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Methods of aggregating GCSE results to predict A-level performance

John F Bell

Research and Evaluation Division
University of Cambridge Local Examinations Syndicate
1 Hills Road
Cambridge  CB1 2EU
( 01223 553849
Fax: 01223 552700
: bell.j@ucles.org.uk

Paper presented at the British Educational Research Association Annual Conference, Cardiff University, September 7-10 2000

Abstract

In this paper, the issue of creating summaries of GCSE results with the objective of predicting A-level results is investigated. This is of interest to the awarding bodies because these predictions can be used in various aspects of research carried out by the awarding bodies. The advantages and disadvantages of using measures such as total GCSE, mean GCSE, or other combinations of GCSE is considered. The effect of these measures is described by applying them to candidates from a sample of examinations.

It was found that the mean GCSE was not the best predictor of success for individual A-level subjects. For predicting high attainment at A-level, the best predictor proved to be the sum of the square roots of the best five GCSE grades. This measure rewards a steady performance on a limited range of subjects. For lower levels of A-level attainment, a different measure was found to be optimal. This was the mean of the squares of the GCSE points for all subjects sat by each candidate. This measure rewards erratic performances.

Disclaimer

The opinions expressed in this paper are those of the author and are not to be taken as the opinions of the University of Cambridge Local Examinations Syndicate.

 

Introduction

...there is always a well-known solution that is simple, neat and wrong.

Menken, H.L. (1920) Prejudices, 2nd Series.

In this paper, methods of combining the GCSE (General Certificate of Secondary Education) grades awarded to candidates will be investigated. For an awarding body, aggregated GCSE scores are useful for predicting A-level examination results. In England, Wales, and Northern Ireland, the GCSE is an examination which is mostly taken by sixteen-year-olds and A-level examinations are usually taken by eighteen-year-olds to gain access to higher education. There are separate examinations for each subject and they are administered by three awarding bodies for England. There are several purposes for aggregating the results of the set of GCSE examinations sat by individual pupils. For example, this is one source of evidence that can be used for maintaining comparability between different syllabuses (Jones, 1997; Bell and Dexter, 2000; Bell and Greatorex, 2000). This was the main reason for initiating this research. There are other purposes for aggregating GCSE results. Important examples are their use in performance tables and in investigating added value.

The aggregation of GCSE scores is not a simple issue because of the diversity of subjects taken by year 11 pupils (16 year olds). Despite the introduction of the National Curriculum in England there is still a considerable degree of flexibility in the choice of subjects (Bell, 1998). A particularly important example of this diversity relates to the core subject of science. Although pupils are required to study science, there is flexibility in the amount of science that they can study (i.e. single award, double award and the three separate sciences). This choice has obvious implications for the uptake of other subjects.

The data used in this paper were extracted from two databases: the 1999 16+ database and the 1999 16+/18+ database. The first database includes all the GCSE results for candidates in English schools born between the 1st September 1982 and the 31st August 1983. The second database contains all the GCSE, AS and A-level results for candidates in English schools born between 1st September 1980 and 31st August 1981. The analyses described in this paper were carried out on several samples extracted from these databases. This was done because the size of the datasets means that it is impractical to carry out the exploratory work described in the paper on the whole data set (e.g., in the 1999 16+ database there are approximately 800,000 candidates entered for more than 5,000,000 examinations). In the first sample, drawn from the 16+ database, the selection was based on the centres in which candidates were entered for GCSEs and it was chosen to investigate the effect of the different measures on all GCSE centres and candidates. The other samples were drawn from the 16+/18+ database. The first A-level sample was used to investigate how well the GCSE summary measures predicted A-level. In addition to these samples, samples of centres were selected for a subset of common A-level subjects. These subjects were general studies, English, mathematics, biology and geography.

This report is divided into the following sections:

Scoring systems for aggregate measures of GCSE performance

Aggregate measures of GCSE performance and their properties

Comparisons of the different aggregate measures

Using aggregate measures to predict the A-level points score

Using aggregate measures to predict results for individual A-level subjects.

Finally the report concludes with a discussion of some of the issues raised by this research.

 

Scoring systems for aggregate measures of GCSE performance

Candidates taking GCSE examinations are awarded grades ranging from A* to G for each subject. In most research involving aggregated GCSE results, the GCSE grades are converted into scores as in the second column of Table 1 (or sometimes the reverse order is used). Then the two simplest aggregations, mean or total, are used. Gray et al. (1999) note that no single summary examination statistic can capture the dimensions of school performance. Gray, Goldstein, & Jesson, (1996) used the total GCSE score in a study of school effectiveness. They made the assumption that the highly correlated nature of the different examination measures meant that they would have obtained similar findings with other measures. They did not, however, rule out the possibility that they had favoured some schools more than others.

Table 1: Conversion of grades into points

 

Usual

Steady

Erratic

Grade

J=1

J=1/2

J=2

A*

8

2.83

64

A

7

2.65

49

B

6

2.45

36

C

5

2.24

25

D

4

2.00

16

E

3

1.73

9

F

2

1.41

4

G

1

1.00

1

U

0

0.00

0

The conventional points system in Table 1 assumes that there is a linear relation between grades and the underlying attainment. This might not be case. It is possible to investigate other relationships which tend to reward steady or erratic performances (Wood, 1991). It could be argued that because candidates are able to specialise at A-level then those whose performance is erratic and who obtain higher grades on some GCSEs compared with others would do better than candidates who obtained a more even grade profile (assuming the candidates choose A-level subjects that are related to those in which they got high GCSE grade scores). Depending on how the scores are aggregated it is possible to reward steady or erratic performances. To investigate this, it is necessary to consider the following power series:

where is the grade score for examination i and j is a constant. The choice of j determines whether erratic or steady performances are rewarded. This can be illustrated by considering the following example. Consider the results of two candidates who have taken five examinations and obtained the following grade scores:

Candidate A: 4, 4, 4, 4, 4 (A steady candidate)

Candidate B: 0, 8, 8, 4, 0 (An erratic candidate)

By setting j=1, neither erratic nor steady candidates are favoured, i.e.

Candidate A scores (4+4+4+4+4)=20

Candidate B scores (0+8+8+4+0)=20

Taking a value j < 1 will favour steady candidates over erratic candidates. For example, take the value j=1/2 (i.e. square roots) gives the following:

Candidate A: (2+2+2+2+2)=10

Candidate B: (0+++2+0)=7.66.

Taking values greater than 1 rewards erratic performances. For example, taking j=2 (i.e. square the scores) gives the following:

Candidate A: (16+16+16+16+16)=80

Candidate B: (0+64+64+16+0)=144

The effect of choosing different values of j is also illustrated in Table 1. In the usual transformation, a grade A* is worth twice as much as a grade D. When the square root transformation is applied, a grade A* is only worth 1.41 times as much as a grade D. However, the effect of squaring the points is even more dramatic. A grade A* is worth 4 times as much as a grade D. This means that the amount of compensation allowed for a good performance on a subject varies with the scoring system. Although there has been no formal suggestion to use a different points scores for GCSE examinations, UCAS have proposed changes for A-levels (e.g. the UCAS tariff, http://www.ucas.ac.uk/new/press/tariff.html). Their proposal would reward steady performances. However, the implications of this change are beyond the scope of this paper. In the remainder of this paper, all three points systems given in Table 1 will be considered.

Aggregate measures of GCSE performance and their properties

There are many different aggregate measures that could be used to summarise GCSE performance. In this section, a number of different measures have been defined and their potential advantages and disadvantages are considered. The aggregate measures of GCSE performance used in this paper are given in Table 2. Each of the measures has been given an identification code that is used in other figures and tables in this paper. Two of the measures use k to denote a value that could be varied. For example, the measure based on the best 5 GCSEs would be denoted as BE5. The measure 'At least 5 Cs at GCSE' has been included because it is used in the published school performance tables. Although this measure has a long history probably dating back to the change from the School Certificate to O-level, it has only been included for completeness and is not seriously considered as a suitable predictor of the grades at A-level (the vast majority of A-level candidates satisfy this requirement).

