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 Title Page
 Table of Contents
 Introduction
 Procedures
 Estimating tree numbers
 Statistical reliabilty of...
 Some remarks
 Summary






Group Title: Mimeo report - Department of Agricultural Economics, University of Florida - EC 64-13
Title: A continuing survey for estimating current numbers of Florida citrus fruit trees
CITATION PAGE IMAGE ZOOMABLE PAGE TEXT
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00071992/00001
 Material Information
Title: A continuing survey for estimating current numbers of Florida citrus fruit trees
Series Title: Agricultural economics mimeo report
Physical Description: 20 p., : tables, ; 28 cm.
Language: English
Creator: Stout, Roy G
Todd, J. W
Publisher: Un. of Florida, Agricultural Experiment Sta.
Place of Publication: Gainesville Fla
Publication Date: 1964
 Subjects
Genre: non-fiction   ( marcgt )
 Notes
Statement of Responsibility: Roy G. Stout and J. W. Todd.
General Note: June 1964.
Funding: Florida Historical Agriculture and Rural Life
 Record Information
Bibliographic ID: UF00071992
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
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 30017011

Table of Contents
    Copyright
        Copyright
    Title Page
        Title Page
    Table of Contents
        Table of Contents
    Introduction
        Page 1
    Procedures
        Page 2
        Sampling of old citrus sections
            Page 3
            Page 4
        Sampling of new citrus sections
            Page 5
    Estimating tree numbers
        Page 6
        Citrus tree numbers for 1961
            Page 6
        Citrus tree numbers for 1962
            Page 7
            Page 8
        Citrus tree numbers for 1963
            Page 9
            Page 10
            Page 11
        Estimating tree numbers for rth year
            Page 12
    Statistical reliabilty of estimates
        Page 13
        Estimated variances
            Page 14
            Page 15
            Page 16
            Page 17
    Some remarks
        Page 18
    Summary
        Page 19
        Page 20
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




JUNE 1964
/j JUNE, 1964


AGRICULTURAL ECONOMICS MIMEO REPORT EC64-13


A CONTINUING SURVEY FOR ESTIMATING

CURRENT NUMBERS OF FLORIDA


CITRUS TREES


ROY G. STOUT
J. W. TODD


THE DEPARTMENT OF AGRICULTURAL ECONOMICS, AGRICULTURAL EXPERIMENT STATION
in cooperation with
THE FLORIDA CROP AND LIVESTOCK REPORTING SERVICE, ORLANDO, FLORIDA
and THE DIVISION OF PLANT INDUSTRY, FLORIDA STATE DEPARTMENT OF AGRICULTURE, GAINESVILLE











CONTENTS



Page

INTRODUCTION . .. .. . ... 1




PROCEDURES ........ . . . 2

Sampling of Old Citrus Sections. . 3

Sampling of New Citrus .Sections e c .e 5




ESTIMATING TREE NUMBERS . . 6

Citrus Tree Numbers for 1961 .. ..... 6

Citrus Tree Numbers for 1962 .. . .. 7

Citrus Tree Numbers for 1963 . 9

Estimating Tree Numbers for rth Year ........ 12




STATISTICAL RELIABILITY OF ESTIMATES. . 13

Estimated Variances. .. 14




SOME REMARKS. .......... .. 18


SUMMARY ., c C . o o c e 0 .. 19









A CONTINUING SURVEY FOR ESTIMATING CURRENT NUMBERS
OF FLORIDA CITRUS TREES


Roy Go Stout* and Jo W0 Todd**



INTRODUCTION


During the three year period (1954-57) a complete enumeration was

made of the citrus trees in Florida, This tree census provided a more

complete breakdown of citrus tree numbers than had.ever been previously

available. These data.became extremely valuable to those who estimate

the size of the crop and for business leaders in the industry,, Today,

various business firms are requiring greater and greater accuracy in

current tree count .information, The Division of Plant Industry's job of

disease control and.inspection requires ever increasing-accuracy of tree

numbers and locations and.the .Crop and Livestock Reporting Service re-

quires increased accuracy in tree.numbers for predicting the forthcoming

production as they rely more on objective methods of making estimates. l/



* Formerly Assistant Agricultural Economist, Florida Agricultural
Experiment Stationso

