GEORGIA HIGHER EDUCATION FACILITIES COMMISSION
FACILITIES INVENTORY AND ENROLLMENT STUDY FALL " 1968
REPORT NO.2:
A Projection of Georgia
Public High School Graduates to 1980
Prepared under the Comprehensive Planning Grant Program of the Higher Education Facilities Act of 1963, as amended.
September, 1970
Dr. Harmon W. Caldwell, Chairman
Members:
John D. Corner James A. Dunlap Dr. Rufus C. Harris Dr. Waights G. Henry, Jr. Dr. Benjamin Mays
Macon, Georgia Gainesville, Georgia Macon, Georgia LaGrange, Georgia Atlanta, Georgia
Officers:
Alex Crumbley, Legal Counsel Shealy E. McCoy, Treasurer William E. Hudson, Executive Secretary Parks A. Dodd, Jr., Associate Executive Secretary
Report prepared by C. L. Hohenstein & Associates
A PROJECTION OF GEORGIA PUBLIC HIGH SCHOOL GRADUATES
TO 1980
GEORGIA, HIGHER EDUCATION FACILITIES COMMISSION
I
805 Candler Building
Atlanta I Gear (Jia
30303
September; 1970
Sununary List of Tables List of Figures
CONTENTS
Page
5 3 4
1.0 General Introduction
6
1.1 Purpose
6
1.2 Approach and Order of Presentation
6
2.0 Projection by Trend Line Extension
7
2.1 General
7
2.2 Projection of Public High School
7
Graduates by Trend Line Extension
2.3 Projection of the Four-Year Moving Sums 11
of Public High School Graduates by Trend
Line Extension
3.0 Projection by Survival of Cohorts
1'5
3.1 General
15
3.2 Student Migration
15
3.3 Cohort Survival, First Grade to
19
Graduation
3.4 Cohort Survival, First Grade to
22
Fifth Grade and Fifth Grade to
Graduation
4.0 Analysis Comparison and Conclusions
35
-2-
Appendix 1 - Work sheets for trend line extension of annual graduates
Appendix 2 - Work sheets for trend line extension of four-year moving sum
Appendix 3 - Work sheets for trend line extension
of cohort survival ratios, first
grade to graduation
1 - grad
Appendix 4 - Work sheets for trend line extension
of cohort survival ratios, fifth
grade to graduation
5 - grad
Appendix 5 - Work sheets for trend line extension
of cohort survival ratios, fifth
grade to graduation
1-5 - grad
Not attached - available upon request.
-3-
Table 1 Table 2 Table 3 Table 4 Table 5 Table 6
Table 7 Table 8 Table 9
Table 10 Table 11 Table 12
List of Tables
Georgia Public High School Graduates
Page 8
Georgia Public High School Graduates
Projection by Least Squares Regression
Line
10
Georgia Public High School Graduates
Projection of Four-Year Moving Sum
by Regression Line
12
Student Migration - Georgia Public
Schools
16
Georgia Public Schools Net Enrollments
and Survival Ratios - First Grade
Through Graduation
20
Georgia Public High School Graduates
Projection Based on First Grade
Enrollments and Projected Survival
Ratios
23
Georgia Public School Net Enrollments
and Survival Ratios - First Through
Fifth Grade
24
Georgia Public School Net Enrollments
and Survival Ratios - Fifth Through
Graduation
27
Georgia Public High School Graduates
Projection Based on Actual and
Projected Fifth Grade Enrollments and
Projected Survival Ratios
29
Comparison of Georgia Survival Ratios
and National Estimated Retention
Rates - Fifth Grade Through Graduation
30
Georgia Public Righ School Graduates
Department of Education Projection
32
Comparison of Projections of Georgia
Public High School Graduates - Number
of Georgia Public High School
Graduates
34
-4-
List of Figures
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8
Georgia Public High School Graduates Annual Graduates
Georgia Public High School Graduates Four-Year Moving Sums
Georgia Public Schools Student Migration
Georgia Public Schools Cohort Survival Ratios First Grade Through Graduation
Georgia Public Schools Cohort Survival Ratio First Grade Through Fifth Grade
Georgia Public Schools Cohort Survival Ratio Fifth Grade Through Graduation
Comparison of National and State Retention Rates Fifth Grade Through Graduation
Georgia Public High School Graduates Comparison of Projections
Page 9
13 17 21 25
28
31 33
-5-
Summary
In this document the number of Georgia public high school graduates are projected each year through 1980. The purpose of this projection is to det~rmine the number of candidates for higher education in Georgia through 1980 for subsequent projection of enrollment in Georgia's institutions of higher education.
