Evaluation of the Two Year Key Stage 3 Project - Communities and ...

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ANNEX C - OPTIONAL TEST MODELLINGMulti-level modelling was used as the method of analysis for the Optional Test results. This is a formof multiple regression. Multiple regression enables us to examine the relationship between thedependent variable of interest (for example the Year 7 Mathematics Optional Test score) and a set ofindependent (predictor) variables. These independent variables include whether the pupils attends aProject or Comparison school and also various background characteristics that have previously beenshown to be associated with attainment (for example prior attainment, the sex of the pupil andeligibility for free school meals). ‘Multi-level’ modelling takes into account the fact that pupils areclustered within schools. Failure to take this clustering into account may result in statisticallysignificant associations being reported between the dependent variable (e.g., mathematics test scores)and an independent variable (e.g., being eligible for free school meals) when such a conclusion is notmerited.The models also allow for the possibility that, for example, at some schools pupils with higher levels ofprior attainment may make greater progress than their schoolmates while at other schools it may bepupils with lower prior attainment who make relatively greater progress.It should be remembered that the range of possible values differs for the independent variables listed inTables C1 to C11. For example, the Key Stage 2 Mathematics variable reported in Table C has astandard deviation of more than 20 points whereas the school’s percentage eligible for free schoolmeals has a standard deviation of only 11 and the eligible for free school meals variable may either takethe value of zero (for those not eligible) or one (for those eligible).One means of comparing the ‘effect sizes’ for different independent variables is to express thecoefficients for continuous variables (such as Key Stage 2 score) in terms of the standard deviation ofthat independent variable and to express changes in the dependent variable in terms of its standarddeviation. In the case of continuous variables this enables us to compare the effect size for each variablefor a comparable change in the value of those variables. That is, even though Key Stage 2 Mathematicsscore is measured in marks (from 1-100) and the number of books in the home on a different scale(from 1-6), we are able to compare the two by expressing both in terms of their own standard deviation(or, as is shown in the figures, for a change of 1.41standard deviations). In the case of the dichotomousvariables such as ‘Project school’ the figures indicate the change in Optional Test scores (expressed interms of their standard deviation) associated with having that characteristic (that is, for example, beinga girl or attending a Project school).Such effect sizes are represented in Figures C1 to C4 as are the degree of precision for each of theestimated values with the lines showing the 95% Confidence Intervals for each coefficient estimated.55
Table C1 - Final model for Year 7 Mathematics Optional Test scoreYr 7 Mathematics ScoreMultilevel results95% ConfidenceintervalParameterEstimateStandarderror Sig. Min. Max.Final modelSchool variance 167.405 58.238 * 53.259 281.551School KS2/constant covar -1.766 0.680 * -3.099 -0.433School KS2 variance 0.022 0.009 * 0.004 0.040Pupil variance 159.027 4.105 * 150.981 167.073Fixed coefficientsConstant -17.346 3.299 * -23.812 -10.880KS2 Mathematics score 1.392 0.034 * 1.325 1.459School level FSM -0.289 0.075 * -0.436 -0.142Project school 6.611 2.033 * 2.626 10.596Quantity of books in home 1.180 0.180 * 0.827 1.533Eligible for FSM -3.667 0.746 * -5.129 -2.205Special educational needs -4.547 0.925 * -6.360 -2.734Female 1.169 0.528 * 0.134 2.204Table C2 - Final model for Year 7 Optional Test score in Mental MathematicsYr 7 Mental MathematicsMultilevel results95% ConfidenceintervalParameterEstimateStandarderror Sig. Min. Max.Final modelSchool variance 5.673 2.152 * 1.455 9.891School KS2/constant covar -0.189 0.096 * -0.377 -0.001School KS2 variance 0.008 0.005 -0.002 0.018Pupil variance 13.098 0.337 * 12.437 13.759Fixed coefficientsConstant 3.331 0.700 * 1.959 4.703KS2 Mental Mathematicsscore 1.042 0.027 * 0.989 1.095Special educational needs -1.669 0.259 * -2.177 -1.161Indian 2.012 0.644 * 0.750 3.274Quantity of books in home 0.202 0.051 * 0.102 0.302Eligible for FSM -0.870 0.211 * -1.284 -0.456School level FSM -0.064 0.018 * -0.099 -0.029Project school 1.380 0.479 * 0.441 2.31956
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RESEARCHEvaluation of the Two YearK
Page 4 and 5:
CONTENTSEXECUTIVE SUMMARY 21. EVALU
Page 6:
nationally expected level for pupil
Page 9 and 10: For schools operating an accelerate
Page 11 and 12: 2.2 Attainment and attitudesThe tim
Page 13 and 14: could follow a Year 7 and Year 8 Ke
Page 15 and 16: Figure 2 - Percentage of Project sc
Page 17 and 18: The analysis of Key Stage 3 results
Page 19 and 20: Table 4 - Proportion of pupils achi
Page 21 and 22: Figure 4 - 2005 Key Stage 3 mathema
Page 23 and 24: Table 6 - Proportion of pupils achi
Page 25 and 26: SummaryIn the case of English, when
Page 27 and 28: 4.4 Attainment summaryThe analysis
Page 29 and 30: to 8 these were in the opposite dir
Page 31 and 32: Figure 10 - Percentage of Year 7 pu
Page 33 and 34: 6. ANALYSIS OF CASE STUDY DATAAs ha
Page 35 and 36: Table 9 - Operationalisation of the
Page 37 and 38: 6.1 Overall viewsMost, though not a
Page 39 and 40: Points of interest for the higher s
Page 41 and 42: The key advantage is opening up Key
Page 43 and 44: 6.3 ProgressionNevertheless, findin
Page 45 and 46: would no longer exist. Both of the
Page 47 and 48: However, as a colleague noted, even
Page 49 and 50: Most commonly the freedom was used
Page 51 and 52: Phase 2 Project and Phase 2 Compari
Page 53 and 54: A11 - Key Stage 3 attainmentProject
Page 55 and 56: A20 - Reported number of books in t
Page 57: The variables listed below were inc
Page 62 and 63: Table C3 - Final model for Year 7 E
Page 64 and 65: Figure C2 - Year 7 English Optional
Page 66 and 67: Table C8 - Final model for Year 8 m
Page 68 and 69: Figure C4 - Year 8 mathematics high
Page 70 and 71: Table C11 - Final model for Year 8
Page 72: Good teachersMy teachers make sure
Page 75 and 76: ANNEX F - CASE STUDY SUMMARIESPhoeb
Page 77 and 78: Abbotswell SchoolThe case study vis
Page 79 and 80: Elsiemaud SchoolThe case study visi
Page 81 and 82: Henryson SchoolThe case study visit
Page 83 and 84: ANNEX G - OTHER EARLY ENTRANTS TO 2
Page 85 and 86: Table G5 - Key Stage 3 Mathematics
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