Table 2: Aggregate measures of GCSE performance

ID

Name

Description

MN

Mean GCSE score

Take the mean GCSE scores for each candidate

TOT

Total GCSE score

Add up all the GCSE scores for each candidate

MNk

Mean GCSE with minimum N fixed

Divide the total scores by n if N>k otherwise by k. E.g. if k was set at 5, AAAAB would lead to a score of 6.8 and AAAA would score 5.6

BEk

Best k GCSE scores

Take the best k GCSE scores

P5C

At least 5 grade Cs

Used in performance tables

For each of the measures in Table 2, it is possible to calculate the measure for each of the scoring systems in Table 1. When the square roots are used, an upper case R is added to the end of the ID and when the squares are used then an upper case S is added. If the square roots scores were used, the measure 'best 5 GCSE scores' would be identified as BE5R.

The reason for developing these measures is that they each have advantages and disadvantages (although whether a characteristic is an advantage or a disadvantage can be subjective). They also favour particular profiles in different ways. This information relating to the characteristics of different measures is given in Table 3.

Table 3: Some characteristics of different measures of GCSE performance

ID

Characteristics

MN

Highest scoring candidates tend to be the most consistent

Resits are penalised

AAAAB (34 points giving a mean of 6.8 points) is worse than AAAA (28 points giving a mean of 7.0 points)

Still influenced by school policy on choice of subjects.

TOT

Candidates who sit very few GCSEs tend to obtain lower scores than ones who do more.

Highest scoring candidates tend to be those who take the most GCSEs.

Number of GCSEs taken may be a policy decision of the centre

Candidates gain by resits

MNk

A compromise between MN and TOT

Choice of k is arbitrary

Favours candidates who take exactly k examinations

BEk

School/national policies which require pupils to take certain subjects have less influence

Choice of k is arbitrary

P5C

Does not discriminate well or at all for high attaining candidates

It is worth noting in passing that the choice of measure would lead to different strategies for maximising school performance. If TOT is used then the best strategy is to enter candidates for more GCSEs (Gray et al. (1999) pointed out that one result of the introduction of performance tables in 1992 was to increase the average number of GCSE examinations sat in the schools in their study). If MN is used then a better strategy would be to reduce the number of entries per candidate.

For the purposes of this paper, two values of k have been considered. Firstly, the value of five has been chosen because of the use of five passes at C in performance tables. Secondly, the value of nine has been chosen because it is the modal number of GCSEs taken by year 11 pupils.

 

Comparisons of the different aggregate measures

For all the samples described in the introduction, the aggregate measures described in the previous section were calculated. For the purposes of these analyses, only those GCSEs taken by the candidates up to and including year 11 were used. The aggregate measures were standardised so that they all had a mean of zero and a standard deviation of 1. This was to investigate the effect of the different measures on the mean aggregate score for the sample of centres considered in this study.

The relationships between the measures are investigated by considering the first sample, which included the full range of GCSE attainment. This sample consisted of all the candidates (9,060) from 50 GCSE centres selected at random from the database. These relationships are illustrated in Figures 1 and 2, which are scatterplot matrices. The point of the plots is simple. When there are many variables to plot against each other in scatterplots, it is logical to arrange the plots in rows and columns using a common vertical scale for all plots within a row (and a common horizontal scale within columns). In the diagonal cells, a frequency polygon indicating the distribution of each measure is given. The first scatterplot matrix (Figure 1) considers the relationships between the three scoring methods by plotting MN, MNR and MNS. The effect of using the square root transformation is that candidates with high scores for MN tend to have lower scores for MNR. Taking the square of the score has the reverse effect. This same general pattern occurs for the other measures.

Figure 1: Scatterplot matrix for measures MN, MNR and MNS

Figure 2 is a scatterplot matrix for the five measures MN, TOT, MN9, BE5 and BE9. It is clear that the values of MN can be very different for some candidates (ones who did well but only attempted a small number of GCSEs). The two measures that exhibit the greatest similarity are MN9 and BE9. As expected, BE9 and TOT tend to differ more for higher levels of performance because more able candidates tend to take more GCSEs. Scatterplot matrices for the measures based on the square roots and the squares of the scores have been included in Appendix A.

Figure 2: Scatterplot matrix for the measures MN, TOT, MN9, BE5 and BE9

Using the standardised aggregate measures as dependent variables, separate multilevel models were fitted to partition the variation into pupil-level and centre-level variation for the first sample. In addition to the aggregate measures that were later used to predict A-level performance, the measure, at least 5 grade Cs - P5C, was included in the analysis. This measure is not used in the remainder of the report because it is not an effective predictor of A-level performance. The results of these analyses have been presented in Table 4. As expected, the intercepts for all the standardised measures are small and near zero. The amount of centre variation is lowest for P5C. This is not surprising because this measure only considers differences toward the middle of the attainment range. For example, selective and independent schools usually have similar very high values of P5C but could differ substantially on the other measures.

Table 4: Results of multilevel models for sample 1

 

Intercept

Centre

Candidates

 

Measure

Est.

s.e.

Est.

s.e.

Est.

s.e.

% of variation

MN

-0.02

0.09

0.39

0.08

0.74

0.01

35

MNR

-0.03

0.09

0.32

0.07

0.79

0.01

29

MNS

-0.01

0.09

0.40

0.08

0.71

0.01

36

TOT

0.03

0.09

0.41

0.08

0.66

0.01

38

TOTR

0.03

0.09

0.41

0.09

0.64

0.01

39

TOTS

0.04

0.09

0.40

0.08

0.69

0.01

37

MN9

0.04

0.09

0.41

0.09

0.66

0.01

38

MN9R

0.03

0.09

0.42

0.09

0.64

0.01

40

MN9S

0.05

0.09

0.40

0.08

0.69

0.01

37

BE5

0.04

0.09

0.40

0.08

0.67

0.01

37

BE5R

0.03

0.09

0.40

0.08

0.64

0.01

38

BE5S

0.04

0.09

0.39

0.08

0.69

0.01

36

BE9

0.04

0.09

0.41

0.08

0.66

0.01

38

BE9R

0.03

0.09

0.40

0.08

0.64

0.01

38

BE9S

0.04

0.09

0.40

0.08

0.69

0.01

37

P5C

0.04

0.08

0.27

0.05

0.78

0.01

26

The mean scores for each centre on each of the aggregated measures are displayed on Figure 3. It is a parallel coordinates plot. Each vertical line is an axis of a particular aggregate measure. The mean aggregate measures of the centres have been plotted on each of the axes. The points for each centre have been joined by line segments. The point of this figure is that if the lines do not cross then the rank order of the centres would not change. This plot indicates that the measures based on mean GCSE are substantially different from the other measures. The fact that the lines in this plot cross means that the choice of measure would affect the position of the centres if a performance table was produced. There is a small group of centres at the bottom of the plot that only enter candidates for a small number of GCSEs per candidate. It should be recognised that the sample was drawn from all centres that offered GCSEs to Y11 pupils in 1999 and includes some that would not normally be included in performance tables. Since there is variation in the centre mean scores for the various measures then it is likely that the different measures might explain different amounts of centre level variation in the multilevel models described in the later sections of this report.

Figure 3: Parallel co-ordinate plot for the means of the standardised measures

The results of these analyses suggest that all the measures are sufficiently different from each other for them to be included in further analysis. All the measures other than P5C will be included in the subsequent multilevel models described in the remaining sections of this paper.

Using aggregate measures to predict the A-level points score

Like GCSE, A-level is awarded in grades, but for A level pass grades range from A to E. At the time of this paper, candidates usually entered three subjects. In this section, the results will be presented of a series of analyses that involved using the aggregate measures to predict total A-level points scores. A-level points were obtained by using the following system: A - 10, B - 8, C - 6, D - 4, E - 2, U/N - 0. Recently UCAS has proposed a new points system for entry to higher education (http://www.ucas.ac.uk/new/press/tariff.html) which is designed to include other qualifications such as Advanced GNVQ and Scottish qualifications. This tariff converts a grade A into 240 points and a grade E into 80 points. There are obviously other methods of aggregating A-level performance but this is beyond the scope of this paper.