Three basic procedures were used for these projections:
(A) Extension of the high school graduate trend line by linear regression~
(B) grade survival of cohorts from first grade to fifth grade, then fifth grade to graduation, projecting both pairs of survival ratios by linear regression and deriving the graduate forecast from the projected survival ratios~ and
(c) grade survival of cohorts from first grade directly to graduation projecting the survival ratio by linear regression and then deriving the graduate forecast based on the projected survival ratios.
All three projections yield reasonably close results. The projection produced by B (above) was selected as the most valid. The 1980 projection of this procedure is 79,319 high school graduates. The probable error
range for the forecast is 2,804 students. Because
of the proximity of projections A and C to this error range, there is a reasonable basis for considering projections A and C to be probable error boundaries of projection B.
Table 12 is a comparison of all three projections.
-6- .
1.0 General Introduction
1.1 Purpose. The purpose of this report is to describe the investigations conducted relating to a projection of public high school graduates in Georgia through 1980. Based on the assumption that recent high school graduates form the bulk of students in higher education institutions, a projection of high school graduates is needed.
1.2 Approach and Order of Presentation. Two approaches to this projection are used. One is an extension of the existing trend of high school graduates over time without regard to any other factors other than the established trend.
The second projection approach is a grade-tograde cohort survival procedure. As of the date of this report, a projection of high school graduates through 1980 requires only a projection of 1969 first grade enrollments which isa relatively riskless estimate. Otherwise all students who will be graduated between now and 1980 are presently enrolled in school systems.
Trend line extensions are made first in Section 2.0, and the projection by cohort survival is Section 3.0. Each of these sections contain an analysis and discussion of the procedure used and the results. Both procedures are analyzed and discussed in Section 4.0 and a composite projection is made.
-7-
2.0 Projection by Trend Line Extension
2.1 General. Two types of trend line extension are made. The first by extending the actual number of public high school graduates for each year, and the second by extending fouryear moving sums of high school graduates for each year. The four-year moving sum (FYMS) is the sum of high school graduates for an indicated year, plus the sum of those in the prior three years. The FYMS may be correlated with total high education enrollment which in part is made up of the most recent Georgia high school graduates plus those of the preceding three years.
In both instances the trend line extension have been made by fitting the historical time series to an equation using the least-squares technique. This equation is used to establish the 1980 high school graduates projection.
2.2 Projection of Public High School Graduates by Trend Line Extension. Table 1 shows Georgia actual public high school graduates from 1950 through 1968. Figure 1 illustrates the past actual enrollments as circled points and the future trend as poin~enclosed by squares.
The trend was produced by a least squares fit of a regression line. The resulting coefficient of correlation was 0.972. Other essential statistical data regarding these computations appeam in Appendix 1. The computed regression line is:
GHS = 2215t - 97801
where GHS = projected Georgia public high school graduates in year t t = the unit and tens digits of the projection year. (i.e. 70 for year 1970)
The projection produced from this line is shown in Table 2. Additionally, the Four Year Moving Sum (FYMS) generated by this projection is shown.
