A GUIDE TO LUE ADDED KEY STAGE 2 TO 4 IN 2013 SCHOOL PERFORMANCE TABLES & RAISEonline Content Summary Interretin School and Puil Grou Value Added Score Pae No. What i Value Added? 3 Calculatin Puil Value Added Score 4 Calculatin School Value Added Score 5 Interretin School Value Added Score 6 Calculatin Puil Grou Value Added Score 10 Interretin Puil Grou Value Added Score 11 The 2013 KS2-4 Value Added Meaure 12 Technical Annex content 14 2 1
SUMMARY INTERPRETING SCHOOL LUE ADDED SCORES Examle of chool information from Performance Table Dilayin a chool information viually on a chart How to interret the information and chart Intitution Name meaure baed on rore between Key Stae 2 and Key Stae 4 (centred around 1,000) Limit of Key Stae 2 to 4 Confidence Interval Uer Lower School A 1,019.9 1,028.6 1,011.1 School B 998.8 1,008.1 989.4 School C 985.9 995.4 976.4 School A 1,000 [NATIONAL AVERAGE SCHOOL SCORE] 1,028.6 1,019.9 1,011.1 School A core i above the national averae and thi i tatitically inificant Thi i becaue the whole rane of the confidence interval i above 1,000 Thi tell u that the uil in thi chool make more rore than averae The hiher the chool core, the more rore the uil in the chool are makin, with 1,000 rereentin the national averae rore. Confidence interval then allow u ae whether the chool core i inificantly above or below the national averae KEY: Uer Confidence Limit School Score Lower Confidence Limit School B 1,000 [NATIONAL AVERAGE SCHOOL SCORE] School C 1,000 [NATIONAL AVERAGE SCHOOL SCORE] 1,008.1 998.8 989.4 995.4 985.9 976.4 School B core i not inificantly different from the national averae Thi i becaue the rane of the confidence interval traddle the national averae of 1,000 Thi tell u that the uil in thi chool make rore comarable with the averae School C core i below the national averae and thi i tatitically inificant Thi i becaue the whole rane of the confidence interval i below 1,000 Thi tell u that the uil in thi chool make le rore than averae
WHAT IS LUE ADDED? When meaurin how effective a chool i, it i imortant to look at how well it uil erform in their tet and examination. However, when evaluatin examination erformance, it i alo imortant to take into conideration that when uil firt join a econdary chool, they have varyin level of ability, i.e. uil have many different tartin oint. The uroe of value added () meaure are to look at how much rore uil have made from the beinnin to the end of their comulory econdary education (i.e. between the end of key tae 2 (KS2) and the end of key tae 4 (KS4) ). Analyi how that there i a very tron relationhi between examination erformance of uil at a reviou key tae and their current key tae. A meaure ue thi relationhi to etimate how well all uil erform in their current key tae exam. We calculate an etimated outcome for each uil at the end of KS4. Thi i done by lookin at the actual KS4 erformance of all uil and workin out the averae KS4 oint achieved by uil nationally of imilar ability at the end of KS2. Thi KS4 etimated outcome can then be comared aaint what the uil actually achieved in their KS4 exam, to ee whether or not they exceeded it. The difference between a uil actual KS4 erformance and their etimated KS4 erformance ive the uil their value added core. The averae core for all uil in a chool can then be calculated to find a chool core, which hel to identify chool whoe uil make more rore or le rore than averae. The ummary diaram on ae 2 how how to interret thee core. The erformance table webite how chool core for the followin ix KS2-4 meaure: KS2-4 Bet 8 lu Enlih and mathematic bonu meaure KS2-4 Enlih Baccalaureate Enlih ubject area meaure KS2-4 Enlih Baccalaureate mathematic ubject area meaure KS2-4 Enlih Baccalaureate cience ubject area meaure KS2-4 Enlih Baccalaureate humanitie ubject area meaure KS2-4 Enlih Baccalaureate lanuae ubject area meaure Pleae ee ae 12 for further information on the ix meaure above. 3