** Agricultural Statistician, Florida.Crop and Livestock Reporting
Service,

I/ Roy G, Stout, "Estimating Citrus Production by Use of the Frame Count
Survey" Journal.of Farm Economics, Volo XLIV, ppo 1037-1049o

Roy Go Stout, Size of Fruit and Droppage Rates.Influence Total Citrus
Production, Agricultural Economics Report 62-2, Florida Agricultural
Experiment Stations and Florida Crop and Livestock Reporting Service,
July, 1961i

B Wo Kelly, "Objective Methods for Forecasting Florida Citrus Pro-
duction" Estadistica .Journal of the Inter-American Statistical
Institute, .March, .19580










Since the completion of the enumeration of 1957, freezing weather,

removal of groves for industrial and residential development, .and the

movement of several million trees from nursery, indicates a need for

updating this .information, 2/ However, the cost of making a complete

enumeration of tree plantings and removals necessary to keep this census

up to date on an annual basis is prohibitive A system of continual

sampling has been.employed as .an.alternative .to complete enumeration,

The objectives of this paper are to: (1) describe the procedures

that are currently being used to.estimate tree numbers, and (2) estimate

the statistical reliability of the estimated tree numbers,


PROCEDURES


The current.sampling plan is designed so that 20 percent of all

citrus and potential citrus -sections are covered each year This will

give complete coverage in five years Basically the sampling plan con-

tains two component parts .in updating the 1954-57 census information0

One is a sampling of land .sections that .contained citrus in the 1954-57

census and the second component.is sampling all land sections considered

to be suitable for plantings but .contained no citrus in the last census

The first survey work.was .commenced.in 1960o Estimates of tree numbers

for 1961, 1962 and 1963 have been completed,






2/ Zach Savage, Movement of Citrus Trees from Florida Nurseries, July lI
1928 to June 30 19623 Agricultural Economics Mimeo Report 63-3,
Department of Agricultural Economics, Florida Agricultural Experiment
Stations, November, 1962o










Sampling of Old Citrus Sections


In preparing the basic sampling maps, every section showing commer-

cial citrus in the 1954-57 census was numbered 1 through 5 in a serpentine

manner in each.countyo 3/ Each year 20 percent of these sections are

visited For example, the first year all sections.numbered five and the

second year all sections numbered two were visited, Records for all com-

mercial groves from the 1954-57 census are used and every commercial grove

listed at that time is visited and a record is made regarding the present

existence or non-existence of the grove

A rate of change in tree.numbers in all groves remaining that existed

in 1957 was made by re-counting trees in a sample of approximately 550

of these remaining groves, This number changes slightly each year due to

rounding to whole numbers within counties, (It was 543 in 1961c) These

sample groves were completely enumerated and.the grove information matched

with 1954-57 information for the same groves to determine a rate of change

in numbers .and other related information A minimum of ten commercial

groves was included in the sample for each county providing there were

that many groves in the sample land sections The number of sample groves

in the larger citrus counties was determined by the ratio of the number of

groves in the county to.the total groves in those counties,

In these old citrus sections all.complete new groves planted since

the 195a-57 census were completely enumerated,. The sample information

for old citrus sections is shown.in the first four columns of Table lo



3/ A commercial grove is all grove property that one .man or organization
owns in a given section,











Table lo--Total and 1961 Sample Number of Sections and Groves
in Florida Citrus Survey by County


Old Citrus Sections


New Citrus
Sections


"Non-citrus"
Sections


Total No, of Total. No, of. Total No, of Total No, of
County Sec- Sec, in Groves Groves in Sec- Sect in Sec- Sec, in
tions Sample in.Co. 161 Sample tions '61 Sample tions '61 Sample