-8-
TABLE 1 Georgia Public High School Graduates
YEAR OF GRADUATION
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
HIGH SCHOOL GRADUATES
19,760 14,958 14,980 20,599 22,880 23,656 25,298 26,984 27,590 31,152 34,127 36,200 36,014 36,259 43,254 51,708 51,842 53,140 53,370
FOUR YEAR MOVING SUM
70,297 73,417 82,115 92,433 98,818 103,528 111,024 119,853 129,669 137,493 142,600 151,727 167,235 183,063 199,944 210,060
Source: Georgia State Department of Education
-9100
90
80 I"tttlmmmE H-++++-+-1-+-t-+++++-+-1+H-++++-H+H-++++-H+!-+-+++-++-J+!-+-U+-+---+ ----+. --' +-j-'+-+++++++-H-+-IH
70
60
," 1-+++--1-----t--l---e--+--I---I-++++ -1-1-
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50
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t t t 1--+-++---+1--+-++---'-1--l---11-------4+1----1--1l-H--++----+-+I+---+-+--+-I+--+------+l+----1-+1- ----.+-1+-1+-+-1--++-+I--+4+---'It-t--++~-_ft~---++H--+--J--+-(+V+-+-++H-+-+++---+HJ---1+-+Hf-+--+++--+-.LH-+H--+H+--+-H++-+++++++-++++-+j-H+--+-j+-+-+-++j++-+++++---H+-H-++H++-+-++++-++++-++J+++++!-I+---++IH-+-++++-++++++++++-++J--H+-H1~
40
~ 30
s::
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~
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UJ
....I..,- .
I-+++++-.+.-k~-+f--H++-H+--H+-I-+--+--~l---+--I---t-+-++\+--+-1+++-I- Georgia
.I.:-+---HH-~++++-I--IH-+-+++++-HH--J-++-'
-+-I+-+--+-++--1-----t-l-e--+--l--+--tf _
Figure 1
Public High School Annual Graduates
Graduates
1l ~
~....10
H-++++-+-+-+-+-H-+-+-+-+-+-l --1-+++++
~+~ ++-H-+-I-+1--+-+-++-1= --f -. :
-I--+-+-+-+-H-I----I-I---l---+--t--l+- ;-+-:--[--1--t-++"--+i-
Legend
o
Actual Graduates
.(!)
""::qj:4-+--+-I-I--I-+-_'i---_I--i---it - ::ti1~if
0
Projection of Graduates by
r-tiFffi- 1---l--+-+=-1-+I_---=+-_-l--I+-_~-'---I--I----l--l--1---II--+----I1-----1I---f-----1t-=if+F_+~~+t-it+f-4+;-=t+-~l~tt--t1~!:i:rtJ-i+---r
;.Jt-l~I'=i-=ij:--I--t-+-+H-I:
Extension of Trend Line
i,,'- -H--__-=_-l-H--+-t-++++++++++++-J-++--H
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o
1950
55
60
65
70
75
80
Year of High School Graduation
-10-
TABLE 2
Georgia Public High School Graduates Projection by Least Squares Regression Line
YEAR OF GRADUATION
HIGH SCHOOL GRADUATES
FOUR YEAR MOVING SUM
1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
54,965 57,179 59,393 61,607 63,821 66,035 68,249 70,463 72,677 74,891 77,105 79,319
213,317 218,654 224,907 233,144 242,000 250,856 259,712 268,568 277,424 286,280 295,136 303,992
-11-
The pitfalls associated with basing projections on line trends only are many. In this case, the abnormal birth rate following World War II caused a substantial increase in high school graduates in 1964 and 1965. The line trend procedure assimilates this and other effects and incorporates the increase as a factor of the projection. The problems of depending solely on line trends are acknowledged but this procedure is recorded here for consideration along with subsequent techniques.
2.3 Projection of the Four-Year Movinq Sums of Public High School Graduates by Trend Line Extension. Table 1 lists the actual Four-Year Moving Sums (FYMS) of public high school graduates. The FYMS is of interest since it represents the generally accepted college-age population who are also basically qualified for college entry by graduation from high school.
A plot of the FYMS on a linear scale reveals exponential trend characteristics. The exponential character of the trend line is confirmed by (1) observation of the linear characteristics when these data are plotted on a semi-logrithmic scale (Figure 2) and by (2) the high coefficient of correlation produced by correlating the logarithms of FYMS with time (0.997530).
The statistical detail of the least squares computional results are contained in Appendix 2. The resulting regression line is
log Y = 0.03120t + 0.20076
where log y = log FYMS
t = the unit and tens digit
of the projection year (i.e., 70 for the year 1970)
Table 3 shows the projection of the FYMS for 1969 through 1980 based on this procedure. These results are shown graphically in Figure 2.