CALCULATING PUPIL LUE ADDED SCORES Individual uil core need to be calculated before a chool core can be roduced. The firt te i to ue a tatitical model to calculate a KS4 etimated outcome for all uil that are at the end of KS4 in 2013. Each uil KS4 etimate i calculated baed on the actual KS4 outcome of all uil nationally with the ame level of achievement at KS2. For examle, calculation of an etimated outcome for a uil who cored an averae of 24 oint at KS2 will be baed on the actual KS4 outcome of all uil nationally that alo cored an averae of 24 oint at KS2. A uil core i then calculated by ubtractin their etimated KS4 outcome from their actual KS4 outcome. Uin the Enlih Baccalaureate mathematic ubject area meaure a an examle, if a uil attain a B in GCSE mathematic (equivalent to 46 oint) and they are etimated to attain a C (equivalent to 40 oint) by the meaure, then the uil ha a Value Added core of +6 oint (46 oint 40 oint). The oitive core tell u that thi uil ha exceeded their etimated KS4 outcome. If the core wa neative, then thi would tell u that the uil cored le than their etimated KS4 outcome. The table below ummarie the calculation decribed above. Puil' Actual KS2 Averae Point Score Performance of all uil with an averae core of 24 at KS2 ued to etimate erformance at KS4 Puil' Etimated KS4 GCSE Math Score Puil' Actual KS4 GCSE Math Score Difference (Actual - Etimate) 24 Point C (40 Point) B (46 Point) +6 Point (46-40) Section B of the technical annex rovide a more detailed decrition of how uil etimated KS4 core and their core are calculated. If you wih to ue ome data to better undertand the uil calculation, a ueful reource i the KS2-4 uil level ready reckoner which RAISEonline 1 uer can find in the Library at www.raieonline.or and it i alo on the erformance table webite at www.education.ov.uk/chool/erformance. 1 RAISEonline i an analytical tool ued by chool which rovide interactive analyi of chool and uil erformance data. 4
CALCULATING SCHOOL LUE ADDED SCORES Once uil core have been calculated, we take the averae of all the uil core within that chool. We then aly the hrinkae factor, an adjutment that rovide a better etimate of core for chool with mall number of uil. Finally, to differentiate between the KS1-2 and KS2-4 meaure, we centre by addin 1,000 to every KS2-4 chool core (KS1-2 core are centred on100). The diaram below how an examle of how a chool core i calculated from an examle of five uil core. STEP 1 - FIND THE AVERAGE OF PUPIL SCORES Puil 1 Score Puil 2 Score Puil 3 Score Puil 4 Score Puil 5 Score Averae of the five Puil Score = School Unhrunken Score STEP 2 - APPLY THE SHRINKAGE FACTOR School Unhrunken Score x Shrinkae Factor = School Shrunken Score STEP 3 - CENTRE THE SCHOOL SCORE School Shrunken Score + 1,000 = Centred Final School Score For more information on calculatin chool core, includin the alication of hrinkae factor, leae ee Section C of the technical annex. 5
INTERPRETING SCHOOL LUE ADDED SCORES We can ue the chool core a a meaure of chool effectivene, but we mut be careful to note that it i baed on a iven et of uil' reult for a articular tet aer on a articular day. A chool could have been equally effective and yet the ame et of uil miht have achieved lihtly different KS4 reult on the day. And the chool would almot certainly have hown lihtly different KS4 reult with a different et of uil. Thi element of uncertainty need to be taken into account when interretin a chool core; thi i done uin confidence interval. A confidence interval i a rane of core within which we are tatitically confident that a chool true core will fall. A chool confidence interval i alway centred on the chool core. For examle, if a chool core i 1,010 and the ize of the chool confidence interval i 5 oint, then the confidence interval rane between 1,005 and 1,015 (i.e. 5 oint either ide of the chool core). The ize of the confidence interval i determined by the number of uil in the chool at the end of KS4. Smaller chool have wider confidence interval becaue their core i baed on a maller number of uil, o there i le evidence on which to jude the chool effectivene. To jude a chool effectivene, both the chool core and the aociated confidence interval need to be taken into account. If the whole rane of the confidence interval i above 1,000 (i.e. the lower confidence limit i reater than 1,000), we can ay the chool core i above the national averae and i tatitically inificant, and we can be confident the chool i helin it uil make better than averae rore. An illutration of how to interret chool core i iven on ae 2. Similarly, when the entire rane of the confidence interval i below 1,000 (i.e. the uer confidence limit i le than 1,000), we can ay