Alachua
Brevard
Broward
Charlotte
Citrus
Clay
Collier
Dade
DeSoto
Duval
Flagler
Glades
Hardee
Hendry
Hernando
Highlands
Hillsboro
Ind, River
Lake
Lee
Manatee
Marion
Martin
Okeechobee
Orange
Osceola
Palm Beach
Pasco
Pinellas
Polk
Putnam
Sarasota
Seminole
Sto Johns
St, Lucie
Sumter
Volusia

Total


23 4
208 41
36 7
35 7
51 10
0 0
2 0
98 19
151 30
12 2
5 1
0 0
292 58
18 3
90 18
125 25
467 93
120 24
619 124
61 12
168 33
192 38
20 4
13 2
440 88
181 36
36 7
282 56
120 23
859 171
128 25
38 7
175 35
22 4
116 23
66 13
233 46

5502 1089


53
1027
196
63
110
0
4
545
613
63
6
0
1304
54
312
863
2332
757
4712
156
421
827
25
17
3568
533
42
1344
695
5242
509
108
958
54
674
105
1061

29353


10
10
10
10
9
0
0
123
10
9
1
0
13
3
9
9
24
10
47
9
9
10
6
4
37
10
8
14
9
53
9
10
9
10
10
9
10

543


25
65
16
22
70
45
2
86
47
0
28
16
194
12
88
89
136
40
142
20
99
64
37
25
44
144
54
111
ill
19
169
74
15
60
22
66
90
51

2287


5
12
3
4
14
9
0
17
9
0
5
3
38
3
17
17
27
8
27
4
19
12
7
5
8
48
10
22
4
33
14
3
12
4
13
18
10

464


317
539
364
157
370
0
450
210
480
0
92
477
144
200
203
761
369
253
155
776
487
615
486
683
434
946
389
359
82
989
311
473
96

406
384
632

14089


7
11
7
11
8
0
9
4
9
0
2
10
3
4
4
15
8
5
3
16
10
13
10
14
9
19
8
7
2
20
7
10
2

8
8
13

296










Sampling of New Citrus Sections


A complete listing was made of all sections that showed land suit-

able for citrus, but did not contain citrus in the 1954-57 census, This

classification was made by use of aerial photographs, soil conservation

maps and consulting with various professional people in each county,

These sections were numbered from one to five in a serpentine manner in

each county and each year one-fifth of these sections are covered and

all plantings .are completely enumerated,

Since this classification of land sections included subjective eval-

uation, a check on the classification was made.by sampling the "non-citrus"

sections, A two percent sample of these "non-citrus" sections is checked

each year During the two years of operation, citrus has been found in

less than 10 of these "non-citrus" sections The last four columns of

Table 1 show the total and number of sample sections.for the new and

"non-citrus" components of the over-all sampling plan,

Dade County, because of local problems, was handled differently.

This .county produces nearly all the state's Persian Limes and avocados

that are sold commercially, as well as a sizeable part of the lychees and

mangos Donna, the 1960 hurricane, struck through the center of this

area causing considerable damage, and it.was deemed necessary to enumer-

ate completely all trees in the sample sections in this county,

As field work is completed by counties, all reports are edited and

punched on IBoM, cards. This information is then summarized and expand-

ed to an estimate of the total trees.for each county,







6


ESTIMATING TREE NUMBERS


The following equations were used to expand the field data to esti=

mates of tree numbers by counties0


Citrus Tree Numbers for 1961


For tree numbers in old groves;


Y = X (1)
A o E i
T Xi

Where Y = 1961 estimate of number of trees for th county in old
groves

Yi = number of trees in ith sample grove in cth county in
1961o

xi = number of trees in ith sample grove in cth county in
1957o

X, = total number of trees in cth county in 1957o


For tree numbers in new grove plantings in old and new sections;

^ 1
Ycn Xj (2)
fn

A
Where Ycn = number of trees in new groves in cth county,

Xj = number.of trees in jth section

f = sampling rate = o2


So, Yen = 5 Xj (3)



For total trees by county;

A A A
Cc = Yo + Yn 4)







6


ESTIMATING TREE NUMBERS


The following equations were used to expand the field data to esti=

mates of tree numbers by counties0


Citrus Tree Numbers for 1961


For tree numbers in old groves;


