# A GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES

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2 SUMMARY INTERPRETING SCHOOL AND COLLEGE VALUE ADDED SCORES Example of how a school or college's value added might be displayed i a table Displayig a school or college's VA visually o a chart How to Iterpret the iformatio ad chart Istitutio Name VA measure based o progress betwee Key Stage 4 ad Level 3 Qualificatios (measure cetred aroud zero ad expressed i grades) Limit of Level 3VA Cofidece Itervals Upper Lower School A School B School C School A NATIONAL AVERAGE SCHOOL VA SCORE = ZERO School A's VA score is above the atioal average ad this is statistically sigificat. This is because the whole rage of the cofidece iterval is above zero This tells us that studets i this school make more progress tha average The higher a school or college's VA score i a qualificatio type, the more progress the studets i the school or college are makig, with zero represetig the atioal average. Cofidece itervals the allow us to assess whether the school or college's VA score is sigificatly above or below the atioal average College B NATIONAL AVERAGE SCHOOL VA SCORE = ZERO College B's VA score is ot sigificatly differet from the atioal average. This is because the rage of the cofidece iterval straddles the atioal average of zero This tells us that studets i this college make progress comparable with the average KEY: Upper Cofidece Limit School VA Score Lower Cofidece Limit School C NATIONAL AVERAGE SCHOOL VA SCORE = ZERO School C's VA score is below the atioal average ad this is statistically sigificat. This is because the whole rage of the cofidece iterval is belowzero This tells us that studets i this school make less progress tha average 2

7 A Level / Applied GCE Sigle Award Grade Poit Score Rebased Poit Score AS Level / Applied GCE AS Sigle Award Grade Poit Score Rebased Poit Score BTEC Level 3 Subsidiary Diploma Grade Poit Score Rebased Poit Score A* A D* A B D B C M C D P D E FAIL 0 0 E FAIL 0 0 FAIL 0 0 7

9 The positive score tells us that this studet has exceeded their estimated A Level Geography outcome. If the Value Added score was egative, the this would tell us that the studet scored less tha their estimated A Level Geography outcome. The tables below summarises the calculatio described above. Example 1 Studet's Actual KS4 Average Poit Score Performace of all studets takig A Level Geography with a average score of 52 at KS4 used to estimate studet's performace i A level Geography (usig a statistical model) Studet's Estimated A Level Geography Outcome Studet's Actual A Level Geography Outcome Differece (Actual - Estimate) 52 Poits B A +1 Grade Example 2 Studet's Actual KS4 Average Poit Score 46 poits Performace of all studets takig A Level Frech with a average score of 46 at KS4 used to estimate studet's performace i A level Frech (usig a statistical model) Studet's Estimated A Level Frech Outcome Betwee a B ad C grade Studet's Actual A Level Frech Outcome B Differece (Actual - Estimate) +0.4 Grades The techical aex (sectio 1) provides a more detailed descriptio of how studets estimated scores ad their Value Added scores are calculated. 9

10 CALCULATING SCHOOL AND COLLEGE VALUE ADDED SCORES FOR INDIVIDUAL QUALIFICATIONS Oce studet VA scores have bee calculated for a particular qualificatio (e.g. OCR Natioal Certificate i Busiess Studies), we take the average of all the studet VA scores i that qualificatio withi the school or college. We the apply the shrikage factor, a adjustmet that provides a better estimate of VA scores for schools ad colleges with small umbers of pupils. The diagram below shows a example of how a school/college VA score is calculated from a example of five studet VA scores i a idividual qualificatio. STEP 1 - FIND THE AVERAGE OF STUDENT SCORES IN THE QUALIFICATION Studet 1 VA Score Studet 2 VA Score Studet 3 VA Score Studet 4 VA Score Studet 5 VA Score Average of the Studet VA Scores = School/College Ushruke VA Score i Qualificatio STEP 2 - APPLY THE SHRINKAGE FACTOR School/College Ushruke VA Score x Shrikage Factor = School/College Shruke VA Score i Qualificatio For more iformatio o calculatig school ad college Value Added scores, icludig the applicatio of shrikage factors, please see sectio two of the techical aex. 10

11 CALCULATING SCHOOL AND COLLEGE VALUE ADDED SCORES FOR QUALIFICATION TYPES The previous sectio showed how to calculate value added scores for each qualificatio offered by a school or college; it is also possible to aggregate a school or college s qualificatio scores up to calculate qualificatio type value added scores for the school or college. The blue shaded area i the diagram shows the qualificatio type level of the hierarchy. A qualificatio type Value Added score (e.g. AS Levels) is calculated by fidig the average of all the qualificatio Value Added scores that belog to the qualificatio type. A school or college s AS Level qualificatio type score would be foud by averagig all the AS Level qualificatio Value Added scores (e.g. AS Level History, AS Level Ecoomics, AS Level Maths) offered by the school. The calculatio is also weighted by the umber of studets takig each qualificatio; this gives greater weight to qualificatios beig take by more studets. The example below demostrates how to calculate a AS Level qualificatio type Value Added score for a school/college offerig three AS levels: AS Level VA Score = (50 x +0.25) + (20 x -0.70) + (100 x +0.35) ( ) = grades AS Level History VA score = Cohort Size = 50 AS Level Ecoomics VA score = Cohort Size = 20 AS Level Maths VA score = Cohort Size =