-12-
Table 3
GEORGIA PUBLIC HIGH SCHOOL GRADUATES PROJECTION OF FOUR-YEAR MOVING SUM BY REGRESSION LINE
Year
Log of FYMS
Four Year Moving Sum (In Thousands)
1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
2.35356 2.38476 2.41596 2.44716 2.47836 2.50956 2.54076 2.57196 2.60316 2.63436 2.66556 2.69676
225.7 242.5 260.6 280.0 300.8 323.3 347.3 373.2 401.0 430.9 463.0 497.3
-13-
Obviously all the reservations which apply to extending the historical trend line of annual public high school graduates also apply to extending the trend line of FYMS. This extension takes into account no other factors other than the past trend. It assumes that whatever forces have acted in the past will continue to act in the same manner in the future.
Because of the alarmingly high projections produced by this procedure, it appears that this curve must flex downward in the future. This trend is likely higher than that which will be realized, but it is not impossible to attain. It is nonetheless a signal which over the years should be watched.
1,000 10
700 7
60~
50q. 400
4
300
3
-14-
II
1200
2
_
100 1 90 9 80 8
rg :s:: III 70 7
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Figure 2
3
~tt~~~~t+~~~~pGeorgia Public High School Graduates Four-Year Moving Sums
20 2
Legend
()
Actual Four-Year Moving Sums
[J
Projection of Four-Year Moving
Sums by Extension of Trend Line
55
60
65
70
75
80
Year of High School Graduation
-15-
3.0 Projection by Survival of Grade Cohorts
3.1 General. Because 1979 high school candidates for graduation are enrolled as first graders in the 1967-68 school year, it is possible to project future graduates by forecasting the survival of the cohorts of these students. Similarly, it is possible to project survival for any combination of intervening years.
Several projection procedures may be used based on the progression of students through the educational system. One is to compute grade-tograde cohort survival. This is, to project second graders based on the trend of the cohort survival ratio of first to second graders, then second to third and so on.
Similarly historical cohort survival can be computed based on age cohorts rather than grade cohorts. Another alternative method based on grade cohorts is to determine the cohort survival ratio directly of first graders to high school graduates. This is the principle method used here. In addition, so as to compare Georgia survival trends with national trends, fifth grade enrollments based on first grade cohort survival have been computed, and then high school graduates are computed based on the projected fifth grade cohort survival.
3.2 Student Migration. The use of survival ratios for forecasting future graduates requires either adjustments for net student migration or an assumption that it is constant. Table 4 lists these migration statistics and Figure 3 illustrates the pattern for Georgia.
Georgia's net student migration is relatively constant. It should be noted that up until the school year 1963-64 when migration data was collected for both Caucasian and Negro students, substantially all of the net gain was from Caucasian immigration. This acts to increase grade-to-grade survival ratio. A continuation
Table 4 STUDENT MIGRATION - GEORGIA PUBLIC SCHOOLS
Year
1961 1962 1963 1964 1965 1966 1967
Into Georgia Elem H.S.
19,558 21,550 20,429 20,788 23,439 24,873 23,760
5,297 5,650 6,044 5,850 6,737 7,052 8,340
Out of Georgia
Elem
H.S.
14,089 15,851 14,978 16,617 17,365 21,288 18,604
3,868 4,290 4,536 4,476 4,939 5,968 6,255
Net Elem
+5,469 5,699 5,451 4,171 6,074 3,585 5,156
Net High School
+1,429 1,360 1,508 1,374 1,798 1,084 2,085
Net Total
+6,898 7,059 6,959 5,545 7,872 4,669 7,241
I
I-' 0' I
Source: Georgia Department of Education
-17-
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-18-
of the net Caucasian immigration gain thus would not act to decrease the current substantially upward cohort survival ratio trend. It is also reasonable to assume that the reported immigration since 1963-64 consists primarily of Caucasian students and that no new forces are at work due to changed student migration patterns.
Consequently, for purposes of this projection it is assumed that the overall migration pattern is reasonably constant and has no significant effect on the projection as to require adjustments because of this factor.
-19-
3.3 Cohort Survival, First Grade to Graduation Table 5 indicates first grade enrollments and the cohorts of these first graders who graduated from Georgia's public high schools. The ratio of these graduates to their total first grade cohorts is the survival ratio. To eliminate decimals, this ratio has been multiplied by 1,000.