the chool core i the national averae and i tatitically inificant. Finally, if the confidence interval traddle the national averae of 1,000, then we can ay that the chool i not inificantly different from the national averae, in other word, we cannot confidently ay that the chool core i definitely above or definitely below the national averae. The table and diaram overleaf how how a chool core and confidence interval hould be interreted to reach one of the three definition above. School A i an examle of a chool that i inificantly above national averae; School B i not inificantly different from national averae; and School C i inificantly below national averae. 6
School A School B School C School Score 1,010 1,000 990 Uer Confidence Interval 1,015 1,005 995 Lower Confidence Interval 1,005 995 985 For more information on the calculation of confidence interval, leae ee Section E of the technical annex. Another ueful reource i the KS2-4 chool level ready reckoner, which demontrate how the number of eliible uil for a core in a chool i linked to the width of a chool confidence interval. RAISEonline uer can find thi in the library at www.raieonline.or and it i alo on the erformance table webite at www.education.ov.uk/chool/erformance. Comarion of Enlih Baccalaureate ubject area core Confidence interval mut alo be taken into account when comarin two or more Enlih Baccalaureate ubject area core within a chool (e.. when comarin a chool Enlih Baccalaureate Enlih core with their Enlih Baccalaureate humanitie core). The ize of the confidence interval for each of the five Enlih Baccalaureate meaure for a chool will vary in ize (a they are baed on different model and different number of uil) but rereent the ame idea each interval define the rane of value within which we are tatitically confident that the chool true core for the reective Enlih Baccalaureate ubject area lie. To jude a chool effectivene in any two Enlih Baccalaureate ubject area, the rane of the two aociated confidence interval need to be comared. If the entire rane of the confidence interval for, ay, Enlih i above the rane of the interval for humanitie (i.e. the lower confidence limit for Enlih i reater than the uer confidence limit for humanitie), we can 7
ay the chool Enlih core i above their humanitie core and i tatitically inificant, and we can be confident the chool i helin it uil make better rore in Enlih than in humanitie. Similarly, if the entire rane of the confidence interval for Enlih wa below the rane of the interval for humanitie (i.e. the uer confidence limit for Enlih i le than the lower confidence limit for humanitie), we can ay the chool Enlih core i below their humanitie core and thi i tatitically inificant, and we can be confident the chool i helin it uil make better rore in humanitie than in Enlih. In the other cae where the two confidence interval overla, then we cannot ay with confidence whether there i any difference between the two core, and hence there i not a inificant difference between how effective the chool i in helin it uil make rore in the two ubject area. The table and diaram below how an examle of how a chool Enlih Baccalaureate core and confidence interval could be interreted. Enlih Math Science Humanitie Lanuae School Score 1,005.0 1,000.0 1,003.5 1,001.5 1,000.5 Uer Confidence Interval 1,007.0 1,002.0 1,006.0 1,004.0 1,004.0 Lower Confidence Interval 1,003.0 998.0 1,001.0 999.0 997.0 Thi chool ha five Enlih Baccalaureate core ranin between 1,000 and 1,005. However, when lookin to comare core acro ubject area, the aociated confidence interval all overla aide for the interval for Enlih and mathematic, where the lower confidence limit for Enlih i reater than the uer confidence limit for mathematic. We are confident then that the chool i helin it uil make better rore in Enlih than in mathematic, but cannot ay there i a inificant difference between how effective the chool i in helin it uil make rore between Enlih and other ubject area, nor indeed any other combination of ubject. ENGLISH SCORE IS HIGHER THAN MATHS SCORE AND THIS IS STATISTICALLY SIGNIFICANT NATIONAL AVERAGE SCORE = 1,000 1,007 1,005 1,003 1,002 1,000 998 1,006 1,003.5 1,001 1,004 1,001.5 999 KEY: 1,004 1,000.5 997 Uer Confidence Limit School Score Lower Confidence Limit ENGLISH MATHS SCIENCE HUMANITIES LANGUAGES 8
