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APPENDIX—NOTE ON THE METHOD OF ESTIMATING THE FUTURE SCHOOL POPULATION GENERAL The school population is the number of children and adolescents enrolled at a given date at public and private primary and post-primary schools. It depends on the number of children and adolescents in the whole population of the Dominion at that date. The school population increases or decreases according to the cumulative number of births in the thirteen-year span from five to eighteen years earlier. The number of children born is reduced by mortality of infants and children, which is very low in New Zealand. The number is increased (or reduced) by net gains (or losses) in external migration of children and adolescents of school age. To estimate the number of school-children of compulsory school age (seven to fifteen years) it is therefore sufficient to consider the number of births in the corresponding earlier years and to allow for losses by mortality and for net gains or losses by external migration. To estimate the number of school-children and students attending primary and post-primary schools, whose ages are either below or above the compulsory school age it is further necessary to determine the proportion of the whole population age group that is likely to be enrolled at a given date. Of the various factors mentioned, the number of births in different years is by far the strongest variable in determining enrolments. Indeed, it was the marked rise in the number of births from the year 1939-40 onwards, resulting in crowded infant departments from 1945 onwards, that drew attention to the expected further increases in school population. DESCRIPTION OP METHOD The school population estimates were based on the observed proportions of school attendance to births in the five years 1945 to 1949 (referred to in the following as base years). These years were most suitable for measuring the factors determining school attendance because the wartime fluctuations in attendance had ceased, and the new school leaving age (raised to fifteen years from Ist February, 1944) was established. The most detailed enrolment records available are for the middle of the school year, the main tabulations of enrolment in the various types of schools in the annual reports being as at Ist July (Tables D and E 1, Age and Classification Tables E 2, 3, 4, 5, 6 in E-l, Tables A 17 and D 8 for the Correspondence School in E-2, and Table H 7 for Maori Schools in E-3). To adjust the numbers of births, which the- Government Statistician publishes in the first instance for calendar years (" New Zealand Official Year-Book," 1947-1949 (page 88), and Monthly Abstract of Statistics, Table 3), it was necessary to recast them for years ending 30th June to correspond to the ages given ill the educational enrolment records. Por the years from 1940 to 1949 the quarterly birth figures (published since 1946 in the Monthly Abstract of Statistics) were taken, and the third and fourth quarter combined with the first and second quarter of the following year, e.g.;— Quarter. Number of Births, f I 9,675 Calendar year, 1944 .. 38,107<j jjj 9 513") I TV Q 74-1 I j 9'850 h = 39,517, year ending 30th June, 1945. Calendar year, 1945 .. 41,651<j jjj 10820^ [iV 10,'568 Since the fluctuations in the numbers of births before 1939 were only of a minor nature it was deemed sufficient to use for the years 1931 to 1939 the yearly figures with 49 per cent, falling in the first and second and 51 per cent, in the third and fourth quarters. These numbers of births are given in columns (1) and (2) of the tables C 1 to 5. Por the base years the following two sets of proportions were calculated : (a) The total enrolments in all schools for each age from five to eighteen years and over as percentages of the births recorded for the corresponding years; (b) The attendance ratios for each age at the four main types of schools (i.e., public and private primary and post-primary schools). If these percentages and ratios are considered it will be noted that they show for the base years some variation which is either—(i) A small variation deviating from an average figure, e.g.— 11-12 enrolment percentages: 94-0, 93-78, 94-08, 94-45, 94-31, with a maximum range of 0.67; attendance ratios public primary schools: 86-8, 86-9, 87-1, 86-8, 87-1, with a maximum range of 0-3 ; or (ii) A variation revealing a moderate trend of increase or decrease, e.g.— 5-6 enrolment percentages : 87-64, 85-62, 83-98, 82-28, 84-71.

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