The trend of ratio can be observed in Figure 4. The strong linear characteristics of this survival ratio produce a regression line with a high coefficient of correlation (0.9919). This regression line is
where:
RHS = 24.745t- 1190
RHS = projected survival ratio
x 103 of high school graduates to first grade cohorts
t ~ the unit and tens digits of the projection year (i.e., 70 for year 1970)
The related'statistical detail is enclosed in Appendix 3.
Using this equation as a basis for projecting the survival ratio, the ratios contained in Table 6 are produced. Multiplying these ratios by actual first grade enrollments produces a graduate projection based on survival ratio trend through the graduating classes of 1979.
Upon analysis, it is obvious tllat actual first grade enrollments are relatively stable but gradually increasing since 1960 (see Table 6). Georgia's increase in public high school graduates comes from the steadily advancing survival ratio from the first grade to graduation.
Based on a continuation of this trend and the regression line produced, Georgia schools will graduate 78.~/o of the 1968-69 first grade cohorts as 89,000 graduates of the classes of 1980. Projections of the intervening years
-20-
Table 5
GEORGIA PUBLIC SCHOOL NET ENROLLMENTS AND SURVIVAL RATIOS, 1ST GRADE TO GRADUATION
School Year Pupils Entered
1st Grade
1940-41 1941-42 1942-43 1943-44 1944-45 1945-46 1946-47 1947-48 1948-49 1949-50 1950-51 1951-52 1952-53 1953-54 1954-55 1955-56 1956-57
1st Grade
149,334 143,176 136,770 131,430 130,076 132,198 125,263 118,543 120,182 118,217 109,703 103,910 111,546 118,869 113,775 108,614 106,563
Graduates
14,980 20,599 22,880 23,656 25,298 26,984 27,590 31,152 34,127 36,200 36,014 36,259 43,254 51, 708 51, 842 53,140 53,370
Year of Graduation
1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
Survival Ratio x 10 3
100 143 169 180 194 204 220 264 280 306 328 349 388 435 456 489 501
Source: Georgia Department of Education
-22-
are shown in Table 6.
At some time in the future the linear trend of this survival ratio will change and likely stabilize around some relatively constant value estimated to be in the 850-900 range. Thus a change in the linear characteristics of the survival ratio will likely occur after 1980.
3.4 Cohort Survival, First Grade to Fifth Grade and Fifth Grade to Graduation. The survival ratios of the first to fifth grades were calculated, along with those of the fifth grade to graduation. Table 7 lists these data, and Figure 5 illustrates the survival ratio.
A different pattern of cohort survival was observed. The survival ratio of first to fifth grade cohorts reached a maximum of 897 and then declined to 875 in 1967-68. It appears to be similar to an early stabilizing control curve, seeking a value of about 890.
Since this ratio appears to have stopped a consistant advance, an attempt to forecast further linear progression is not justified. A constant survival ratio of 0.890 has been used to project fifth grade enrollments from 1968-69 to 1972-73 which is necessary to ultimately obtain a 1980 graduate forecast by this procedure.
Table 8 lists actual and projected fifth grade enrollments and the resulting graduating cohorts. Figure 6 shows the trend of the fifth grade to graduation cohort survival ratio.
A regression line was fitted to these data and produced a coefficient of correlation of 0.98168.
The line computed is: y = 19.65t - 747.19.
where y = survival ratio of Georgia fifth
grape to graduating cohorts x 103
t = the units and tens digits of the
year
-23-
Table 6
GEORGIA PUBLIC HIGH SCHOOL GRADUATES PROJECTION BASED ON FIRST GRADE ENROLLMENTS AND PROJECTED SURVIVAL RATIOS
School Year Pupils Entered
1st Grade
1957-58 1958-59 1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68 1968-69
First Grade Enrollment
105,763 104,855 104,664 106,757 107,904 110,779 112,947 110,807 111,627 112,324 112,265 112,800(P)
Projection Year of
HS Graduation
1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
Projected Survival
Ratjo x J 03
517 541 566 591 616 640 665 690 715 739 764 789
Projected Graduates
54,679 56,726 59,239 63,093 66,468 70,898 75,109 76,456 79,813 83,007 85,770 88,999
(p) - Projected
Source: First Grade Enrollments through School Year 1967-68 from Georgia Department of Education; Other Data Projected.