KS2-4 Bet 8 value added ercentile The KS2-4 Bet 8 core for Maintream chool have been earated into ercentile, hown in the table below. The ercentile illutrate the ditribution of KS2-4 Bet 8 core, and how where chool are laced nationally comared to other chool baed on their core. They are derived from national reult for maintream chool only. KS2-4 'Bet 8' meaure (centred on 1,000) All Maintained Maintream Percentile School 1,033.5 and above To 5% of chool nationally 1,013.9 to 1,033.4 Next 20% of chool nationally 1,005.5 to 1,013.8 Next 15% of chool nationally 995.1 to 1,005.4 Middle 20% of chool nationally 986.9 to 995.0 Next 15% of chool nationally 966.0 to 986.8 Next 20% of chool nationally Below 965.9 Bottom 5% of chool nationally The ercentile for 2013 hown above are rovided for information only, and the band into which an individual chool fall will not be ublihed in chool erformance table. It i imortant to note that the ercentile are alicable to 2013 amended data only. Snake lot are a ueful way of reentin ercentile. The nake lot below imly reeat the information hown in the table above but in a way that enable the national ditribution to be more eaily undertood. 9
10
CALCULATING PUPIL GROUP LUE ADDED SCORES The chool erformance table in 2013 include information to hihliht how uil of different tartin abilitie erform within each chool. Puil are roued baed on their erformance at the end of an earlier key tae. In the econdary chool erformance table, uil are roued baed on their erformance at KS2. The value added core will be hown for uil reviouly erformin: Below the exected level (Level 4) at KS2; At the exected level (Level 4) at KS2; Above the exected level (Level 4) at KS2. The averae uil core for the three uil rou decribed above will be reented for each of the ix KS2-4 meaure in the main erformance table for individual chool. Similarly, the averae uil core for diadvantaed uil defined, for erformance table uroe, a thoe who are either eliible for free chool meal (FSM) or are looked after children (CLA) will be reented for each of the ix KS2-4 meaure in the erformance table, aain available for individual chool. The averae core for a articular uil rou in a chool i calculated a the averae of the core for each individual uil that belon to that uil rou in the chool. A hrinkae factor i not alied to uil rou within chool. A hrinkae factor i only alicable when calculatin chool core and i not aroriate for alyin to ubet of uil within chool or to national level fiure. A a reult, for chool with all uil belonin to one uil rou (for examle, all uil were at the exected level at KS1), the uil rou core will differ lihtly to the chool core. In thee cae the unhrunken (uil rou) core hould be ued when comarin core for that uil rou and the hrunken (chool) core hould be ued when comarin the chool to all uil nationally. 11
INTERPRETING PUPIL GROUP LUE ADDED SCORES We can alo ue the chool uil rou core a a meaure of chool effectivene for a articular uil rou uin a imilar method a chool core. Similarly, it i imortant to note that thi core i baed on a iven et of uil reult (who belon to a uil rou) for a articular tet aer on a articular day. To comare uil rou core, confidence interval are alo calculated to ive a rane of core within which we are tatitically confident that a chool uil rou core will fall. There are two way in which a uil rou core can be comared; to the national averae for all uil (1,000) or the national uil rou averae. For an exlanation of how to interret confidence interval, leae refer back to ae 6 (Interretin School Value Added Score) and an illutration of how to interret uil core i alo iven in technical annex A. 12
THE 2013 KS2-4 LUE ADDED MEASURES There are ix KS2-4 value added meaure ublihed in the 2013 erformance table; the Bet 8 qualification lu Enlih and mathematic bonu meaure and five Enlih Baccalaureate meaure. KS2-4 Bet 8 lu Enlih and mathematic bonu meaure The Bet 8 lu Enlih and mathematic bonu meaure i ued to ee how effective chool have been in helin their uil rore from KS2 to a broad rane of ubject at KS4. The meaure etimate how uil erform in their bet 8 GCSE (or equivalent qualification) with uil receivin an additional bonu for their erformance in GCSE Enlih and mathematic. A uil erformance in their bet 8 qualification (lu the Enlih and mathematic