Other research into the relationship between GCSE and A-level has indicated that the relationship between the two measures is non-linear. The relationship was investigated using the second sample which consisted of all the pupils taking both A-levels and GCSEs (2,057 pupils) from a randomly selected sample of 50 A-level centres. This was investigated using the following scatterplot. The A-level score was plotted against the GCSE score and a locally weighted regression line was fitted.

Plots were produced for all fifteen measures. However, for illustrative purposes only the plots for the first aggregate measure have been included. Figure 4 is a scatterplot of the total A-level score against the standardised mean GCSE score. The line generated by the lowess smoother indicates that there might be a small departure from linearity. This was investigated by including a quadratic term in the subsequent mulitilevel models.

Figure 4: Scatterplot of A-level score and standardised mean GCSE score

The following multilevel model was fitted:

where is the A-level points score for candidate j from centre i,

is a constant,

is the aggregate measure of GCSE performance,

are slope parameters,

is a random slope parameter,

and is a random error term.

All the aggregate measures of GCSE performance were standardised with mean zero and variance one for only those candidates with both GCSE and A-level results. This means that the value of the intercepts in the multilevel models can be interpreted as the A-level performance of candidates at the mean of the aggregate measure. For most of the measures, this is a total A-level score of approximately 16 points (e.g, 2 Cs and 1 D). The results for the multilevel models are presented in Table 5. The differences in the amount of reduction in candidate and centre level error are not large for most of the measures. However, the best measure seems to be MNS followed by BE5.

For the most powerful models used here, the standard deviation of the centre parameters is 2.3 A-level points (or just over 1 grade in one of three subjects). It is probable that a more sophisticated model with more explanatory variables would explain more of this centre level variation. Although any difference between centres could mean that the choice of centres has an effect on a candidate's life chances, after accounting for prior achievement the amount of centre level variation is not large.

Table 5: Results for the multilevel models with total A-level points score

Name

Int.

s.e.

Meas.

s.e.

Meas2

s.e.

Centre

s.e.

Cand.

s.e.

Total

None

16.5

0.8

-

-

-

-

26.1

6.6

95.5

3.0

123.6

MN

16.4

0.4

8.5

0.2

1.2

0.1

5.5

1.5

41.1

1.3

46.6

MNR

16.0

0.4

8.9

0.2

1.6

0.1

6.0

1.6

43.0

1.4

49.0

MNS

17.2

0.4

8.4

0.2

0.5

0.1

5.3

1.5

40.1

1.3

45.4

TOT

15.7

0.5

9.8

0.2

2.0

0.1

9.2

2.4

48.9

1.5

58.1

TOTR

15.4

0.7

10.9

0.3

2.1

0.1

16.9

4.4

62.4

2.0

79.3

TOTS

16.7

0.4

8.3

0.2

1.1

0.1

5.9

1.7

44.0

1.4

50.4

MN9

15.4

0.7

10.9

0.2

2.3

0.1

5.9

1.7

42.9

1.4

48.8

MN9R

14.9

0.5

15.0

0.3

2.8

0.1

8.0

2.4

48.6

1.5

56.6

MN9S

16.4

0.4

8.5

0.2

1.4

0.1

6.3

1.7

42.3

1.3

48.6

BE5

15.4

0.4

11.6

0.2

2.3

0.1

5.1

1.4

41.4

1.3

46.5

BE5R

14.5

0.4

18.0

0.4

3.1

0.1

5.3

1.5

42.7

1.3

48.0

BE5S

16.0

0.4

8.7

0.2

1.7

0.1

5.5

1.5

42.0

1.3

47.5

BE9

16.4

0.4

8.5

0.2

1.4

0.1

5.6

1.6

42.3

1.3

47.9

BE9R

14.8

0.5

15.4

0.3

2.8

0.1

7.9

2.4

48.5

1.5

56.4

BE9S

16.4

0.4

8.5

0.2

1.4

0.1

5.6

1.6

42.3

1.3

47.9

There is an obvious problem with the above table. It has been assumed that the total A-level points score is based on the current points system. Obviously similar issues as were raised for aggregating GCSE results could be considered. There is need for research because of recent proposals to change the A-level points system. It would be interesting to explore the use of these different measures in more complex analyses. However, for the purposes of the awarding body, this is not an issue and a greater concern is how well the aggregate measures predict performance on individual A-level subjects.

Using aggregate measures to predict results for individual A-level subjects

In the following sub-section, individual A-level subjects have been considered. General studies, English, mathematics, biology and geography were selected for analysis in this section because they have large entries and cover a range of assessment styles. General studies is of particular interest because, by its nature, it might be more related to steady performances than erratic performances. The analyses described in this section used five samples, one for each subject, of all candidates from a random sample of 250 A-level centres.

It is inappropriate to fit an ordinary multilevel model to an ordinal outcome such as an A-level grade. Although it is possible to model A-level grades with proportional odds models (Fielding, 1999), this requires strict assumptions that do not seem to hold in practice. For this reason, the binary response variables will be analysed using multilevel logistic regression. For the purposes of this paper, three grade boundaries, A/B, B/C and E/U, have been considered, i.e., the probability of being 'at grade A', the probability of getting 'at least grade B' and the probability of getting 'at least grade E'. The issue of the type of model for examination grades is considered in greater detail in Bell and Dexter (2000).

The following multilevel model was fitted.

where is the probability of candidate j from centre i obtaining at least grade x,

is a constant,

is a slope parameter,

is an aggregate measure of GCSE performance,

is a random centre level error term,

is a random candidate level error term.

The multilevel model described above was fitted for the three dependent variables ('at grade A', 'at least grade B' and 'at least grade E') for the null or empty model and for each of the fifteen measures and for each of the five subjects. These three boundaries were chosen because they are boundaries determined by judgement in the grade awarding process. The full results for all 240 analyses are given in Appendix B. In addition to the estimation of the model parameters by MLwin the explained variance and the unexplained variance at the centre and candidate level were calculated using the procedures described in Snijders & Bosker (1999).

The explained and unexplained variance statistics for all subjects at grade A are presented in Table 6. The measure that explains the most variation has been highlighted in bold. In this case, BE5R is the best measure for all subjects except geography. For example, BE5R explains 73% of the variation for general studies. As a measure BE5R favours candidates who have a consistent performance on five subjects.

Table 6: Explained variation for the logistic models for the dependent variable 'at grade A'