Y = X (1)
A o E i
T Xi

Where Y = 1961 estimate of number of trees for th county in old
groves

Yi = number of trees in ith sample grove in cth county in
1961o

xi = number of trees in ith sample grove in cth county in
1957o

X, = total number of trees in cth county in 1957o


For tree numbers in new grove plantings in old and new sections;

^ 1
Ycn Xj (2)
fn

A
Where Ycn = number of trees in new groves in cth county,

Xj = number.of trees in jth section

f = sampling rate = o2


So, Yen = 5 Xj (3)



For total trees by county;

A A A
Cc = Yo + Yn 4)









A
Where Cc = total number of trees in cth county.

and for the state;




A
T = 'C (5)

Where T = estimated total number of trees in the state


Citrus Tree Numbers for 1962


The second 20 percent of the land sections and associated sample of

groves in these.sections were surveyed in 1962o Estimates of tree numbers

were derived for 1962 utilizing the data from both the 1961 and 1962 sam-

ple data, In order to combine the two samples, the one year old trees

were removed from the 1962 sample and an estimate of the number of one

year old trees was made from the sample alone. Once the one year old

trees were removed from the 1962 sample it was the equivalent of a second

sample for 1961, hence, the two samples were combined for estimating coun-

ty and state totals Then the estimated number of one year old trees was

added to give the final estimate for the 1962 season, Equation (1) was

extended as follows to estimate the number of trees in old groves in 1962


A Yil+ Eyi2 ,Pi2 Pi2
Y = ------- + Xc (6)
oxil xi2 C Xi2

Where Yco = 1962 estimate of number of trees for cth county,

yil = number of trees in ith sample grove in cth county in
1961.

Yi2 = number of trees in ith sample grove in cth county in
1962.









Pi2 = number of one year old trees in ith sample grove in cth
county in 1962o

il = number of trees in 1957 in the 1961 it sample grove in
cth county

xi2 = number of trees in 1957 in the 1962 ith sample grove in
cth county

Xc = number of trees in county in 1957,


The procedure for estimating the tree numbers in new grove

consists of extending equation (2).


Ycn = Xjl


1 ( Xj2 P ] + -
f2 ( 2 f2


plantings


LPj2 (7)


A
Where Y n= number of trees in new groves in cth county in 1962-

Xjl = number of trees in jth sample section in 1961o

Xj2 = number of trees in jth sample section in 1962c

Pj2 = number of one year old trees in jth sample section in
1962

fl = sampling rate in 1961 = o20o f2 = sampling rate in
1962 = .,2


Since fl = f2, equation (7) becomes;


Ycn 2,5 [ Xjl + Z Xj2 Pj2j + 5 2Pj2


The total number of trees for each county and the state for 1962 was then

estimated as indicated in equations (4) and (5),










The total number of trees for all citrus, all orange, and all grape-

fruit for 1961, 1962, and 1963 by counties as estimated by foregoing pro-

cedures and for 1957 as reported from the complete census, are shown in

Tables 2 and 3. 4/


Citrus Tree Numbers for 1963


The freezes of December 12-14, 1962 caused considerable damage to,

and killed outright, many citrus trees. Consequently, it was decided to

prepare estimates of tree numbers for 1963 based only on survey data con-

ducted following the freeze. It was .alsofelt that the normal 20 percent

of sections and the approximately 550 groves would not be sufficient in

size due to greater variability between groves brought about by the

freeze,




4/ Some writers have indicated that the simple ratio estimates by strata
should not be used if the sample size is small, William Go Cochran,
Sampling Techniques, John Wiley and Sons, Inc,, New York, 1953,
pp .130-313. Morris He Hansen, William No Hurwitz, William G, Madow,
Sample Survey Methods and Theory, Volo 1, John Wiley and Sons, Inc,,
1953, ppo 198-200o One reason for this warning is that if there is a
bias in these small samples and the bias is accumulated over all
strata, there may be.a considerable error in the total0 Cochran says
that unless there is good empirical evidence to the contrary, a
combined ratio estimate is to be recommended. The combined ratio
estimate does not give ratio estimates for the strata (in this case,
the county), but only a total for the universe0. To compare these two
methods each county was expanded on a direct estimate for 1957 and
1961o These estimates were summed for the state and these totals
used to form the combined ratio estimate.for the state This com-
bined ratio times 1957 tree numbers gave the 1961 estimate, The es-
timate for all citrus trees for the state in groves that existed in
1957 by use of the stratified ratio estimate as described in this
report was 44,301,200 trees, The combined ratio procedure gave an
estimate of 44,321,300 total .citrus trees, a difference of 20,100
trees or about 005 percent0 The difference in the two procedures for
all oranges was lo6 percent and for all grapefruit it was 4ol percent