bonu) i exreed a a oint core. A uil value added core i calculated by findin the difference between the oint core they actually achieved in their bet 8 qualification (lu Enlih and mathematic bonu) and the oint core they were etimated to achieve. More information on convertin rade to oint core, and the calculation of a uil bet 8 qualification, can be found at the link below. RAISEonline uer can find more information on convertin rade to oint core and the calculation of a uil bet 8 qualification in the library at www.raieonline.or, and thee can alo be found on the erformance table webite at www.education.ov.uk/chool/erformance. KS2-4 Enlih Baccalaureate meaure In addition to the KS2-4 Bet 8 lu Enlih and mathematic bonu meaure, the deartment ha alo ublihed five KS2-4 value added meaure howin how chool have heled rore their uil in each of the Enlih Baccalaureate ubject area (Enlih, mathematic, cience, lanuae and humanitie) comared with their eer nationally. A uil ha a earate etimated KS4 outcome calculated for each of the five Enlih Baccalaureate ubject area. Thee etimate are then comared aaint a uil bet core in the qualification that feed into each Enlih Baccalaureate ubject area. For examle, if a uil achieved a B in GCSE eorahy and a C in GCSE hitory then it i the GCSE eorahy reult (the uil bet reult in the Enlih Baccalaureate humanitie ubject area) which i ued to comare aaint the etimated KS4 outcome for the Enlih Baccalaureate humanitie ubject area meaure. A uil then ha a value added core calculated for each ubject area by findin the difference between their actual KS4 attainment in the ubject area and their etimated KS4 attainment in the ubject area. All uil are included in the Enlih and mathematic ubject area meaure. However, only the uil that have taken the required 13
qualification at the end of KS4 are included in the cience, lanuae and humanitie ubject area meaure. Chane in KS2-4 meaure in 2013 In 2013 one further amendment to the KS2-4 meaure wa made to the way in which uil rou confidence interval are calculated. Further information on thi can be found in Section E of the technical annex. 14
A GUIDE TO LUE ADDED KEY STAGE 2 TO 4 IN 2013 SCHOOL PERFORMANCE TABLES & RAISEonline TECHNICAL ANNEX Content A. Interretin chool value added core for uil rou diadvantaed uil Pae No. B. Calculatin Puil Value Added Score 16 C. Calculatin School Value Added Score 20 D. Calculatin Puil Grou Value Added Score 23 E. Calculatin Confidence Interval 25 F. Secial School Value Added Score 28 G. KS2 Teacher Aement Adjutment 28 H. Dicountin/cain rule for AS level / hiher corin qualification I. Value Added Model Coefficient for 2013 33 15 30 15
SECTION A - INTERPRETING SCHOOL LUE ADDED SCORES FOR PUPIL GROUPS DISADNTAGED PUPILS Examle of a School Information from Performance Table for diadvantaed uil Dilayin a School Information for Diadvantaed Puil Viually on a Chart How to Interret the Information and Chart Diadvantaed Puil Bet 8 meaure - diadvantaed uil 1004.0 Bet 8 Other lower examle 95% confidence of oible limit for outcome diadvantaed uil 1002.2 Bet 8 uer 95% confidence limit for diadvantaed uil 1005.8 Other examle of oible outcome NATIONAL AVERAGE SCHOOL SCORE = 1,000 NATIONAL AVERAGE SCORE FOR DISADNTAGED PUPILS The core for diadvantaed uil i above the national averae for all uil and the national averae for diadvantaed uil and both reult are tatitically inificant. Thi i becaue the whole rane of the confidence interval i above 1,000 and the national averae for diadvantaed uil. Thi tell u that diadvantaed uil in thi chool make more rore than averae for all uil and diadvantaed uil nationally KEY: Uer Confidence Limit School Score ALL PUPILS DISADNTAGED BELOW NO SIG ALL PUPILS DISADNTAGED NO SIG ABOVE ALL PUPILS DISADNTAGED NO SIG BELOW ALL PUPILS DISADNTAGED ABOVE NO SIG Lower Confidence Limit National Averae Score for Diadvantaed Puil ALL PUPILS DISADNTAGED BELOW BELOW ALL PUPILS DISADNTAGED NO SIG NO SIG ALL PUPILS DISADNTAGED ABOVE BELOW ALL PUPILS DISADNTAGED BELOW ABOVE NO SIG ABOVE BELOW Not Sinificantly Different Above averae and thi i tatitically inificant Below averae and thi i tatitically inificant Note: core are alo available for non-diadvantaed uil and low, middle and hih attainer 16