General Studies

Mathematics

English

Biology

Geography

Measure

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

None

0.00

0.23

0.77

0.00

0.15

0.85

0.00

0.19

0.81

0.00

0.25

0.75

0.00

0.18

0.82

MN

0.66

0.07

0.27

0.47

0.05

0.48

0.39

0.09

0.52

0.69

0.07

0.25

0.47

0.09

0.44

MNR

0.70

0.06

0.24

0.49

0.04

0.47

0.43

0.08

0.49

0.71

0.06

0.23

0.50

0.08

0.42

MNS

0.62

0.08

0.30

0.45

0.05

0.50

0.35

0.10

0.55

0.65

0.08

0.27

0.43

0.10

0.47

TOT

0.45

0.13

0.42

0.32

0.10

0.58

0.29

0.11

0.61

0.50

0.14

0.36

0.36

0.12

0.53

TOTR

0.28

0.18

0.54

0.18

0.14

0.68

0.16

0.14

0.70

0.31

0.18

0.51

0.20

0.13

0.66

TOTS

0.54

0.10

0.36

0.39

0.07

0.54

0.32

0.10

0.58

0.59

0.10

0.31

0.41

0.11

0.48

MN9

0.64

0.06

0.30

0.46

0.04

0.50

0.41

0.08

0.51

0.67

0.06

0.26

0.48

0.09

0.43

MN9R

0.68

0.05

0.27

0.50

0.04

0.47

0.47

0.06

0.46

0.71

0.05

0.25

0.54

0.07

0.39

MN9S

0.60

0.08

0.32

0.44

0.05

0.51

0.35

0.09

0.56

0.64

0.08

0.28

0.44

0.10

0.46

BE5

0.66

0.05

0.29

0.51

0.05

0.45

0.41

0.09

0.50

0.68

0.07

0.25

0.46

0.09

0.45

BE5R

0.73

0.04

0.24

0.57

0.03

0.41

0.52

0.07

0.42

0.76

0.05

0.19

0.51

0.08

0.41

BE5S

0.61

0.07

0.32

0.47

0.05

0.48

0.35

0.10

0.55

0.64

0.08

0.28

0.42

0.10

0.48

BE9

0.63

0.06

0.31

0.46

0.04

0.49

0.41

0.08

0.51

0.68

0.06

0.26

0.48

0.09

0.43

BE9R

0.67

0.05

0.27

0.51

0.03

0.46

0.50

0.06

0.44

0.73

0.05

0.22

0.55

0.07

0.38

BE9S

0.60

0.07

0.33

0.44

0.05

0.51

0.35

0.09

0.56

0.65

0.08

0.28

0.44

0.10

0.46

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

It is interesting to note that for that the proportion of centre level variation is relatively small for all subjects. A possible explanation for this is that these high performing candidates are taking most of the responsibility for their learning. (This a characteristic of higher levels of education. For a discussion of levels, see Bell and Greatorex, 2000.) The differences in the amount of centre level variation between Mathematics and English, for example, could reflect the nature of assessment in these subjects. For mathematics, the marking is objective and it is clear what a candidate has to do to achieve well and for English, the marking is more subjective and a candidate would need more guidance to produce good answers. It should also be noted that the amount of unexplained centre level variation is highest for TOT, TOTR and TOTS. These measures are influenced by centres' policies on the number of GCSEs they allow Y11 pupils to sit. Given that many candidates do not change centre between GCSE and A-level, then some of the centre level variation is spurious since it is not the result of A-level teaching but of entry policies for GCSE.

In Table 7, the explained and unexplained variance for multilevel logistic regression models for the dependent variable 'at least grade B' are presented. The results display a similar pattern to the previous Table. However, the explained variation tends to be lower.

Table 7: Explained variation for the logistic models for the dependent variable 'at least grade B'

General

Mathematics

English

Biology

Geography

Measure

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

None

0.00

0.24

0.76

0.00

0.14

0.86

0.00

0.13

0.87

0.00

0.25

0.75

0.00

0.13

0.87

MN

0.61

0.09

0.31

0.42

0.05

0.53

0.34

0.08

0.57

0.61

0.07

0.32

0.44

0.07

0.49

MNR

0.63

0.08

0.29

0.42

0.04

0.53

0.36

0.08

0.57

0.62

0.06

0.31

0.44

0.07

0.49

MNS

0.59

0.09

0.32

0.43

0.05

0.52

0.33

0.09

0.58

0.61

0.08

0.32

0.44

0.08

0.49

TOT

0.46

0.12

0.42

0.30

0.08

0.61

0.26

0.09

0.66

0.49

0.12

0.40

0.34

0.09

0.57

TOTR

0.28

0.17

0.55

0.17

0.11

0.72

0.12

0.10

0.78

0.30

0.17

0.53

0.18

0.11

0.71

TOTS

0.54

0.09

0.37

0.38

0.06

0.56

0.31

0.09

0.61

0.58

0.08

0.34

0.42

0.08

0.51

MN9

0.57

0.08

0.35

0.40

0.04

0.55

0.35

0.08

0.57

0.60

0.06

0.33

0.46

0.07

0.47

MN9R

0.59

0.07

0.34

0.40

0.04

0.55

0.38

0.07

0.55

0.61

0.05

0.33

0.45

0.07

0.48

MN9S

0.57

0.08

0.35

0.41

0.05

0.54

0.33

0.09

0.58

0.60

0.07

0.33

0.43

0.08

0.49

BE5

0.57

0.07

0.36

0.45

0.04

0.51

0.35

0.08

0.57

0.60

0.08

0.33

0.43

0.07

0.50

BE5R

0.63

0.05

0.31

0.51

0.03

0.46

0.43

0.07

0.50

0.65

0.06

0.29

0.44

0.08

0.48

BE5S

0.55

0.08

0.37

0.43

0.05

0.52

0.32

0.09

0.59

0.57

0.08

0.34

0.41

0.07

0.51

BE9

0.57

0.08

0.35

0.41

0.04

0.55

0.35

0.08

0.57

0.60

0.06

0.33

0.44

0.07

0.49

BE9R

0.60

0.07

0.34

0.42

0.04

0.54

0.40

0.07

0.53

0.62

0.05

0.32

0.46

0.07

0.47

BE9S

0.57

0.08

0.35

0.41

0.05

0.54

0.33

0.09

0.59

0.60

0.07

0.33

0.44

0.07

0.49

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

The final set of analyses is for the dependent variable 'at least grade E'. The amounts of explained and unexplained variation are presented in Table 8. These results are completely different from those for the other two grades. Firstly, the amount of variation explained is much smaller. Secondly, the best aggregate measure is MNS rather than BE5 and, thirdly, the amount of unexplained centre level variation is much greater.

The results for grade E mean that candidates who do badly on most of their GCSE subjects but very well on a few have a greater probability of success at A-level than candidates who have consistent mediocre grades. This is plausible because candidates have specialised at A-level and will have opted to study subjects that are closely related to those GCSE subjects in which they did well. The greater level of centre variation would suggest the centres are more likely to influence the performance of weaker candidates. Again this is a plausible result.

Table 8: Explained variation for the logistic models for the dependent variable 'at least grade E'

General

Mathematics

English

Biology

Geography

Measure

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

EXP

UC

UP

None

0.00

0.30

0.70

0.00

0.23

0.77

0.00

0.18

0.82

0.00

0.30

0.70

0.00

0.32

0.68

MN

0.34

0.18

0.48

0.28

0.14

0.58

0.31

0.10

0.58

0.33

0.21

0.46

0.34

0.18

0.48

MNR

0.30

0.19

0.51

0.24

0.15

0.61

0.29

0.10

0.61

0.27

0.22

0.51

0.27

0.21

0.53

MNS

0.38

0.17

0.45

0.33

0.15

0.53

0.38

0.09

0.53

0.40

0.18

0.41

0.41

0.16

0.43

TOT

0.14

0.27

0.59

0.12

0.22

0.66

0.16

0.13

0.71

0.22

0.22

0.56

0.20

0.25

0.55

TOTR

0.04

0.30

0.66

0.04

0.23

0.72

0.05

0.16

0.80

0.07

0.27

0.66

0.06

0.30

0.64

TOTS

0.28

0.22

0.50

0.24

0.18

0.58

0.32

0.10

0.58

0.37

0.19

0.44

0.37

0.18

0.45

MN9

0.19

0.23

0.58

0.14

0.20

0.66

0.22

0.11

0.67

0.28

0.20

0.52

0.29

0.20

0.51

MN9R

0.09

0.27

0.65

0.06

0.22

0.72

0.11

0.13

0.76

0.17

0.22

0.60

0.29

0.21

0.50

MN9S

0.31

0.20

0.50

0.26

0.16

0.58

0.33

0.10

0.57

0.38

0.18

0.44

0.39

0.16

0.44

BE5

0.20

0.23

0.57

0.15

0.19

0.66

0.20

0.12

0.68

0.29

0.21

0.50

0.28

0.19

0.53

BE5R

0.11

0.26

0.63

0.06

0.22

0.72

0.11

0.14

0.75

0.26

0.21

0.54

0.23

0.20

0.57

BE5S

0.28

0.21

0.51

0.24

0.16

0.59

0.29

0.11

0.60

0.35

0.19

0.46

0.34

0.17

0.49

BE9

0.18

0.24

0.58

0.13

0.21

0.66

0.20

0.12

0.68

0.28

0.20

0.52

0.28

0.21

0.52

BE9R

0.08

0.28

0.65

0.05

0.23

0.72

0.06

0.14

0.79

0.17

0.22

0.61

0.17

0.25

0.59

BE9S

0.29

0.21

0.50

0.25

0.17

0.58

0.32

0.10

0.58

0.38

0.18

0.44

0.38

0.17

0.45

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

 

Discussion

In this paper it has been demonstrated that the scoring system chosen to aggregate GCSE results can have a significant impact on the amount of variation in A-level results that can be explained. It is also possible to devise a number of different measures of aggregate GCSE performance. It has been demonstrated that these measures have different characteristics and can be influenced by school policies on examination entrance. The choice of measure could change the rank order of centres in a performance table.

