15. A simple question
How much of the variability in pupil attainment is attributable to
schools level factors and how much to pupil level factors?
First of all we have to define what we mean by “variability”
16. A toy example – first we calculate the mean
Overall mean(0)
Two schools each with two pupils.
Overall mean= (3+2+(-1)+(-4))/4=0
3
2
-1
-4
attainment
School 2School 1
17. Calculating the “variance”
Overall mean(0)
3
2
-1
-4
attainment
School 2School 1
The total variance is the sum of the squares of the departures of the
observations around mean divided by the sample size(4) =
(9+4+1+16)/4=7.5
18. The variance of the school means around the overall mean
3
2
-1
-4
attainment
School 2School 1
Overall mean(0)
2.5
-2.5
The variance of the school means around the overall mean=
Total variance =7.5
(2.52+(-2.5)2)/2=6.25
19. The variance of the pupils scores around their school’s
mean
3
2
-1
-4
attainment
School 2School 1
2.5
-2.5
The variance of the pupils scores around their school’s mean=
The variance of the school means around overall mean = (2.52+(-
2.5)2)/2=6.25
Total variance =7.5=6.25+1.25
((3-2.5)2 + (2-2.5)2 + (-1-(-2.5))2 + (-4-(-2.5))2 )/4 =1.25
20. Returning to our question
How much of the variability in pupil attainment is attributable to
schools level factors and how much to pupil level factors?
In terms of our toy example we can now say
6.25/7.5= 82% of the total variation of pupils attainment is
attributable to school level factors
1.25/7.5= 18% of the total variation of pupils attainment is
attributable to pupil level factors
40. ‘MathAch’ ≈ 48.52 -3.26 x Public + 2.30 x
Homework - 0.50 x HomePublic
(1.88) (3.02) (3.71) (1.59)
‘MathAch’ ≈ 48.52 -3.26 x Public + 2.30 x
Homework - 0.50 x HomePublic
(1.88) (3.02) (3.71) (1.59)
41. ‘MathAch’ ≈ 52.72 -6.05 x Public + 0.92 x
Homework - 0.68 x HomePublic
(0.12) (0.38) (0.42) (0.10)