SECTION B CALCULATING PUPIL LUE ADDED SCORES Behind each KS2-4 meaure it a earate tatitical model. The ix model enerate an etimate of attainment for each uil, reectively in their bet eiht GCSE and equivalent outcome (lu a earate bonu for attainment in each of Enlih and mathematic), and their bet KS4 outcome in each of the five Enlih Baccalaureate ubject area (the bet accountin for multile ubject entrie for examle, a uil can enter for more than one lanuae). The etimated KS4 attainment outcome are exreed a a oint core, and are baed on the erformance nationally of all uil with the ame KS2 rior attainment. The core for a uil i then calculated a the difference (oitive or neative) between the model etimate for uil like them nationally and their actual KS4 attainment. Puil eliibility for incluion in model Puil are included in the Bet 8, Enlih Baccalaureate Enlih and Enlih Baccalaureate mathematic model if: their key tae 4 attainment can be matched to their attainment at key tae 2; they have a KS2 averae oint core that i reater than zero; they do not have a direarded outcome in all three KS2 tet / teacher aement; they attend a maintained maintream chool (includin academie and city technoloy collee) ee Section F for calculation of ecial chool core. Further uil eliibility criteria exit in the cae of Enlih Baccalaureate cience, humanitie and lanuae meaure: they mut have comleted a coure of tudy in eliible ubject() within each reective ubject area, i.e. have entered the ubject Note: ubject entry i not a re-requiite for incluion in Enlih Baccalaureate Enlih and mathematic meaure. All maintained maintream and ecial chool will have a core for all ix KS2-4 meaure, rovided they have at leat one eliible uil for each meaure. Methodoloy for uil calculation The model roduce coefficient to be alied to the uil level KS2 rior attainment variable decribed below. We ue the ame rior attainment 17
variable for all ix KS2-4 meaure. For each meaure, the etimated KS4 attainment of the uil E i iven by: where: E c 2 3 c KS2APS c KS2APS c KS APS 1 2 3 2 c4 ENGDEV c5 MATDEV KS2 APS i the uil KS2 averae oint core (APS) 2 KS 2APS i the uil KS2 APS quared 3 KS 2APS i the uil KS2 APS cubed i the difference between the uil KS2 ENGDEV Enlih core and their KS2 APS i the difference between the uil KS2 MATDEV c i c mathematic core and their KS2 APS are the coefficient from the model i the contant from the model Note that the value c i and c will be different for each of the ix KS2-4 meaure. The value of thee coefficient for all ix KS2-4 meaure can be found in technical annex I. The core of the uil,, i then calculated a the difference between their actual reult and their etimate ( E ), iven by: where: A A E, i the uil actual oint core Note that core are centred on 0. Worked examle 1 (referrin to Bet 8 meaure) A uil at the end of key tae 4 ha the followin attainment: Surname Jone Forename Gillian KS2 fine rade averae oint core 31.54 KS2 Enlih 30.18 KS2 mathematic 31.44 KS4 Enlih oint (GCSE rade) 46 (B) KS4 mathematic oint (GCSE rade) 52 (A) KS4 oint in caed bet eiht GCSE and equivalent outcome 412 KS4 Enlih bonu oint 46 KS4 mathematic bonu oint 52 18
Gillian etimated Bet 8 attainment i calculated by inertin the followin value, reflectin her KS2 outcome, into the formulae iven above for E : Notation Decrition Puil value KS2 APS KS2 APS 31.54 2 KS 2APS KS2 APS quared 994.77 3 KS 2APS KS2 APS cubed 31375.10 ENGDEV KS2 Enlih minu KS2 APS -1.36 MATDEV KS2 mathematic minu KS2 APS -0.10 The table below reent the value for 2013 Bet 8 model coefficient: Coefficient Alied to Coefficient c Contant alied to all uil 118.148119 c 1 KS2 APS 17.754536 2 c 2 KS 2APS -0.651857 c 3 3 2APS KS 0.014643 c 4 ENGDEV 3.946191 c 5 MATDEV 1.843685 Gillian etimated Bet 8 attainment, E c E, i then calculated a: 2 3 c KS2APS c KS2APS c KS APS 1 2 3 2 c4 ENGDEV c5 MATDEV 17.75453631.54 0.651857994.77 0.014643 31375.10 3.946191 1.36 1.843685 0.10 118.148119 118.148119 559.978065 648.447788 459.425589-5.36681976-0.1843685 483.55 (to 2 decimal lace, or d..) Gillian actual Bet 8 attainment i iven by A C B B 412 46 52 510. Therefore, her core i iven by: A E 510 483.55 26.45 (2 d..). 8 e m 19