Table 2,--Total Number of
Census in 1957,


Trees for All Citrus by Counties from Completed
and Estimated for 1961, 1962, and 1963


County


Alachua
Brevard
Broward
Charlotte
Citrus
Clay
Collier
Dade
DeSoto
Duval
Flagler
Glades
Hardee
Hendry
Hernando
Highlands
Hillsboro
Indian River
Lake
Lee
Manatee
Marion
Martin
Okeechobee
Orange
Osceola
Palm Beach
Pasco
Pinellas
Polk
Putnam
Sarasota
Seminole
Sto Johns
St, Lucie
Sumter
Volusia
Others

State


1957


1961
(Number of


42
1126
355
89
114
2
3
641
721
10
6
0
1483
45
572
1654
2458
1266
7825
177
653
1104
133
17
5197
884
114
2334
1041
8494
377
163
1116
29
1990
171
1080


43486


24
1345
285
84
132

2
354
676
5
7

2398
83
869
1986
3936
1442
8796
134
740
1407
326
24
4963
1222
110
2281
915
9383
412
145
1394
21
2207
247
964


49219


1962
Trees in Thousands)

31
1.511
305
107
146
3
62
327
858
6
12
28
2513
143
875
2016
3821
1731
9696
148
984
1131
573
40
4831
1354
122
2803
741
9453
385
135
1448
19
2545
255
998


52156


0 = less than 1,000


-= no citrus,


a/ Included in Others for 1963e


1963


a/
1595
352
200
96
a/
155
346
1011
a/

76
2268
208
761
2007
3519
2182
7517
170
987
747
1276
110
4098
1095
165
1825
450
9241
306
164
1075
a/
3242
179
888
36

48348










Table 3,--Total Number of Trees for All Orange and All Grapefruit by
Counties from Completed Census in 1957, and Estimated
for 1961,.1962, and 1963

County All.Orange All Grapefruit
1957 1961 1962 1963 1957 1961 1962 1963
(Number of Trees in .Thousands)

Alachua 38 22 28 a/ 2 1 2 a/
Brevard 736 893 1054 1134 305 360 345 319
Broward 295 209 243 292 46 66 50 48
Charlotte 49 44 92 179 9 6 4 7
Citrus 96 114 130 87 8 4 4 1
Clay 1 1 a/ 0 a/
Collier 2 1 62 150 1 -
Dade 64 22 20 18 31 5 5 5
DeSoto 586 562 758 879 100 82 58 50
Duval 8 4 4 a/ a/
Flagler 5 5 10 a7 0 1/
Glades 0 28 76 0 0
Hardee 1356 2247 2353 2132 75 48 51 44
Hendry 35 78 131 195 7 2 7 8
Hernando 465 785 758 667 36 17 11 5
Highlands 1160 1635 1619 1568 312 158 183 197
Hillsboro 2006 3427 3331 3027 252 231 210 185
Indian River 431 525 687 1098 756 813 937 964
Lake 5816 6608 7338 5681 1106 1073 1037 772
Lee 106 94 102 124 45 19 25 22
Manatee 396 483 721 753 187 161 171 124
Marion 997 1344 1080 716 56 23 19 15
Martin 101 270 510 1056 10 12 38 33
Okeechobee 14 20 35 75 2 2 3 16
Orange 4232 4047 4014 3426 322 219 234 160
Osceola 740 1109 1222 984 56 41 47 49
Palm Beach 69 67 74 115 25 24 25 24
Pasco 1982 2002 2442 1563 203 126 155 124
Pinellas 477 448 401 279 495 405 295 142
Polk 5758 6983 7085 7092 1934 1566 1577 1462
Putnam 317 356 338 258 17 16 12 12
Sarasota 122 109 112 139 35 30 16 16
Seminole 888 1169 1252 883 83 71 47 45
Sto Johns 26 17 16 a/ 1 1 1 a/
St. Lucie 951 1190 1436 197'4 813 731 778 917
Sumter 154 236 235 156 5 6 6 3
Volusia 875 820 830 749 67 44 41 34
Others 29 1

