,1 percent for early and midseason oranges and 32.5 per
cent for Valencia oranges. An estimate was made of the important factors
contributing to these average annual changes. Variations in number of
fruit per tree was estimated to contribute 29.8 percent to the varia
tion in Valencia production. Fruit drop was 30.4 percent, fruit size
14c4 percent, tree numbers 1ol percent and other factors 14.3 percent,
For early and midseason oranges the estimated contribution of each
factor to the average annual change was; number of fruit per tree 44,3
percent, fruit size 21o5 percent, fruit drop 9,5 percent, tree numbers
and other factors 20,4 percent,