From preliminary analyses described in this paper, it would seem that the differences between most of the measures of aggregate GCSE performance in predicting the total A-level score are not great. However, this was not the main focus of the paper. There is a need to investigate the properties of these measures with different aggregate measures of A-level performance, large samples and more complex models.

The main focus of this paper (and the main emphasis for awarding bodies) is the prediction of performance in individual A-level subjects. The results of the multilevel analyses were particularly interesting because different aggregate measures were found to be appropriate for predicting high A-level grades compared with low A-level grades. The best measure for predicting good A-level grades was BE5R, which is calculated by taking the square root of the GCSE points score and adding up the transformed points for the best five results. This measure favours candidates who perform consistently on a limited range of, presumably relevant, subjects. This could also explain some of the reduction of the centre level variation. School and national policies (e.g., the National Curriculum which only applies to state-maintained schools) could result in candidates being forced to enter subjects in which they cannot do well. For example, some centres might only offer double award GCSE science while others might offer a choice between single and double award. Candidates who disliked science could have lower aggregate measures of GCSE performance for the first set of centres compared with the second set for those measures that include all GCSE results. This could result in spurious conclusions about the differential centre effectiveness of A-level teaching.

For lower levels of A-level performance, the best measure was MNS. This is the arithmetic mean of the squares of GCSE scores. This measure favours erratic candidates. The fact that an aggregation that rewards erratic performances has the most explanatory power is probably related to the fact that candidates specialise at A-level. It is reasonable to assume that candidates choose A-levels in subjects that are related to their best GCSE results. This means that an erratic candidate would tend to have higher GCSE grades in the subjects they specialise in at A-level than might a steady candidate (e.g., AAACCCEEE compared with CCCCCCCCC where underlining denotes the subject for A-level).

The overall conclusion is that the choice of aggregate measure is important and that the assumption that the mean GCSE score is the best predictor is unjustified. There is a need for further research with these measures, particularly, with the more complex models used to investigate substantive issues such as a comparability study. It would be interesting to extend this research to other A-level subjects. In particular, the results described here may not generalise to subjects such as modern foreign languages, music and art.

References

Bell, J.F. (1998). Patterns of subject uptake and examination entry 1984-1997. Paper presented at the British Educational Research Association Annual Conference. Belfast: Queen's University (Available from Education-line at http://www.leeds.ac.uk/educol/index.htm).

Bell, J.F., & Dexter, T. (2000). Using multilevel models to assess the comparability of examinations. Paper to be presented at the Fifth International Conference on Social Science Methodology of the Research Committee on Logic and Methodology (RC33) of the International Sociological Association (ISA). Cologne: University of Cologne.

Bell, J.F., & Greatorex, J. (in prep.). A review of research in levels, profiles and comparability. London: QCA (available online at http://www.qca.org.uk).

Fielding, A. (1999). Why arbitrary points scores? Ordered categories in models of educational progress. Journal of the Royal Statistical Society, Series A - Statistics in Society, 163, 3, 303-328.

Gray, J., Goldstein, H., & Jesson, D. (1996). Changes and improvements in schools' effectiveness: trends over five years. Research Papers in Education, 11, 1, 35-51.

Gray, J., Hopkins, D., Reynolds, D., Wilcox, B., Farrell, S., & Jesson, D. (1999). Improving Schools. Performance and Potential. Buckingham: Open University Press.

Jones, B. E. (1997). Comparing Examination Standards: is a purely statistical approach adequate? Assessment in Education, 4, 2, 249-262.

Snijders, T. A. B., & Bosker, R. J. (1999). Multilevel Analysis. An introduction to basic and advanced multilevel modeling. London: Sage Publications.

Wood, R. (1991). Assessment and Testing: A Survey of Research. Cambridge: Cambridge University Press.

 

Appendix A: Scatterplot matrices

Figure A1: Scatterplot matrix for measure rewarding steady candidates

Figure A2: Scatterplot matrix for measure rewarding erratic candidates

 

Appendix B: Results of logistic regression analyses

Note that for each sample the standardisation was carried out using the mean and standard deviation of the samples. This means that the constant parameter can be interpreted as the logit of the probability of obtaining at least a grade x for an average pupil from an average centre. The means and variances vary from sample to sample because of sampling error and the fact that the entries for subjects differ. Some of the analyses were carried out with MLin and other analyses were carried out using MIXOR because of estimation problems with MLwin. MLwin had a tendency to converge to a solution with zero centre variance for some data sets. The centre level standard error for the analyses carried out using MIXOR is for the standard deviation at the centre level rather than the variance. The means and variances for the samples can be found in Table B16.

Table B1: Multilevel model results for general studies with dependent variable 'at grade A'

(MIXOR)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-1.99

0.10

1.01

0.08

0.00

0.23

0.77

MN

-3.23

0.15

2.85

0.05

0.86

0.11

0.66

0.07

0.27

MNR

-3.29

0.14

3.06

0.05

0.80

0.11

0.70

0.06

0.24

MNS

-3.09

0.15

2.63

0.05

0.92

0.11

0.62

0.08

0.30

TOT

-2.55

0.11

1.89

0.04

1.05

0.09

0.45

0.13

0.42

TOTR

-2.26

0.10

1.29

0.03

1.07

0.09

0.28

0.18

0.54

TOTS

-2.78

0.12

2.21

0.05

0.89

0.10

0.54

0.10

0.36

MN9

-2.94

0.10

2.64

0.04

0.68

0.09

0.64

0.06

0.30

MN9R

-2.79

0.10

2.86

0.03

0.64

0.07

0.68

0.05

0.27

MN9S

-2.96

0.12

2.49

0.05

0.78

0.10

0.60

0.08

0.32

BE5

-3.04

0.10

2.73

0.04

0.62

0.09

0.66

0.05

0.29

BE5R

-2.92

0.09

3.19

0.03

0.51

0.09

0.73

0.04

0.24

BE5S

-3.01

0.12

2.49

0.05

0.72

0.10

0.61

0.07

0.32

BE9

-2.91

0.10

2.60

0.04

0.67

0.09

0.63

0.06

0.31

BE9R

-2.77

0.10

2.85

0.04

0.64

0.06

0.67

0.05

0.27

BE9S

-2.94

0.11

2.45

0.05

0.75

0.10

0.60

0.07

0.33

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B2: Multilevel model results for general studies with dependent variable 'at least grade B'

(MIXOR)

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-0.83

0.09

1.01

0.07

0.00

0.24

0.76

MN

-1.07

0.09

2.56

0.08

0.95

0.09

0.61

0.09

0.31

MNR

-1.23

0.09

2.66

0.08

0.90

0.09

0.63

0.08

0.29

MNS

-0.97

0.09

2.49

0.08

0.96

0.09

0.59

0.09

0.32

TOT

-0.93

0.09

1.88

0.04

0.95

0.07

0.46

0.12

0.42

TOTR

-0.90

0.09

1.28

0.03

1.04

0.08

0.28

0.17

0.55

TOTS

-0.91

0.09

2.20

0.06

0.83

0.07

0.54

0.09

0.37

MN9

-1.02

0.08

2.33

0.05

0.73

0.07

0.57

0.08

0.35

MN9R

-1.03

0.08

2.39

0.03

0.69

0.06

0.59

0.07

0.34

MN9S

-0.95

0.09

2.33

0.07

0.80

0.08

0.57

0.08

0.35

BE5

-1.03

0.08

2.30

0.04

0.66

0.08

0.57

0.07

0.36

BE5R

-1.04

0.07

2.58

0.03

0.55

0.07

0.63

0.05

0.31

BE5S

-0.98

0.08

2.22

0.06

0.75

0.08

0.55

0.08

0.37

BE9

-1.01

0.08

2.31

0.05

0.70

0.07

0.57

0.08

0.35

BE9R

-1.03

0.08

2.42

0.03

0.68

0.06

0.60

0.07

0.34

BE9S

-0.94

0.08

2.30

0.06

0.76

0.08

0.57

0.08

0.35

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B3: Multilevel model results for general studies with dependent variable 'at least grade E'