State 31352 37944 40552 37554 7402 6363 6394 5799

0 = less than 1,000o = no citrus,


a/ Included in Others.for 1963o










In order to obtain a larger sample for estimating tree.numbers,

additional crews were employed and.the sample that was surveyed just

prior to the freeze in 1963 was re-surveyed in 1963, In addition, the

sample that was normally scheduled for 1963 was also completed, Thus,

tree numbers for 1963 were based on an equivalent.two year sample using

formulas as described for estimating the tree numbers in 1962o Those

few counties that completely escaped freeze damage were not re-surveyed,

Estimates for these counties .in 1963 were based on three years of survey

information,

During the first two years of the survey tree ages were assigned

according to size of bearing.surface, This procedure would create prob-

lems in estimating tree numbers for 1964 and later years For example,

in 1964 the problem would arise in equations 6, 7, and.9 in distinguish-

ing between the number of new plantings during the survey year and one

year old trees so classified.because of reduced bearing surface from

the freeze To adjust to this situation the actual age based on date of

planting was determined for each grove enumerated in addition to the

classification into age groups by size of bearing surface, In future

years the actual age grouping .will be used in estimating total tree num-

bers and the age groups by size .of bearing surface will be used to allo-

cate the total numbers into age groups


Estimating Tree Numbers for r'h Year


All information to the rth year can be utilized in preparing the

rth year estimate if the information .is adjusted for plantings between

the first and the rth year-










Equation.(6) can be re-stated in.general terms as follows;


g r

o i=1 j=1 Yij
cor x c
g r
i Z xij
i=1 j=l


g r-1



g r-I
LE Z ij+l
i=1 j=l


A
Where Y = estimate of number of trees in old groves for cth
county in rth year.

yij = number of trees in ith grove for jth sample year,

xij = number of trees for ith grove for jth sample year that
were present in 1957,

Xc = number of trees in cth county in 1957o

Pi j+l= number of trees in young plantings in ith grove for
jth sample year of ages one to ro

(Note, The first sample contains.the trees that were one year old

in 1961, hence, Pi,j+l rather than Pij)c

Equation (7) can be written in general form as;


A1 k r k r
Ycnr rf Xij + ) (j-1) Pij
r i=1 j=1 i=1 j=1


(10)


A
Where Y


Xij

Pij


= estimated number of trees of new plantings in cth
county for rth year,

= number of trees in ith section of jth year,

= number of trees in young plantings in ith grove for
jth sample year of agesone to ro


STATISTICAL RELIABILITY OF ESTIMATES


The systematic sampling procedure was used to select the sample sec-

tions and groves because of the greater ease in selecting the samples

and maintaining the information in an orderly manner for such a large










and continuing sample The effect of the systematic sampling on the var-

iance, in a few of the large counties, was found to be small0 Consequent-

ly, the variances in this report were not adjusted for this effect Also

the computations on the ratio variances become complex if adjustments for

this sampling plan.are made Since simple random sampling procedures us-

ually estimate larger variances than.systematic sampling and after study-

ing the two estimates in two large citrus counties, it was decided that

the systematic sampling component could be ignored without significant

change in the results, recognizing that any bias would likely be on the

high side,

The following equations .were used to compute variance and sampling

errors for the county and state estimates,


Estimated Variances


For old groves;
co 2 2
s (Yco) = (-f) yi + R xi 2Rc (11)
nco(nco-l)

