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- -L--t++++-l+-l 50 1-+++--1-----t---+--l'---l--+---1-++---I---l----+--I--1-+---1-I-l-+++++-+-+--+-H--J-+++-H--+-H---l-+++-H---l--I--+-++++-H---l--I--+-++++-H--+-I--+-++-l 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:: 1tI U:o:Js ~ ~ .-1 2 0 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 ll--iHI-i_t-+++'--+t--'T-I+H+--\--l-+-i--+-+-t-t-t--H-++-++-H-++-I--t-H 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 !~ '.sj.::I CU III 60 I:I:sI 6 '-~-lt" -,--t--H---+---t-+--++-+-+--H-I-t---t- Ir-I !o iils-:!: irzl 40 4 I-! III ~ I Io:-:s! ~ - -- 30 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- 1 I ~II t:1 { \ \ \ \ \ \ \ \ \ \ I I I I t I I I ~. \ \ \ \ \ ~ ,J. :S .,,1I ~z ~I 'XI I I I I I I t I ,I I I I I I I ~ I I I I I I I I I I \ \ \\\ )\ ~\ ) / / / / / ( ,I I I I ~ J J I I I 1 \ \ \ I t I I I I L l/) r-l o0 s:: 'fi .8 U)-IJ CV) lIS U l-I -.-I :> 0.6 :~:s til o. 4 tt:tttttt-tttt-m-tttti+ttt-m++ttl-++t+t-H-t+-I-H++++H-t++~H-+++t-H++--J-t...H=l=I O. 3 H-H-H-t+t+++++++++++-I-+++++-I- I Figure 5 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 HII-----+++--+HI---+--I-+I---++-+--H+---++----I++-+---+++-!----I++-------+<+----+el--+--++-I----+~++-J--~-lEtt_ti~-fITl=l-_tI:t~=-_-=i-d-i1+:~n-Etf _ -r -~- - I +~ "1=t-1~fi~ ==1- =- -+-1_+-+-+-+-+-++-+-+ l++-++-H-+-H+++I ~-I -- -r-.-H-----j--H1-H-Hi-+-H--I--I l o 50 55 60 65 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.