POPULATION AND ENROLMENT PROJECTION TECHNIQUES Enrolment ratio method

Process To make projection using the ratio method, one must have a projected state population. Without the projected population, the ratio can be projected independently and then only the exercise of the district level can be projected using the statistics below:

Where: Pi(t) =population of ith district at time ‘t’

Pc(t)=population of the state at time to which district ‘i’ belongs.

The calculation is based on the assumption that, the larger (state) population projection, to which the district belongs, is available. Thus, if the district population is to be projected for the period 2005 to 2015, the state projected population must be available and provided by the Ghana Statistical Service.

Even though enrolment is considered as a function of population, in using the rate of growth techniques, population factor variables; state and population in different classes may not be provided. However, demographic pressures may be experienced. In view of this, the enrolment ratio method stands out to be better. This is based on enrolment ratio and the result extrapolated into the future by applying suitable mathematical techniques or a specific logic. The availability of projected data for 4-5 years ( kinder- gartens) age - group; 6 - 11 years primary age-group and 12-14 years Junior High School age-group alongside enrolment figures can be of help for the projection.

The following steps therefore need to be considered:

Step I. population projections during the years in question (2009-2013) are required to be worked out, if not readily available.

Step II. Calculation of enrolment ratio from 2000 to 2002, as per Table 1 below. Table 1: Enrolment Ratio projection for years 2000-2004.

Year Enrolment in classes 1 to 6

(million) Population (6-11 years million) Enrolment ratio (%)

2000 12 18 12/18*100=67% 2001 13 19 13/19*100=68% 2002 15 20 15/20*100=75% Projections (GIVEN) 2003 21 X 0.89=18.00 21 89 2004 22 X 0.98=21.56 22 98

Step III. Project enrolment ratios during 2003-2004 by the method of least squares (to be treated next) or by any other suitable method or logical assumptions

Step IV. Obtain enrolment ratios from 2003 to 2004 by just taking the percentage of enrolment to projected population.

87 | P a g e

Method of Least Squares

Process

Enrolment figures for some years are plotted on a graph

A line popularly referred to as regression line is extended beyond the plotted lines

Estimations are calculated on the basis of which future enrolment can be worked out

The general form of equation used for this method is:

Y=a+b*x---(2) x=years

a= constant

b= slope which gives the best fitting line if equation (2), transforms to

Y=5+6x, the estimation or projection of any year, x, can be calculated. Advantage

This method uses all available observations within the specified years. Grade Ratio Methods

Process

Data requirements

The following data is very important when dealing with this method:

Enrolment and number of repeaters for at least two consecutive years; School entrance age population for over two consecutive years; The number of graduates in each year for the final grade and

Targets on certain items such as promotion, repetition, dropout rates and admission rates.

This is best explained using the table below:

Table 2: Enrolment in Basic Schools (BS) in1-6 in District X Year of

enrolment BS1 BS2 BS3 BS4 BS5 BS6 Total

2010 201 160 150 180 165 206 1062

2011 196 161 149 184 142 240 1072

Promotion rate or grade ratio is obtained by dividing the number of pupils in one year by the enrolment in the grade below in the previous year.

In notation,

Grade Ratio= x100 Where ‘E’ is the enrolment

‘t’ is Year and ‘g’ is Grade • • • • • • • E t+1g+1 E tg

The grade ratio from BS 1 to BS 2 will be;

The grade ratios for the other classes can thus be calculated. Mostly, the rates for several consecutive years can be calculated and the averages adopted for decisions for short term projections.

The chart below provides an example of projections for enrolment in three years

The grade ratios are marked on the arrows. The simplistic nature of the calculations, which are real, makes it suitable for promotion and enrolment projections.

Flow Rate Model

Introduction One of the methods that keep closer reality is the flow rate model. Basically, enrolment in a given grade and year is divided into students promoted from a grade below them and those repeating the same grade.

Enrolment in BS1,2011 161 Enrolment in BS1,2010 201= 0.80 174 169 174 166 154 190 184 186 191 .98 .97 .8 .83 1.2 .98 .97 .86 .83 1.2 .98 .97 .86 .83 1.2 t+3 t+3 t+3 6th 5th 4th 3rd 2nd 1st Year t t+1 t+1 t+1 Year t 2007 2008 2009 2010 6th 5th 4th 3rd 2 1st nd 88 | P a g e a/b

c x/yz x/yz x/yz x/yz x/yz

a/b

c x/yz x/yz x/yz x/yz x/yz

a/b

89 | P a g e

Where a=number of new entrants (determined by policy) b=repeaters in primary 1

c=total of new entrants and repeaters (enrolment in primary 1) x=promotes from lower class

y=repeaters in the same class z=total of x and y (enrolment)

The row boxes across the years, 2008, 2009, and 2010 contain the year current enrolment in the classes. The number of new entrants is indicated in the top left boxes (determined by policy). The top left of each box, x, provides the number of pupils coming from a grade below and promoted as shown by the slant arrows from top left to right down below. The y variable indicates the number of repeaters determined by applying the repetition rate shown by the vertical arrows indicating the enrolment of the same grade the previous year. The z, gives the total of pupils promoted and repeaters. These are mathematically expressed as;

and respectively.

PROJECTION OF TEACHER REQUIREMENT AND PROJECTION OF SCHOOL