(MLwin)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

1.66

0.10

1.38

0.19

0.00

0.30

0.70

MN

2.56

0.12

1.51

0.08

1.23

0.20

0.34

0.18

0.48

MNR

2.42

0.11

1.38

0.08

1.24

0.20

0.30

0.19

0.51

MNS

2.70

0.12

1.68

0.09

1.24

0.20

0.38

0.17

0.45

TOT

2.06

0.11

0.89

0.07

1.54

0.22

0.14

0.27

0.59

TOTR

1.80

0.10

0.47

0.05

1.49

0.21

0.04

0.30

0.66

TOTS

2.46

0.12

1.36

0.08

1.45

0.22

0.28

0.22

0.50

MN9

2.21

0.10

1.05

0.07

1.30

0.20

0.19

0.23

0.58

MN9R

1.93

0.10

0.67

0.07

1.35

0.20

0.09

0.27

0.65

MN9S

2.50

0.12

1.42

0.08

1.30

0.21

0.31

0.20

0.50

BE5

2.20

0.11

1.08

0.08

1.36

0.21

0.20

0.23

0.57

BE5R

1.94

0.10

0.77

0.08

1.33

0.20

0.11

0.26

0.63

BE5S

2.44

0.12

1.35

0.08

1.39

0.21

0.28

0.21

0.51

BE9

2.17

0.11

1.02

0.07

1.38

0.21

0.18

0.24

0.58

BE9R

1.90

0.10

0.63

0.07

1.40

0.20

0.08

0.28

0.65

BE9S

2.47

0.12

1.39

0.08

1.38

0.21

0.29

0.21

0.50

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B4: Multilevel model results for mathematics with dependent variable 'at grade A'

(MIXOR)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-1.33

0.07

0.58

0.07

0.00

0.15

0.85

MN

-1.77

0.07

1.80

0.05

0.31

0.08

0.47

0.05

0.48

MNR

-1.78

0.07

1.85

0.05

0.29

0.08

0.49

0.04

0.47

MNS

-1.74

0.07

1.73

0.05

0.33

0.08

0.45

0.05

0.50

TOT

-1.57

0.07

1.35

0.04

0.56

0.08

0.32

0.10

0.58

TOTR

-1.46

0.08

0.94

0.03

0.66

0.08

0.18

0.14

0.68

TOTS

-1.63

0.07

1.54

0.05

0.43

0.09

0.39

0.07

0.54

MN9

-1.68

0.06

1.74

0.04

0.28

0.08

0.46

0.04

0.50

MN9R

-1.62

0.06

1.86

0.03

0.25

0.08

0.50

0.04

0.47

MN9S

-1.69

0.06

1.67

0.05

0.33

0.08

0.44

0.05

0.51

BE5

-1.79

0.06

1.93

0.04

0.34

0.08

0.51

0.05

0.45

BE5R*

-1.72

0.06

2.14

0.03

0.23

0.08

0.57

0.03

0.41

BE5S

-1.80

0.07

1.80

0.05

0.32

0.08

0.47

0.05

0.48

BE9

-1.69

0.06

1.76

0.04

0.27

0.08

0.46

0.04

0.49

BE9R

-1.63

0.06

1.92

0.03

0.24

0.08

0.51

0.03

0.46

BE9S

-1.70

0.07

1.68

0.05

0.32

0.08

0.44

0.05

0.51

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B5: Multilevel model results for mathematics with dependent variable 'at least grade B'

(MIXOR)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-1.33

0.07

0.58

0.07

0.00

0.15

0.85

MN

-1.77

0.07

1.80

0.05

0.31

0.08

0.47

0.05

0.48

MNR

-1.78

0.07

1.85

0.05

0.29

0.08

0.49

0.04

0.47

MNS

-1.74

0.07

1.73

0.05

0.33

0.08

0.45

0.05

0.50

TOT

-1.57

0.07

1.35

0.04

0.56

0.08

0.32

0.10

0.58

TOTR

-1.46

0.08

0.94

0.03

0.66

0.08

0.18

0.14

0.68

TOTS

-1.63

0.07

1.54

0.05

0.43

0.09

0.39

0.07

0.54

MN9

-1.68

0.06

1.74

0.04

0.28

0.08

0.46

0.04

0.50

MN9R

-1.62

0.06

1.86

0.03

0.25

0.08

0.50

0.04

0.47

MN9S

-1.69

0.06

1.67

0.05

0.33

0.08

0.44

0.05

0.51

BE5

-1.79

0.06

1.93

0.04

0.34

0.08

0.51

0.05

0.45

BE5R

-1.72

0.06

2.14

0.03

0.23

0.08

0.57

0.03

0.41

BE5S

-1.80

0.07

1.80

0.05

0.32

0.08

0.47

0.05

0.48

BE9

-1.69

0.06

1.76

0.04

0.27

0.08

0.46

0.04

0.49

BE9R

-1.63

0.06

1.92

0.03

0.24

0.08

0.51

0.03

0.46

BE9S

-1.70

0.07

1.68

0.05

0.32

0.08

0.44

0.05

0.51

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B6: Multilevel model results for mathematics with dependent variable 'at least grade E'

(MLwin)

Measure

const

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

1.75

0.08

0.98

0.15

0.00

0.23

0.77

MN

2.42

0.10

1.26

0.06

0.82

0.15

0.28

0.14

0.58

MNR

2.31

0.09

1.13

0.06

0.81

0.14

0.24

0.15

0.61

MNS

2.54

0.10

1.43

0.07

0.91

0.14

0.33

0.15

0.53

TOT

2.02

0.09

0.78

0.06

1.08

0.16

0.12

0.22

0.66

TOTR

1.85

0.09

0.45

0.05

1.06

0.16

0.04

0.23

0.72

TOTS

2.31

0.10

1.18

0.07

1.01

0.16

0.24

0.18

0.58

MN9

2.11

0.09

0.84

0.06

0.99

0.16

0.14

0.20

0.66

MN9R

1.91

0.09

0.51

0.05

1.03

0.16

0.06

0.22

0.72

MN9S

2.37

0.10

1.21

0.07

0.91

0.15

0.26

0.16

0.58

BE5

2.10

0.09

0.87

0.06

0.95

0.15

0.15

0.19

0.66

BE5R

1.89

0.09

0.52

0.06

1.00

0.15

0.06

0.22

0.72

BE5S

2.31

0.10

1.16

0.06

0.91

0.15

0.24

0.16

0.59

BE9

2.09

0.09

0.82

0.06

1.03

0.16

0.13

0.21

0.66

BE9R

1.90

0.10

0.49

0.05

1.05

0.16

0.05

0.23

0.72

BE9S

2.34

0.10

1.18

0.07

0.97

0.16

0.25

0.17

0.58

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate pupil level)

Table B7: Multilevel model results for English with dependent variable 'at grade A'

(MLwin)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-2.04

0.08

0.76

0.13

0.00

0.19

0.81

MN

-2.76

0.10

1.58

0.07

0.54

0.12

0.39

0.09

0.52

MNR

-2.79

0.10

1.70

0.08

0.51

0.11

0.43

0.08

0.49

MNS

-2.68

0.09

1.45

0.06

0.57

0.12

0.35

0.10

0.55

TOT

-2.49

0.08

1.25

0.06

0.57

0.11

0.29

0.11

0.61

TOTR

-2.26

0.08

0.86

0.06

0.64

0.12

0.16

0.14

0.70

TOTS

-2.51

0.09

1.34

0.06

0.54

0.12

0.32

0.10

0.58

MN9

-2.74

0.09

1.61

0.08

0.51

0.11

0.41

0.08

0.51

MN9R

-2.75

0.09

1.83

0.10

0.46

0.10

0.47

0.06

0.46

MN9S

-2.67

0.09

1.44

0.06

0.55

0.12

0.35

0.09

0.56

BE5

-2.76

0.10

1.64

0.08

0.56

0.12

0.41

0.09

0.50

BE5R

-2.81

0.10

2.02

0.09

0.54

0.12

0.52

0.07

0.42

BE5S

-2.69

0.09

1.45

0.06

0.57

0.12

0.35

0.10

0.55

BE9

-2.76

0.09

1.62

0.08

0.50

0.11

0.41

0.08

0.51

BE9R

-2.76

0.09

1.93

0.10

0.45

0.10

0.50

0.06

0.44

BE9S

-2.67

0.09

1.44

0.06

0.53

0.12

0.35

0.09

0.56

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B8: Multilevel model results for English with dependent variable 'at least grade B'