12 Which Qualificatio Types are Icluded? I order for a qualificatio type (e.g. A Levels) to be icluded withi Level 3 Value Added, it must first be a Level 3 qualificatio type but it also must have a graded outcome. This meas that the qualificatio type eeds to have four or more possible outcomes, for example, A Levels have seve differet outcomes (A*, A, B, C, D, E ad FAIL). Additioally, there eeds to be a miimum of 80 studets ad 5 istitutios offerig the qualificatio type atioally i order for it to be icluded i Level 3 Value Added. The list below shows some of the qualificatio types icluded i Level 3 Value Added for the publicatio based o 2012/13 examiatio data. Qualificatio Type A Levels AS Levels Exteded Project (Diploma) Pre-U Qualificatios Applied GCE A Level Qualificatios Iteratioal Baccalaureate Free Stadig Maths Qualificatios BTEC Level 3 Qualificatios 12

15 we ca say that the school/college is ot sigificatly differet from the atioal average for the qualificatio, i other words, we caot cofidetly say that the school or college s VA score is defiitely above or defiitely below the atioal average for the qualificatio. The table ad diagram below shows how a school/college s VA score ad cofidece itervals should be iterpreted to reach oe of the three defiitios above. School A is a example of a school that is sigificatly above atioal average, College B is ot sigificatly differet from atioal average, ad School C is sigificatly below atioal average. School A School B School C VA Score Upper Cofidece Limit Lower Cofidece Limit For more iformatio o the calculatio of cofidece itervals, please see the techical aex. 15

22 5. u is a 1 matrix of the idividual exam record VA scores ad (upper case gamma) is a 1 5 matrix cotaiig the five coefficiets for this particular qualificatio. Y is a 1 matrix of the outcome attaimet y of each exam record for this particular qualificatio ad X is a x 5 matrix, where each row of X is give , x, x, x, x 6. For example, for a sigle case, if a learers had a average prior attaimet score of x = 45 ad a outcome attaimet of y = 210 ad the key coefficiets were: 0 = = = = = The applyig the equatio for a sigle studet would give: u Y u y Would be equal to: X T , x 1, x 2, x, 3, x 4 u = 210 ( x x x x ) u = u = Expressed as a matrix of three cases this would be equivalet to: Y, X x x x x x 4 x Therefore a example of u would be: 5.95 u If a cadidate has achieved the highest possible grade for a qualificatio the their value added score should ot be lower tha 0. I some cases 22

23 the atioal lie of expected attaimet fitted by the statistical model ca lead to studets with high prior attaimet values beig give a estimated attaimet value above the maximum grade. 9. For example, o a AS level, a studet could be give a estimated attaimet value of 76 rebased QCA poits whe the maximum attaiable grade, a A grade, is oly worth 75 poits. I this case the studet would usually be give a score of -1 however this is overwritte with a score of 0. Studets whose estimates are below the maximum grade do ot have their scores modified. 23

25 2 I this formula, x is defied as, x, x ad S is the Natioal 1 avg avg Covariace matrix for the particular qualificatio for which the calculatios are beig performed The calculate the variace ratio usig the error term from the MLM output: Fially, calculate the shrikage factor : 18. The overall istitutio VA score U for the give qualificatio is the give by: U VA Calculatio of cofidece itervals aroud a school or college s qualificatio VA score 19. Usig the stadard error, it is possible to calculate cofidece itervals aroud a school or college s qualificatio value added score. Cofidece itervals represet the rage withi which we ca be cofidet that the avg school or college s true value added score lies. The stadard error of U is give by: The 95% cofidece iterval aroud a school or college s qualificatio value added score is the give by: U

27 25. It is the possible to calculate 95% cofidece itervals aroud the school or college s qualificatio type value added score. The first step i doig this is to calculate the stadard error for the qualificatio type: VA Qual ExamQualSu bj 1 ExamQualSu bj ExamQuals 2 2 QualSubj 26. The fial step is to the use the qualificatio type stadard error to calculate cofidece itervals aroud the value added score usig the followig equatio: VAQual 1.96 VA qual 27

31 be above the atioal average ad statistically sigificat whe their value added score is above zero ad the lower ed of the 95% cofidece iterval is above zero. This ca be expressed formulaically as: ( ) 31

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