-24-
Table 7
GEORGIA PUBLIC SCHOOL NET ENROLLMENTS AND SURVIVAL R~TIOS 1ST TO 5TH GRADE
School Year Pupils Entered
1st Grade
1945-46 1946-47 1947-48 1948-49 1949-50 1950-51 1951-52 1952-53 1953-54 1954-55 1955-56 1956-57 1957-58 1958-59 1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68 1968-69
1st Grade
5th
-Gr-ad-e
132,198 71,099 125,263 72,782 118,543 74,219 120,182 77,539 118,217 80,940 109,703 78,833 103,910 76,890 111,546 85,215 118,869 95,673 113,775 93,224 108,614 91,019 106,563 92,042 105,763 91,666 104,855 93,629 104,664 93,762 106,757 95,686 107,904 96,484 110,779 98,115 112,947 98,660 110,807 98,624 111,627 99,348 112,324 99,968 112,265 99,886 112,800(P}100,392
School Year Pupils Entered
5th Grade
1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 (P) 1969 (p) 1970 (p) 1971 (p) 1972 (P)
Survival Ratio x 103
538 580 626 645 684 719 740 765 806 821 839 865 869 895 896 897 894 886 875 890* 890* 890* 890* 890*
* Estimated Stable Value. See Figure 5
(p) = Projection
Source:
First Grade Enrollments through School Year 1967-68 and All Fifth Grade Enrollments from Georgia Department of Education; Other Data Derived or Projected.
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H--H-H-H-+++++-+-++-I~-r-+-~+++-e--+---+--
*~- 1--+-1-+-1-+-+--+-+--1-+--1--1--1---1-+--1--
Georgia Public Schools Cohort Survival Ratio First Grade through Fifth Grade t-t--r-+ir-+ir-+i--H
1-" 0.2
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55
60
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70
75
80
Year of Fifth Grade Completion
-26-
This equation was used to project the survival ratio to 1980. Then using actual fifth grade enrollments through 1967-68, and fifth grade projected enrollment through 1972 based on the first to fifth grade projection, a graduate projection through 1980 was made which appears in Table 8.
It should be noted that the survival ratios of the first to fifth grade cohorts reached a maximum at about 900 and then declined slightly as if hunting for a point of stability.
The survival ratios of fifth grade to graduation cohorts is still consistently rising as student retention through high school graduation increases. Consequently increases in the number of high school graduates between 1969-1980 will likely result from better retention between the fifth grade and graduation rather than as a result of increased student population.
The trend of Georgia fifth grade to graduation survival ratios may be compared to national "retention rates" (Table 9). National retention rates are actually the survival through graduation per thousand fifth grade cohorts and are comparable to Georgia survival ratios.
Since the graduating class of 1950, these national retention rates have risen from 505 steadily to 721 in 1967 with no indication of change in rate of change. It is reasonable to anticipate that comparable state survival ratios also will continue to rise linearly at least to 721 without rate change. Further, the national experience le~ds credence to the possibility that the 1980 Georgia overall level of 789 is obtainable without stabilizing about a constant prior value. Thus credibility is also indicated for the graduate projection produced by that survival ratio.
Finally, it is interesting to note by inspection of Figure 7, that the state survival ratio seems to be advancing at a rate greater than the national rate and thus closing with the national retention rates. The trend indication is that they will be the same in 1981 at approximately 920.