(MLwin)

Measure

Const.

s.e

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-0.94

0.06

0.50

0.08

0.00

0.13

0.87

MN

-1.22

0.07

1.41

0.05

0.49

0.09

0.34

0.08

0.57

MNR

-1.24

0.07

1.44

0.06

0.45

0.08

0.36

0.08

0.57

MNS

-1.18

0.07

1.37

0.05

0.51

0.09

0.33

0.09

0.58

TOT

-1.11

0.06

1.13

0.05

0.43

0.08

0.26

0.09

0.66

TOTR

-1.02

0.06

0.70

0.05

0.44

0.07

0.12

0.10

0.78

TOTS

-1.13

0.07

1.29

0.05

0.46

0.08

0.31

0.09

0.61

MN9

-1.21

0.07

1.41

0.05

0.46

0.08

0.35

0.08

0.57

MN9R

-1.22

0.06

1.51

0.06

0.41

0.07

0.38

0.07

0.55

MN9S

-1.21

0.07

1.36

0.05

0.49

0.09

0.33

0.09

0.58

BE5

-1.24

0.07

1.43

0.05

0.49

0.09

0.35

0.08

0.57

BE5R

-1.17

0.07

1.67

0.07

0.46

0.08

0.43

0.07

0.50

BE5S

-1.21

0.07

1.33

0.05

0.50

0.09

0.32

0.09

0.59

BE9

-1.21

0.07

1.42

0.05

0.45

0.08

0.35

0.08

0.57

BE9R

-1.23

0.06

1.57

0.07

0.40

0.07

0.40

0.07

0.53

BE9S

-1.17

0.07

1.36

0.05

0.48

0.09

0.33

0.09

0.59

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B9: Multilevel model results for English with dependent variable 'at least grade E'

(MLwin)

Measure

const

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

2.08

0.08

0.70

0.13

0.00

0.18

0.82

MN

2.77

0.10

1.33

0.07

0.57

0.12

0.31

0.10

0.58

MNR

2.61

0.09

1.25

0.06

0.56

0.12

0.29

0.10

0.61

MNS

2.92

0.10

1.55

0.08

0.57

0.12

0.38

0.09

0.53

TOT

2.40

0.08

0.85

0.06

0.61

0.12

0.16

0.13

0.71

TOTR

2.19

0.08

0.44

0.04

0.64

0.12

0.05

0.16

0.80

TOTS

2.72

0.09

1.34

0.08

0.58

0.12

0.32

0.10

0.58

MN9

2.53

0.09

1.03

0.06

0.55

0.12

0.22

0.11

0.67

MN9R

2.30

0.08

0.68

0.06

0.56

0.12

0.11

0.13

0.76

MN9S

2.79

0.08

1.39

0.08

0.56

0.12

0.33

0.10

0.57

BE5

2.48

0.09

0.98

0.07

0.59

0.12

0.20

0.12

0.68

BE5R

2.64

0.08

0.69

0.07

0.60

0.12

0.11

0.14

0.75

BE5S

2.68

0.09

1.25

0.07

0.59

0.12

0.29

0.11

0.60

BE9

2.49

0.09

0.98

0.06

0.58

0.12

0.20

0.12

0.68

BE9R

2.26

0.08

0.51

0.05

0.59

0.12

0.06

0.14

0.79

BE9S

2.76

0.10

1.36

0.08

0.58

0.12

0.32

0.10

0.58

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B10: Multilevel model results for biology with dependent variable 'at grade A'

(MIXOR)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-1.65

0.10

1.09

0.07

0.00

0.25

0.75

MN

-2.80

0.11

3.02

0.08

0.89

0.11

0.69

0.07

0.25

MNR

-2.83

0.10

3.18

0.08

0.80

0.10

0.71

0.06

0.23

MNS

-2.69

0.11

2.84

0.08

0.97

0.11

0.65

0.08

0.27

TOT

-2.25

0.11

2.15

0.05

1.28

0.10

0.50

0.14

0.36

TOTR

-2.03

0.11

1.43

0.04

1.17

0.07

0.31

0.18

0.51

TOTS

-2.42

0.11

2.52

0.07

1.12

0.10

0.59

0.10

0.31

MN9

-2.67

0.10

2.91

0.07

0.82

0.10

0.67

0.06

0.26

MN9R

-2.58

0.09

3.07

0.06

0.65

0.09

0.71

0.05

0.25

MN9S

-2.62

0.10

2.77

0.08

0.96

0.11

0.64

0.08

0.28

BE5

-2.86

0.11

3.03

0.07

0.93

0.10

0.68

0.07

0.25

BE5R

-3.06

0.12

3.67

0.10

0.98

0.11

0.76

0.05

0.19

BE5S

-2.73

0.11

2.76

0.07

0.96

0.10

0.64

0.08

0.28

BE9

-2.69

0.10

2.93

0.08

0.80

0.11

0.68

0.06

0.26

BE9R

-2.73

0.10

3.32

0.08

0.72

0.10

0.73

0.05

0.22

BE9S

-2.64

0.11

2.78

0.08

0.90

0.11

0.65

0.08

0.28

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B11: Multilevel model results for biology with dependent variable 'at least grade B'

(MIXOR)

Measure

Const

s.e.

slope

s.e.

Centre

s.e.

EXP

UC

UP

None

-0.55

0.08

1.13

0.07

0.00

0.25

0.75

MN

-0.64

0.08

2.53

0.08

0.75

0.08

0.61

0.07

0.32

MNR

-0.69

0.08

2.57

0.07

0.69

0.08

0.62

0.06

0.31

MNS

-0.56

0.08

2.50

0.07

0.79

0.08

0.61

0.08

0.32

TOT

-0.56

0.08

2.01

0.05

0.98

0.07

0.49

0.12

0.40

TOTR

-0.61

0.08

1.36

0.04

1.07

0.06

0.30

0.17

0.53

TOTS

-0.49

0.08

2.35

0.07

0.73

0.08

0.58

0.08

0.34

MN9

-0.62

0.07

2.43

0.06

0.64

0.08

0.60

0.06

0.33

MN9R

-0.67

0.07

2.46

0.04

0.54

0.07

0.61

0.05

0.33

MN9S

-0.55

0.08

2.45

0.07

0.72

0.08

0.60

0.07

0.33

BE5

-0.68

0.08

2.46

0.06

0.78

0.07

0.60

0.08

0.33

BE5R

-0.73

0.08

2.72

0.04

0.74

0.07

0.65

0.06

0.29

BE5S

-0.61

0.08

2.35

0.06

0.80

0.08

0.57

0.08

0.34

BE9

-0.62

0.08

2.44

0.06

0.63

0.07

0.60

0.06

0.33

BE9R

-0.67

0.07

2.52

0.04

0.54

0.07

0.62

0.05

0.32

BE9S

-0.54

0.08

2.44

0.07

0.70

0.07

0.60

0.07

0.33

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B12: Multilevel model results for biology with dependent variable 'at least grade E'

