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Group Title: Agricultural economics mimeo report - Department of Agricultural economics, University of Florida - EC64-12
Title: Some factors contributing to year to year variations in Florida orange production
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Permanent Link: http://ufdc.ufl.edu/UF00071972/00001
 Material Information
Title: Some factors contributing to year to year variations in Florida orange production
Physical Description: 31 p. : ; .. cm.
Language: English
Creator: Stout, R.G
Publisher: Department of Agricultural economics, University of Florida
The Florida Crop and Livestock Reporting Service
Place of Publication: Gainesville, Fla.
Orlando, Fla.
Publication Date: 1964
 Subjects
Genre: non-fiction   ( marcgt )
 Notes
Funding: Agricultural economics mimeo report - Department of Agricultural economics, University of Florida - EC64-12
Statement of Responsibility: by R.G. Stout.
 Record Information
Bibliographic ID: UF00071972
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
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Resource Identifier: oclc - 67639666
clc - 000472440

Table of Contents
    Copyright
        Copyright
    Title Page
        Title Page
    Table of Contents
        Table of Contents
    Introduction
        Page 1
        Purpose
            Page 1
        Method
            Page 1
    Annual variations in orange production
        Page 2
        Page 3
    Annual variations in factors
        Page 4
        Tree numbers
            Page 5
            Page 6
            Page 7
            Page 8
        Number of fruit per tree
            Page 9
        Size of fruit
            Page 10
            Page 11
            Page 12
            Page 13
        Droppage rates
            Page 14
            Page 15
    Reliability of estimates of factors
        Page 16
        Page 17
        Tree numbers
            Page 18
            Page 19
        Number of fruit per tree
            Page 20
        Size of fruit
            Page 21
        Droppage Rates
            Page 22
    Equation for estimating orange production prior to harvest
        Page 23
        Page 24
    Estimated components of changes in annual production
        Page 25
        Page 26
    Average relative importance of the factors
        Page 27
        Page 28
        Page 29
        Page 30
    Summary
        Page 31
Full Text





HISTORIC NOTE


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source
(EDIS)

site maintained by the Florida
Cooperative Extension Service.






Copyright 2005, Board of Trustees, University
of Florida













Some Factors Contr uting
to Year to Year Var nations in
Florida Orange Pro auction
-- .








April, 1964
Agricultural Economics Mimeo
S" Report EC64-12


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


Page


1


1


1



2



4


5


9


10


14



16


18


20


21

22


0 0 0


0 0 0






0 0 0




0 0 0
co c

0 0 0


o 0 0


0 0 0

0 0 0
. ,o


a .






SOME FACTORS CONTRIBUTING TO YEAR-TO-YEAR
VARIATIONS IN FLORIDA ORANGE PRODUCTION


Roy Go Stout



INTRODUCTION


Year-to-year 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 year-to-year 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 YEAR-TO-YEAR
VARIATIONS IN FLORIDA ORANGE PRODUCTION


Roy Go Stout



INTRODUCTION


Year-to-year 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 year-to-year 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 YEAR-TO-YEAR
VARIATIONS IN FLORIDA ORANGE PRODUCTION


Roy Go Stout



INTRODUCTION


Year-to-year 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 year-to-year 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 year-to-year 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 mid-season

oranges has been 460,000 boxes; the figure for Valencias is 670,000 boxes

As-shown in Figure 1, considerable variation about this average trend line

occurred, thereby indicating that a considerable portion of the year-to-

year variations in orange production occurred during the period 1950-51

to 1962-63. The 36.8 million box early and mid-season production in

1950-51 was the lowest during the period; it rose to a high of 52o3

million in 1961-62 and declined, following .the December, 1962 freeze,

to 43.5 million for the 1962-63 season and 24o4 million for 1963-64,

Valencia production during the past 12 years has been more variable

from year to year than early and mid-season varieties Output in

1950-51 was 30.5 million with a high in 1961-62 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 mid-season and 808 million

boxes for Valenciaso Early and mid-season orange production showed an

average absolute percentage change for the 12 year period of 802 percent,



















Actual
Production


Early and
Mid-season


Valencias


Trend Line
Y = 43,20 + ,46X


/
S\ /



Trend Line Actual
Y = 3218 + 067X Production


1952-53 1954-55 1956-57 1958-59 1960-61
1952-53 1954-55 1956-57 1958-59 1960-61


1962-63
1962-63


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-


1950-51


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 1961-62.