-27-
Table 8
GEORGIA PUBLIC SCHOOL NET ENROLLMENTS AND SURVIVAL RATIOS, 5TH GRADE TO GRADUATION
School Year
Pupils Entered 5th Grade
Year of
Survival
5th Grade
Enrollment Graduates Graduation Ratio x 103
1942-43
70,083
19,760
1950
282
1943-44
68,599
14,958
1951
218
1944-45
66,746
14,980
1952
224
1945-46
68,493
20,599
1953
299
1946-67
67,985
22,880
1954
337
1947-48
68,147
23,656
1955
348
1948-49
70, 72 7
25,298
1956
35lS
1949-50
71,099
26,984
1957
380
1950-51
72,782
27,590
1958
379
1951-52
74,219
31,152
1959
420
1952-53
77,539
34,127
1960
440
1953-54
80,940
36,200
1961
447
1954-55
78,833
36,014
1962
457
1955-56
76,890
36,259
1963
472
1956-57
85,215
43,254
1964
508
1957-58
95,673
51, 708
1965
540
1958-59
93,224
51, 842
1966
556
1959-60
91,019
53,140
1967
584
1960-61
92,042
53,370
1968
579
Source:
First Grade Enrollments and High School Graduates from Georgia Department of Education; Other Data Derived.
-29-
Table 9
GEORGIA PUBLIC HIGH SCHOOL GRADUATES PROJECTION BASED ON ACTUAL AND PROJECTED FIFTH GRADE ENROLLMENTS AND PROJECTED SURVIVAL RATIOS
School Year Pupils Entered
5th Grade
Fifth Grade Enrollment
1961-1962 1962-1963 1963-1964 1964-1965 1965-1966 1966-1967 1967-1968 1968-1969 1969-1970 1970-1971 1971-1972 1972-1973
91,666 (A) 93,629 (A) 93,762 (A) 95,686 (A) 96,464 (A) 98,115 (A) 98,660 (A) 98,621 (p) 99,351 (p) 99,965 (p) 99,920 (p) 100,362 (p)
Year of Cohort
Graduation
1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980
Projected Survival Ratioxl0 3
608 628 647 667 687 706 726 746 766 785 805 824
Projected Graduates
55,732 58,799 60,664 63,823 66,270 69,269 71,627 73,571 76,102 78,412 80,435 82,698
A - Actual P - Projected
Source:
First Grade Enrollment Through 1967-68 from Georgia Department of Education; Other Data Projected or Derived.
-30-
Table 10
COMPARISON OF GEORGIA SURVIVAL RATIOS AND NATIONAL ESTIMATED RETENTION RATES
5TH GRADE TO GRADUATION
School Year Pupils Entered
5th Grade
1942-43 1944-45 1946-47 1948-49 1950-51 1952-53 1954-55 1956-57 1958-59 1959-60
Year of High School Graduation
1950 1952 1954 1956 1958 1960 1962 1964 1966 1967
Georgia Survival Ratio x 103
282 224 337 358 379 440 457 508 556 584
Estimated National
Retention Rate
505 522 553 581 582 621 642 676 717 721
Source:
National Retention Rate; U. S. Department of Health, Education and Welfare, Digest of Educational Statistics, 1967 Edition, Table 8. Other data derived.
1000
-31-
900
800
/
.- .
-
,
700 National Retention
Rate Per 1,000
!
Fifth Grade Students ,
--..
. . . . . .r
-
l/)
+s::J60 0
0' 't1
.B
tI)
0'
~pO ('(
J.l
C)
:5 .I.I.-.l
~
8o. 4 0 0
.-l
J.l 0' ll.
~300
~
...so...:.,:
s::.
.0..,' 2 0 0
~
Georgia Survival Ratio x 103
-
-
Figure 7
comparison of National
and State Retention Rates
I Fifth Grade Through Graduation
I - -.-
- ..
.. -
-
).00
0'
;;IV
55
5)
J)
J
)
In
Year of High School Graduation
-32-
Table 11
GEORGIA PUBLIC HIGH SCHOOL GRADUATES GEORGIA DEPARTMENT OF EDUCATION PROJECTION
Year of Graduation
1969 1970 1971 1972 1973 1974 1975
High School Graduates
54,908 55,897 56,887 57,877 58,867 59,857 60,846
Increase Over Previous Year
1,538 989 990 990 990 990 989
Source: Georgia Department of Education
100
-33-
90
. A - Projection by reqreSS-l.on
line of graduates.
,
I,
B - Cohort survival
,
80
first through fifth
grades and fifth
through graduation.
C - Projection by cohort
70
survival, first grade
through graduation based
on projected survival
rates.
