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Projections of Education Statistics to 2021

NCES 2013-008
January 2013

Introduction to Projection Methodology: High School Graduates

Projections in this edition

This edition of Projections of Education Statistics presents projected trends in the number of high school graduates from 2009-10 to 2021-22. These projections were made using three models:

  • The National High School Graduates Model was used to project the number of public high school graduates, the number of private high school graduates, and the total number of high school graduates for the nation.
  • The State Public High School Graduates Model was used to project the number of public high school graduates for individual states and regions.
  • The National Public High School Graduates by Race/Ethnicity Model was used to project the number of public high school graduates for the nation by race/ethnicity.

Overview of approach

All the high school graduates models first calculated the number of high school graduates as a percentage of grade 12 enrollment based on historical data. Single exponential smoothing was used to project this percentage. The projected percentage was then applied to projections of grade 12 enrollment.

Assumptions underlying this approach

The percentage of 12th-graders who graduate was assumed to remain constant at levels consistent with the most recent rates. This methodology assumes that past trends in factors affecting graduation rates, such as dropouts, migration, and public or private transfers, will continue over the forecast period. No specific assumptions were made regarding the dropout rate, retention rate, or the rate at which alternative credentials are awarded. The combined effect of these proportions is reflected implicitly in the graduate proportion. In addition to student behaviors, the projected number of graduates could be affected by changes in graduation requirements, but this is not considered in the projections in this report.

For more details on the steps used for projections of high school graduates, see "Procedures used in all three high school graduates models," below.

Procedures used in all three high school graduates models

The following steps were used to project the numbers of high school graduates:

Step 1. For each year in the historic period, express the number of high school graduates as a percentage of grade 12 enrollment. This value represents the approximate percentage of 12th graders who graduate. For information about the specific historical data and analysis periods used for the National High School Graduates Model, the State Public High School Graduates Model, and the National Public High School Graduates by Race/Ethnicity Model, see the description of the appropriate model, later in this section of appendix A.

Step 2. Project the percentage of 12th-graders who graduate from step 1. This percentage was projected using single exponential smoothing with a smoothing constant chosen to minimize the sum of squared forecast errors. Because single exponential smoothing produces a single forecast for all years in the forecast period, the same projected percentage of grade 12 enrollment was used for each year in the forecast period.

Step 3. Calculate projections of the numbers of high school graduates. For each year in the forecast period, the projected percentage from step 2 was applied to projections of grade 12 enrollment to yield projections of high school graduates.

National High School Graduates Model

This model was used to project the number of public high school graduates, the number of private high school graduates, and the total number of high school graduates for the nation. Public and private high school graduates were projected separately. The public and private projections were then summed to yield projections of the total number of high school graduates for the nation.

For details of the procedures used to develop the projections, see “Procedures used in all three high school graduates models,” above.

Data used in the National High School Graduates Model

Public school data on graduates and grade 12 enrollment. Data on public school 12th-grade enrollments and high school graduates from the NCES Statistics of Public Elementary and Secondary School Systems for 1972-73 to 1980-81 and the NCES Common Core of Data (CCD) for 1981-82 to 2008-09 were used to develop national projections of public high school graduates.

Private school data on graduates and grade 12 enrollment. Data on private school 12th-grade enrollments for 1989-90 through 2009-10 and high school graduates for 1988-89 through 2008-09 were used to develop national projections of private high school graduates. The data were from the biennial NCES Private School Universe Survey (PSS) from 1989-90 to 2009-10 with data for 12th grade enrollment the same as the year of the survey and the data for high school graduates for the preceding year (i.e. the 2009-10 PSS presents high school graduates for 2008-09). Since the PSS is collected in the fall of odd-numbered years, data for missing years were estimated using data from the PSS. For 12th grade enrollment, estimates for missing years were linear interpolations of the prior year’s and succeeding year’s actual values. For high school graduates, estimates for the missing years were the interpolations of the high school graduates to estimated 12th grade enrollment percentages for the prior and succeeding years multiplied by the estimated enrollments for the current year.

Public and private school enrollment projections for grade 12. Projections of grade 12 enrollment in public schools and in private schools were used to develop projections of public high school graduates and private high school graduates, respectively. The grade 12 enrollment projections were made using the grade progression method. For more information, see Section A.1. Elementary and Secondary Enrollment, earlier in this appendix.

Accuracy of national high school graduates projections

Mean absolute percentage errors (MAPEs) for projections of graduates from public high schools were calculated using the last 21 editions of Projections of Education Statistics, while MAPEs  for projections  of graduates from private high schools were calculated using the last 10 editions. Table B, below, shows MAPEs for both public and private school graduation projections.