Ye


1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962

Abso
Ave


Table l,--Florida Orange Production

ar Early & Mid-season
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
1-61 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 year-to-year 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 mid-season 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.mid-season 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 mid-season varie-

ties in the 1960-61 season. The following year (1961-62) Valencia pro-

duction exceeded early and mid-season production for the first time,

Non-bearing 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
1950-51 1952-53 1954-55 1956-57 1958-59 1960-61 1962-63



Figure 2,--Reported Number of Bearing Early and Mid-season Trees,

Source: Florida Crop and Livestock Reporting Service, Annual Citrus
Summary, 1950-51 to 1962-63,















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
1950-51 1952-53 1954-55 1956-57 1958-59


1960-61 1962-63


Figure 3.--Reported Number of Bearing Valencia Trees.

Source: Florida Crop and Livestock Reporting Service, Annual Citrus
Summary, 1950-51 to 1962-63o


Y = 7.958 + ,467X













9,0 -


8.0-


7,0 -


6#0 -

E- Early and /
5.0
44 Mid-season- /




3.0 .




^^ IValencia
1,0 -


0 -



1950-51 1952-53 1954-55 1956-57 1958-59 1960-61 1962-63



Figure 4,--Reported Number of Non-Bearing Early and Mid-season and
Valencia Trees.

Source: Florida Crop and Livestock Reporting Service, Annual Citrus
Summary, 1950-51 to 1962-63.









From 1951-52 until 1958-59 Valencia non-bearing trees outnumbered early

and mid-season by an average of around 300,000 trees, Since 1959-60

early and mid-season 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 1956-57 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 (1956-57 through 1962-63) average number of fruit

per tree for the early and mid-season 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 99-109o

Bo Wo Kelly, "Objective Methods for Forecasting Florida Citrus Pro-
duction" Estodistica, Journal of the Inter-American Statistical
Institute, Marchi .19 58e .









estimates varied from a low of 1,005 in 1959-60 to a high of.1,380 in

1957-58, The same seven year average for Valencias was 893 with a high

of 1,056 in 1957-58 and a low of 740 in 1958-59,

The 1963-64 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 mid-season 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 mid-season 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 mid-season 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 forecastso-4/ 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 62-2, July, 1961c













Early and
Mid-season


Average


1400 -


1300 -


1200 -


1100


1000


900


800


700


600 -


500 -


0


1956-57


1958-59


1960-61


Figure 5,--Average Number of Fruit Per Tree as of September 1, Early
and Mid-season and Valenciaso


Valencias Average


1962-63









ten year average size of early and mid-season 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 mid-season 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 year-to-year change can be in

the.order of 20 percent. For example, the 1955-56 October size was 10o64

cubic inches and the following year the size was 8.54, The 1955-56 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 1958-59 and 1959-60 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 6--Early and Mid-season 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

mid-season types.

The year-to-year variations for Valencias are quite similar to the

behavior for early and mid-season types. Coefficients of variation cal-

culated in .the.same manner were almost identical for both Valencias and

early and.mid-season types0 It was .111 percent for October sizes (11,5

for early and mid-seasons) and 8.6 percent for harvest sizes (8.1 per-

cent for early and mid-season). 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 mid-season0 The trend is sharper

downward for Valencias, .153 cubic inches per year as compared with ,107

for early and mid-season 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
1958-59


1960-61


Figure 7,--Valencia Average Volume Per Fruit for October 1 and April 1,


/


Average


1954-55


1956-57


1962-63


- ----- --~- --^-~-~ 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 mid-season season, This is a

big reason for Valencia droppage being approximately twice the early

and mid-season droppage rate (Figure 8). The early and mid-season

droppage had an eight year average of 15.9 percent as compared with an

eight year average of 32.9 percent for Valencias, The year-to-year

variations.in the Valencia droppage, however, is much greater than for

the early and mid-season 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 1961-62 season, High droppage has occurred in years

of high moisture and humidity, as in 1960-61,as well as those of freez-

ing temperatures, as in 1962-63o


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 state-wide 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 Mid-season


1956-57
1956-57


1958-59


1960-61


Figure 80--Average Percent of Fruit on Trees
Dropped Off Prior to Harvest.