60
D - Projection by Georgia
Department of Education.
C
B
A
/
D
50
(/)
'8
lIS
g(/)
~4 0
~ .r-l (/) Q)
+l
.glIS 30
lIS 1-1
t!) r-l
oo
'fi 2 ~
til "'l
',
.r-l
:I:
10
o
50
-
--
-','
Figure 8
Georgia Public High School Graduates
,
Comparison of Projections
,!
Legend
i,
0
Actual Graduates
,
I
55
60
D
Points on Indicated
Projections
_. -..- .
--
_.-
65
70
75
80
Year of High School Graduation
Table 12 COMPARISON OF PROJECTIONS OF GEORGIA PUBLIC HIGH SCHOOL GRADUATES
Number of Georgia Public High School Graduates
Projection Year of
HS Graduation
Trend Extension By Regression (Line A)
Cohort Survival lst-5th-Grad (Line B)
Cohort Survival 1st-Graduation
(Line C)
Forecast of Georgia Dept of Education
(Line D)
1969
54,965
55,732
54,679
54,908
1970
57,179
58,799
56,726
55,897
1971
59,393
60,664
59,239
56,887
1972 .1973 1974
61,607 63,821 66,035
63,823
63,093
57,877
I
66,270
66.468
58,867
w
~
69,269
70,898
59,857
I
1975
68,249
71,627
75,109
60,846
1976
70,463
73,571
76,456
1977
72,677
76,102
79,813
1978
74,891
78,412
83,007
1979
77,105
80,435
85,770
1980
79,319
82,698
88,999
-35-
4.0 Analysis, Comparison and Conclusions
In this section, a comparison is made of the three high school graduate projections prepared here and that of the Georgia Department of Education which appears in Table 11.
The five-year projection of the Georgia Department of Education is more conservative than any of those made here. The Georgia Department of Education projection is a linear extension of 1965-68 experience subsequent to the "baby boom" effect on high school graduates. This projection has validity in that it linearly projects the most recent fouryear experience. However, it should be noted that all of the procedures used here produced projections greater than these five-year forecasts.
Table 12 shows the projections resulting from the three main procedures used here, and Figure 8 comparatively illustrates these projections. All three projections have high correlation coefficients, and all three of the projections are relatively close.
The projection based on a regression line of the trend of graduates (Projection A) produces the most conservative estimate of those developed here. The procedure projecting the largest number of graduates is that of cohort survival of first graders directly with high school graduates. (Projection C)
It is important to note at this point that Georgia's increase in high school graduates over the next decade will apparently result from improved student survival through the school system rather than any substantial school-age population changes. In addition, student survival from the first to fifth grades seems to be stabilizing in the range of 900 fifth graders per 1,000 entering first grade cohorts. Thus, the bulk of the increase stems from survival from the sixth grade through graduation.
Because of this we believe the forecasting procedure using cohort survival based on first to fifth grade survival, then fifth grade to
-36-
graduation to be the logically superior approach for these projections.
Concerning the potential error of the estimate, the standard error of the estimate of projection A, which is least complicated to apply, is 2,941 students. Utilizing the normal curve area factor which produces a 9~~ confidence interval, (1.29), the 1980 potential error range is between 75,515 and 84,123 (about the mean of 79,319). This is a net range of 7,608 which appears to us to be reasonable (at three standard deviations the range is 8823).
The 1980 range between the lowest projection (line A at 79,319) and the highest projection (line C at 88,999) is 9,680, which approximates the dispersion about line A in 1980 calculated above. We believe this lends credibility to the use of Lines A and C as approximate boundaries of the actual high school graduate dispersion ~round line B in 1980. That is, we believe line A to be validly a minimum estimate and line C a maximum estimate.
The application of standard errors of estimate to the count of projected high school graduates is more complex since the forecasted statistic was survival ratio, and for line B is a two step forecast. Projected graduates were then derived from these projected survival ratios. We do not believe these computations would prove 9f additional value.
In summary, it is our opinion that:
(1) the 1980 projection error range will be approximately between 7,600 and 8,800 high school graduates;
(2) projection B is the most likely estimate of graduates; and
(3) lines A and C can function as conservative and optimistic estimates respectively.