(MLwin)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

1.93

0.10

1.44

0.20

0.00

0.30

0.70

MN

2.92

0.12

1.53

0.08

1.46

0.22

0.33

0.21

0.46

MNR

2.70

0.11

1.31

0.07

1.41

0.21

0.27

0.22

0.51

MNS

3.14

0.13

1.79

0.09

1.44

0.22

0.40

0.18

0.41

TOT

2.53

0.11

1.15

0.07

1.31

0.20

0.22

0.22

0.56

TOTR

2.15

0.10

0.61

0.06

1.34

0.19

0.07

0.27

0.66

TOTS

2.99

0.12

1.67

0.09

1.38

0.20

0.37

0.19

0.44

MN9

2.75

0.11

1.32

0.07

1.29

0.20

0.28

0.20

0.52

MN9R

2.43

0.10

0.97

0.06

1.22

0.19

0.17

0.22

0.60

MN9S

3.06

0.13

1.69

0.09

1.35

0.21

0.38

0.18

0.44

BE5

2.78

0.11

1.38

0.07

1.35

0.21

0.29

0.21

0.50

BE5R

2.56

0.10

1.25

0.07

1.26

0.20

0.26

0.21

0.54

BE5S

2.98

0.12

1.58

0.08

1.37

0.21

0.35

0.19

0.46

BE9

2.74

0.11

1.33

0.07

1.25

0.20

0.28

0.20

0.52

BE9R

2.41

0.10

0.96

0.07

1.20

0.19

0.17

0.22

0.61

BE9S

3.05

0.13

1.68

0.09

1.31

0.21

0.38

0.18

0.44

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B13: Multilevel model results for geography with dependent variable 'at grade A'

(MLwin)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-1.64

0.08

0.71

0.12

0.00

0.18

0.82

MN

-2.45

0.10

1.88

0.08

0.70

0.14

0.47

0.09

0.44

MNR

-2.47

0.10

1.99

0.09

0.67

0.13

0.50

0.08

0.42

MNS

-2.34

0.10

1.75

0.07

0.72

0.14

0.43

0.10

0.47

TOT

-2.11

0.09

1.49

0.07

0.73

0.14

0.36

0.12

0.53

TOTR

-1.85

0.08

1.00

0.06

0.66

0.12

0.20

0.13

0.66

TOTS

-2.26

0.10

1.68

0.07

0.72

0.14

0.41

0.11

0.48

MN9

-2.44

0.10

1.93

0.08

0.68

0.14

0.48

0.09

0.43

MN9R

-2.49

0.10

2.15

0.10

0.62

0.13

0.54

0.07

0.39

MN9S

-2.35

0.10

1.77

0.07

0.72

0.14

0.44

0.10

0.46

BE5

-2.44

0.10

1.85

0.08

0.67

0.13

0.46

0.09

0.45

BE5R

-2.49

0.10

2.04

0.09

0.67

0.13

0.51

0.08

0.41

BE5S

-2.35

0.10

1.70

0.07

0.68

0.14

0.42

0.10

0.48

BE9

-2.44

0.10

1.92

0.08

0.67

0.13

0.48

0.09

0.43

BE9R

-2.50

0.10

2.17

0.10

0.62

0.13

0.55

0.07

0.38

BE9S

-2.36

0.10

1.77

0.07

0.70

0.14

0.44

0.10

0.46

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate pupil level)

Table B14: Multilevel model results for geography with dependent variable 'at least grade B'

(MLwin)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

-0.47

0.06

0.48

0.08

0.00

0.13

0.87

MN

-0.62

0.07

1.72

0.06

0.50

0.09

0.44

0.07

0.49

MNR

-0.65

0.07

1.73

0.06

0.47

0.08

0.44

0.07

0.49

MNS

-0.57

0.07

1.72

0.06

0.51

0.09

0.44

0.08

0.49

TOT

-0.52

0.07

1.41

0.06

0.54

0.09

0.34

0.09

0.57

TOTR

-0.49

0.07

0.90

0.05

0.52

0.08

0.18

0.11

0.71

TOTS

-0.52

0.07

1.65

0.07

0.50

0.09

0.42

0.08

0.51

MN9

-0.62

0.07

1.79

0.06

0.51

0.09

0.46

0.07

0.47

MN9R

-0.65

0.07

1.74

0.07

0.48

0.09

0.45

0.07

0.48

MN9S

-0.57

0.07

1.71

0.06

0.51

0.09

0.43

0.08

0.49

BE5

-0.63

0.07

1.67

0.06

0.46

0.09

0.43

0.07

0.50

BE5R

-0.65

0.07

1.75

0.06

0.56

0.10

0.44

0.08

0.48

BE5S

-0.58

0.07

1.63

0.06

0.46

0.06

0.41

0.07

0.51

BE9

-0.61

0.07

1.73

0.06

0.49

0.06

0.44

0.07

0.49

BE9R

-0.65

0.07

1.78

0.07

0.49

0.07

0.46

0.07

0.47

BE9S

-0.56

0.07

1.71

0.06

0.50

0.06

0.44

0.07

0.49

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B15: Multilevel model results for general studies with dependent variable 'at least grade E'

(MLwin)

Measure

Const.

s.e.

slope

s.e.

centre

s.e.

EXP

UC

UP

None

2.44

0.11

1.52

0.08

0.00

0.32

0.68

MN

3.40

0.14

1.52

0.10

1.25

0.09

0.34

0.18

0.48

MNR

3.20

0.13

1.29

0.08

1.30

0.08

0.27

0.21

0.53

MNS

3.58

0.15

1.78

0.11

1.19

0.09

0.41

0.16

0.43

TOT

2.94

0.12

1.08

0.08

1.49

0.09

0.20

0.25

0.55

TOTR

2.60

0.11

0.55

0.07

1.51

0.08

0.06

0.30

0.64

TOTS

3.40

0.14

1.63

0.11

1.31

0.09

0.37

0.18

0.45

MN9

3.24

0.13

1.36

0.09

1.30

0.09

0.29

0.20

0.51

MN9R

2.93

0.12

1.37

0.08

1.37

0.09

0.29

0.21

0.50

MN9S

3.51

0.17

1.70

0.11

1.22

0.09

0.39

0.16

0.44

BE5

3.20

0.13

1.31

0.09

1.18

0.09

0.28

0.19

0.53

BE5R

3.02

0.12

1.16

0.09

1.15

0.10

0.23

0.20

0.57

BE5S

3.36

0.14

1.52

0.10

1.17

0.08

0.34

0.17

0.49

BE9

3.20

0.13

1.33

0.09

1.31

0.09

0.28

0.21

0.52

BE9R

2.88

0.12

0.97

0.08

1.38

0.09

0.17

0.25

0.59

BE9S

3.48

0.15

1.68

0.11

1.22

0.09

0.38

0.17

0.45

(EXP - explained variance, UC - Unexplained variance at the centre level, UP - unexplained variance at the candidate/pupil level)

Table B16: Means and variances of the GCSE measure for the five individual A-level samples

 

Geography

Mathematics

Biology

General

English

Meas.

Mean

s.d.

Mean

s.d.

Mean

s.d.

Mean

s.d.

Mean

s.d.

MN

6.0

0.8

6.4

0.8

6.3

0.8

6.2

0.8

5.7

0.8

MNR

2.4

0.2

2.5

0.2

2.5

0.2

2.5

0.2

2.4

0.2

MNS

36.9

9.1

42.1

9.8

41.5

10.1

40.3

10.0

34.0

9.3

TOT

57.8

8.7

61.3

10.5

61.3

9.7

60.1

10.1

51.1

9.5

TOTR

23.5

2.6

24.1

3.2

24.2

2.8

23.9

3.0

22.9

2.9

TOTS

359.9

91.3

404.7

106.2

401.5

104.6

387.3

104.0

328.3

93.0

MN9

5.9

0.8

6.3

0.9

6.3

0.9

6.2

0.9

5.7

0.9

MN9R

2.4

0.2

2.5

0.3

2.5

0.2

2.5

0.3

2.4

0.2

MN9S

36.8

9.2

41.7

10.3

41.3

10.3

39.8

10.3

33.8

9.5

BE5

32.5

3.8

34.4

4.2

34.2

4.0

33.6

4.3

31.4

4.1

BE5R

12.7

0.8

13.1

1.0

13.0

0.9

12.9

1.1

12.5

1.0

BE5S

215.1

48.3

242.6

51.0

238.5

52.0

231.2

52.6

201.9

49.0

BE9

54.4

7.1

57.8

8.4

59.6

7.81

56.5

8.3

51.9

8.0

BE9R

21.9

1.7

22.6

2.3

22.6

1.9

22.3

2.2

21.4

2.1

BE9S

340.2

82.9

385.0

93.5

385.0

93.0

368.1

93.1

313.6

85.1

 

 

 

This document was added to the Education-line database on 12 September 2000