For more information, see Table B.

For more information about MAPEs, see Section A.0. Introduction, earlier in appendix A.

State Public High School Graduates Model

This edition of Projections of Education Statistics contains projections of public high school graduates from 2009-10 to 2021-22 for each of the 50 states and the District of Columbia, as well as for each region of the country. The state projections of high school graduates were produced in two stages:

  •  first, an initial set of projections for each state was produced; and
  •   second, these initial projections were adjusted to sum to the national public school totals produced by the National High School Graduates Model.

For each region, the high school graduate projections equaled the sum of high school graduate projections for the states within that region.

Initial set of state projections

The same steps used to produce the national projections of high school graduates were used to produce an initial set of projections for each state and the District of Columbia. A separate smoothing constant, chosen to minimize the sum of squared forecast errors, was used to calculate the projected percentage of 12th grade enrollment for each jurisdiction.

For details on the steps used to develop the initial sets of projections, see “Procedures used in all three high school graduate models,”earlier in this section of appendix A.

Adjustments to the state projections

Public school data on graduates and grade 12 enrollment at the state level. State-level data on public school 12th-grade enrollments and high school graduates from the NCES Statistics of Public Elementary and Secondary School Systems for 1980-81 and the NCES Common Core of Data (CCD) for 1981-82 to 2008-09 were used to develop these projections.

Public school projections for grade 12 enrollment at the state level. State-level projections of grade 12 enrollment in public schools were used to develop the state-level projections of public high school graduates. The grade 12 enrollment projections were made using the grade progression method. For more information, see Section A.1. Elementary and Secondary Enrollment, earlier in this appendix.

Accuracy of state public high school graduate projections

Mean absolute percentage errors (MAPEs) for projections of the number of public high school graduates by state were calculated using the last 16 editions of Projections of Education Statistics. Table A-10 on pages 104-105 show MAPEs for the number of high school graduates by state.

National Public High School Graduates by Race/Ethnicity Model

The projections of public high school graduates by race/ethnicity were produced in two stages:

  • first, an initial set of projections for each racial/ethnic group was produced; and
  • second, these initial projections were adjusted to sum to the national public school totals produced by the National High School Graduates Model.

Initial set of projections by race/ethnicity

The same steps used to produce the national projections of high school graduates were used to produce an initial set of projections for each of the following five racial/ethnic groups: White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaska Native. For example, the number of White public high school graduates was projected as a percentage of White grade 12 enrollment in public schools. A separate smoothing constant, chosen to minimize the sum of squared forecast errors, was used to calculate the projected percentage of 12th-grade enrollment for each racial/ethnic group.

Adjustments to the projections by race/ethnicity

The projections of public high school graduates by race/ethnicity were adjusted to sum to the national projections of public high school graduates shown in table 12 on page 49. This was done through the use of ratio adjustments in which all high school graduate projections by race/ethnicity were multiplied by the ratio of the national high school graduate projection to the sum of the high school projections by race/ethnicity.

Data and imputations used in the Public High School Graduates by Race/Ethnicity Model

Public school data on graduates and grade 12 enrollment by race/ethnicity. Data on public high school graduates and grade 12 enrollment by race/ethnicity from the NCES Common Core of Data (CCD) for 1994-95 to 2008-09 were used to develop these projections. In those instances where states did not report their high school graduate data by race/ethnicity, the state-level data had to be examined and some imputations made. For example, in 1994, Arizona did not release high school graduate data by race/ethnicity. It did, however, release grade 12 enrollment numbers by race/ethnicity for that year. So, to impute the high school graduate numbers by race/ethnicity for that year, Arizona’s total number of high school graduates for 1994 was multiplied by the state’s 1994 racial/ethnic breakdowns for grade 12 enrollment. In 2008-09, jurisdictions could classify high school graduates by an additional racial/ethnic group—those of two or more races. As only five states used this reporting category, those numbers were proportioned among the other five racial/ethnic groups by each of the five ethnic groups’ shares of total number of high school graduates, excluding those of two or more races. When a sufficient number of states use this racial/ethnic group, projections will be developed for this group.

Public enrollment projections for grade 12 by race/ethnicity. Projections of grade 12 enrollment in public schools by race/ ethnicity were used to develop the projections of public high school graduates by race/ethnicity. The grade 12 enrollment projections were made using the grade progression method. For more information, see Section A.1. Elementary and Secondary Enrollment, earlier in this appendix.

Accuracy of enrollment projections by race/ethnicity

Because this is the third edition of Projections of Education Statistics to include projections of public high school graduates by race/ethnicity, the difference between the projections and actual data for a reasonable sample of time points cannot yet be determined.

For more information, see Table A-10.

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