1962-63




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 re-establish.tree number data after the freeze,

an accelerated program was installed,, Additional .crews were hired on a

short-time basis and :he 1961 sample was re-surveyed 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 sampling-error 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.mid-point.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 Inter-American 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.1961-62 through 1963-64 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 3o--Number.of .Sample Trees, Average Fruit.Per.Tree and Required
Sample Size for.Sampling Error.of 2 Percent for
September.Limb Count.Survey

Early and
Mid-season Valencias All Orange

Number of 1961-62 1144 1280 2424
Sample Trees 1962-63 1244 1332 2576
1963-64 1252 1348 2600

Average Number of 1961-62 1183 1009 1091
Fruit Per Tree 1962-63 1363 911 1129
1963-64 492 541 517


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 .mid-season .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 mid-season oranges in

1961-62, 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 40--Number of Fruit Measured, Average Size and Relative
Sampling Error, Florida Oranges

Early and Mid-season -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)

1961-62 3960 10,95 o10 3940 1165 0o8

1962-63 4020 10o62 08 3740 10,80 08

1963-64 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 1959-60

season is shown in Table 5o The sampling error for early and mid-season

droppage varied from 1l7 to 2o4 percent,.whereas the Valencias ranged

from a sampling error of.2,3 percent'in 1961-62 to a 7.0 percent for

1963-64, The interval for the 1960-61 season was 11,2 to 15,6 percent

droppage for early and mid-season 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 & Mid-season 184 1959-60 12 5 2.0
210 1960-61 13o4 2o2
300 1961-62 10o4 lo9
282 1962-63 164 2o4
226 1963-64 11o8 lo7

Valencias 142 1959-60 20 9 5o3
192 1960-61 2506 309
368 1961-62 19o9 2o3
182 1962-63 4408 6,9
336 1963-64 17o9 7o0

a/ Early and Mid-season, 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(n-l) 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 1-D S
(1) P = ., -. -, p
Tt C 1-Di S t-
t-1 t-1 t-1 t-1


Where t subscript = current year
t-1 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,
t-l

t t 1-D S Ot
(2) Pt l-Dt 0 *P
S. ...PS t-i
t-1 Ct-1 1-Dt-l St- t-1


Where Ot and Ot-1 are the total effects-of 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

St-l
0t ..
(3) T T C 1-D S

t-1 C t-1 l-Dt-l 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 year-to-year 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 1962-63 season

for Table 6, This trend factor was a .3 percent increase each year,






26

Table 60--Percent Change in Factors and Production.from Preceding Year
and Average Change for Early and Mid-season Oranges,
1957-58 to 1963-64 Season
Frut Fui


Fruit


Year Tree Noso Noo

1957-58 + 03 +13o3

1958-59 + o3 -20o4

1959-60 + o3 8.6

1960-61 + 03 +21o5

1961-62 + o3 3ol

1962-63 + o3 +15o2

1963-64** -113 -58o2

Absolute
Average lo9 20o0

SIn 1963-64 actual change used
reduced to non-bearing status
* Change from 1961-62.


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 70--Percent Change in Factors and Production from Preceding Year
and Average Change for Valencia Oranges, 1957-58 to 1963-64 Season

Fruit Fruit Fruit
Year Tree Noso No_ Size DrE Other Production

1957-58 + 40O +13ol 4o9 -26o4 605 -2300

1958-59 + o3 -29.9 +10o2 +2603 +3304 +3005

1959-60 + 7,4 706 + 6.9 -12o0 + 05 + 903

1960-61 + .li + 1ol -12o4 -11.3 + 5o8 -16o0

1961-62 +12o7 +25,3 602 +21o4 lo6 +5803

1962-63 -13o4 907 7.3 -33,6 + 606 -48o7

1963-64* -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 1961-62 year The June 10, 1964 estimate is used for
the Valencia production for the 1963-64 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 mid-season oranges was -3,1 percent in

1961-62, whereas 1963-64 showed a 58,2 percent decrease from the 1961-62

season (because of the December, 1962 freeze the 1963-64 ~sascn was re-

lated to the 1961-62 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 1960-f61 and the largest,

-46.4 percent in 1963-64 (Table 7).


AVERAGE RELATIVE IMPORTANCE OF THE FACTORS


Precise methods of analysis to accurately allocate the year-to-year

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" Journ-l of Ari-L"'url
Research 20: 557-575, 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 year-to-year 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 year-to-year change in

trends in early and mid-season 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 mid-season and 19.0 percent for Valencias.

Changes in fruit sizes were similar by types; the figures were 907 per-

cent for early and mid-season 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 mid-season types. All other factors or a residual ef-

fect averaged 9.2 percent for early and mid-season and 9,1 percent for

Valencias.

The changes in production from the preceding year averaged 15,1

percent for early and mid-season 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
mid-season 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 mid-season 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 10o--Relative Importance of Factors Affecting Average Annual
Change in Early and Mid-season .Orange Production









most important factors in Valencia change in production is number per

tree and droppage and for early and mid-season 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 year-to-year 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 mid-season 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 mid-season 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,




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