2 A
Where s (Y ) = the estimated variance of the estimate of total
trees in old groves in 1961 in the cth county,

Nco = total number of groves in cth county in 1957,

nco = sample number of groves in cth county for 1961,

Yi
Rc --- for cth county,
xi

yi = number of trees in ith sample grove in cth county for
1961,

xi = number of trees in ith sample grove in cth county for
1957o

(l -f) = finite correction factor, f = sampling rate,










Equation (11) is also appropriate in estimating the variance for 1962,
2 2
but nco, Y xi, and x ii are combined for both years after the one year

old trees are removed from each grove as indicated in equation (6),

For new groves;


2 2
2 2 co 2 s cn
s2(Y ) = M (1-f) + M (l-f)
cn co m c mcn
co on


(12)


2 A
Where s (Y ) = estimated variance of the estimate of total trees in
new groves in 1961 in cth county

M c= total number of old citrus sections in cth county in
1957o

mco= sample number of old citrus sections in cth county in
1961o
2
s = variance of the number of trees per section in old
c citrus sections for cth county in 1961,

Mcn mcn, and s2 have similar meaning for new citrus sections
cn c cn
in 19610


The estimated variance .for new groves in 1962 requires equation (12)

to be modified to include the estimated variance of the number of one

year old trees,


2 A
Where.s (Yn)

M = M

2
s and
col


2
s and
co2


2 2 2 2
2 col co2 2 cnc 2 (_13)
,) = M (1-f) + M (l-f)
O m the cntota
co m co J Ln mcn


estimated variance of the total number of trees in
new groves in c county in 1962o

Smc, and mcn are as defined in equation (12)o

2
cn estimated variance of the number of two year old
and older trees in old and new sections in
1962o
2
s = estimated variances for one year old trees in
cn2 old and new sections in 1962o










For total trees;


2 A 2 A 2 A
s (C) = s ( ) + s (Y ) (14)
c co cn

Where s (C) = estimated variance of the total trees in cth county
for each year of 1961 and 1962,

2 A 2 A
s(T) = s (C) (15)
c
2 A
Where s (T) = estimated variance of .the total trees in the state
for each year of 1961 and 1962,


Sampling Errors


The relative sampling error.for each county.was computed by:


soeo = t x 100
Cc


and for the state by;

tOCVs (T)
see = x 100
A
T

Where tI = the small sample normal deviate value at A05 level


The sampling .errors for the .state estimates indicate that the state

figures on.all citrus, all orange and.all grapefruit are reliable figures

(Table 4), The counties with the larger number of trees show the smallest

sampling errors. Lake County, with nearly nine million trees, had the

lowest sampling error of 6o0 percent, .followed by Polk County with ten

million trees and a sampling error of 803 percent in 1961,

The combined samples for making the 1962 estimates improved the reli-

ability of most county estimates as well as increasing the precision of










Table 40--Relative Sampling Errors of Estimated Total Number of All


Citrus, All Orange and
and State


All Citrus
1961 1962
(Percent)


All Grapefruit Trees,
of Florida by Years*


All Orange
1961 1962
(Percent)


by Counties


All Grapefruit
1961 1962
(Percent)


Alachua
Brevard
Broward
Charlotte
Citrus
Clay
Collier
Dade
DeSoto
Duval
Glades
Hardee
Hendry
Hernando
Highlands
Hillsboro
Indian River
Lake
Lee
Manatee
Marion
Martin
Okeechobee
Orange
Osceola
Palm Beach
Pasco
Pinellas
Polk
Putnam
Sarasota
Seminole
St, Johns
Sto Lucie
Sumter
Volusia

State


* CC = 005


County


22ol
13o8
57,5
905
10305


219o1
14o6


3800

24o5
14o1
15o5
12o7
6,0
2408
14o9
16o5


12,6
2062
15o8
14ol
25o7
8o3
15o6
1403
23,8
22o2
906
29o0
23o0


4,3


2200
22l1
20o9
3504
55o6
7202
7203
30o2
26o7
37,8
145,7
10,4
35o2
15ol
804
12.1
11.1
6,7
16o4
12o7
22o5
31,9
25.4
604
13o3
702
10,4
10o9
600
14o6
14o6
33ol
13o9
11o5
13,0
12,2

2,7


2303
21ol
5906
17o6
117 4


4708
12ol


3103

29o8
16o7
20o7
16,3
18,6
1804
14ol
19,6


2209
11,8
11,2
17,2
55,2
71ol
18ol
17o4
2704
22,7
18,0
35,5
26,9

409


2203
2602
21o2
4709
5800
81ol
7404
4602
29,1
25o5
145 7
9,3
3608
15o6
1001
16o9
17,4
9,7
25,6
17o5
3207
41ol
31o2
6,4
507
7,2
10o5
4309
806
14,7
18,4
38o8
15ol
14,0
13o3
2006


85,8




48,1
41,3





20o8
10o7
lo3
904
27,1
6,2



54,0
62,3
3,8
2602
20,0
13o6

53o2


10,5


87o8

34o6
16,8
71o4


4402
30o6


19,1
10o2
170,3
26,3
19o6
703
1004
20,3
4o6
83ol
77,5
7,2
22,9
28o0
3,7
31,6
17o6
7o6
2608
74o2
7,8
27,5
6,0
2202
4807


3o6










the state estimates Slightly over 50 percent of all citrus trees are

in counties with a sampling error of nine percent or less and 70 percent

in counties with a sampling error of 12 percent or less, By type, 37

percent of the orange and 56 percent of the grapefruit trees were in

counties with sampling errors of nine percent or less and 64 and 72 per-

cent respectively in counties with sampling errors of 12 percent or less

Sampling errors for the 1963 estimated tree numbers were not com-

putedo It is likely true that the freeze created greater variation in

estimated tree numbers, thereby, causing sampling errors in 1963 larger

than in 19620


SOME REMARKS


In conducting a continuous survey of this type, several problems

are encountered One problem, as indicated by the sampling error of

the counties with small number of trees, is having tree numbers that

may be smaller than the previous year, even though no layman type ex-

planation is available This was not too serious a problem.in deriving

estimates for 1962 although it may be more of a problem in future years.

One way of handling this would be to publish data every other year, but

the industry is extremely interested in this information being released

on an annual basis The service aspects of such a report may justify

editing the figures to make the published figures remain in line, Large

groves and large new plantings, as are presently taking place in the

lower east coast counties, particularly Martin, will undoubtedly give

estimates in some years that will not be in line with the previous year's

estimate, In such cases an "educated" editing of the data.may be in

order









The amount of field work would, and sampling errors could., be re-

duced somewhat if some more elaborate design were used in classifying

and sampling the potential citrus land sections, since trees are found

in only about 25 percent of the sections However, this visiting these

large numbers of sections with no trees does not effect the estimate of

the tree numbers and the present scheme fits the needs of the Division

of Plant Industry's disease.and pest control program and it reduces the

possibility of missing new sections containing citrus,

All field work is performed by employees of the Division of Plant

Industry, largely composed of five crews of two men each, traveling in

jeeps that maneuver in and out.of most groves0 Considerable information

on root stocks, diseases, spacings, .etc, is obtained in addition to the

tree numbers by age and variety The annual cost of the survey and tab-

ulations is about $85,000, The complete census in 1954-57 cost about

one-third of a million dollars With increased wages and other costs,

such an undertaking would be considerably more today0 Therefore, con-

sidering that the needs of the Division of Plant Industry are met as

well as obtaining data for a continuous updating of the number of citrus

trees, the costs of the present survey seem to be well justified,


SUMMARY


This report has discussed a procedure for updating tree numbers on

an annual basis from a date of complete enumeration and some statistical

analysis of the reliability of these estimates0 Estimates for the years

1961, 1962, and 1963 have been completed and field work for the 1964 sea-

son is under wayo The analysis indicates that the estimated state numbers







20


are quite reliable and that the estimates in most counties are suffi-

ciently accurate for many business.decisions and sampling procedures,

The reduction in the sampling errors as additional years are incorpor-

ated into the estimates should increase the reliability of the tree

numbers beyond the level presented in this report,




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