Worked examle 2 (referrin to Enlih Baccalaureate mathematic meaure) Gillian etimated Enlih Baccalaureate mathematic attainment i calculated by inertin the ame value for her KS2 outcome a in Worked examle 1 above into the formulae for E only with different coefficient value alied. The table below reent value for Enlih Baccalaureate mathematic model coefficient: Coefficient Alied to Coefficient c Contant alied to all uil 8.511209 c 1 KS2 APS -0.798763 2 c 2 KS 2APS 0.105289 c 3 3 KS 2APS -0.001276 c 4 ENGDEV -0.006707 c 5 MATDEV 1.046849 Gillian etimated Enlih Baccalaureate mathematic attainment, then calculated a: E c 2 3 c KS2APS c KS2APS c KS APS 1 2 3 2 c4 ENGDEV c5 MATDEV E, i - 0.798763 31.54 0.105289 994.77-0.001276 31375.10-0.006707 1.36 1.046849 0.10 8.511209 8.500342 25.192985 104.738339 40.0346276 0.00912152 0.1046849 47.93 (2 decimal lace, or d..) Gillian actual Enlih Baccalaureate mathematic attainment i iven by A 52. Therefore, her core i iven by: A E 52 47.93 4.07 (2 d..). 20
SECTION C CALCULATING SCHOOL LUE ADDED SCORES The core for a chool i then calculated a the averae core of all uil in the chool, with an adjutment made by way of the alication of a hrinkae factor for each chool. Methodoloy for chool calculation The chool KS2-4 core, where: S, i iven by: 1000 S, i the hrinkae factor for the chool i the averae core for all eliible uil within the chool, iven by: where: n 1 n n 1, n i the number of eliible uil in the chool i the um of the core of eliible uil within the chool The hrinkae factor, S, i an adjutment which rovide a better etimate for core for chool with mall number of uil in the calculation, iven by: B S W B n where: B W i the national variance between chool i the national variance within chool Note each of the ix KS2-4 meaure will have a earate value for both B and W, which are alo available in technical annex H. 21
Worked examle 1 ( Bet 8 continuation) Let u then ay that Gillian i one of 100 uil in her chool KS4 cohort, who ain a rane of Bet 8 core: Puil # Puil name core 1 Gillian 26.90 2 Linday -2.04 100 David 32.75 Sum 986.35 The next te in the calculation i to calculate, the averae Bet 8 core for all eliible uil within the chool KS4 cohort: n 1 n 26.90 2.04 32.75 100 986.35 9.864 100 (to 3 d..) We next calculate the hrinkae factor, uin 2013 Bet 8 amended model value for B (466.331989) and W (4080.673625): B 466.331989 S 0.920 (3 d..) W 4080.673625 B 466.331989 n 100 Hence the final Bet 8 core for thi chool,, i iven by: S 1000 0.9209.864 1009. 075 1000 (3 d..) Note: We would ublih thi core a 1009.1, but retain the decimal lace for thi examle for illutrative uroe for the confidence interval calculation. Worked examle 2 (Enlih Baccalaureate mathematic continuation) Similarly, Gillian i one of 100 uil in her chool KS4 cohort who ain a rane of Enlih Baccalaureate mathematic core: Puil # Puil name core 1 Gillian 4.08 2 Linday -0.36 100 David 3.57 Sum 99.25 The next te in the calculation i to calculate, the averae core for all eliible uil within the chool KS4 cohort: 22
n 1 n 4.07 0.36 3.57 100 99.25 0.993 100 (3 d..) We next calculate the hrinkae factor, uin EBacc mathematic amended model value for B (5.013297) and W (46.038763): B 5.013297 S 0.916 (3 d..) W 46.038763 B 5.013297 n 100 Hence the final EBacc mathematic core for thi chool, S 1000 0.9160.993 1000. 909, i iven by: 1000 (3 d..) Note: We would ublih thi core a 1000.9, but retain the decimal lace for thi examle for illutrative uroe for the confidence interval calculation. 23
SECTION D CALCULATING PUPIL GROUP LUE ADDED SCORES The core for any articular uil rou (e.. diadvantaed uil, uil reviouly erformin above level 4 at KS2 etc.) in a chool i calculated a the averae core of all uil that belon to the uil rou in the chool. Similarly, the core for a articular uil rou nationally i calculated a the averae core of all uil that belon to the uil rou nationally. Methodoloy for uil rou calculation The uil rou KS2-4 core for any chool,, i iven by: where: 1000, i the averae core for all eliible uil that belon to the uil rou within the chool, iven by: where: n n 1 n 1, n i the number of eliible uil that belon to the uil rou within the chool i the um of the core of eliible uil that belon to the uil rou within the chool Note a hrinkae factor i not alied to uil rou within chool. Methodoloy for national uil rou calculation The national KS2-4 core for a uil rou, G, i iven by: where: where: PG n PG 1000, G PG i the averae core for all eliible uil that belon to the uil rou nationally, iven by: npg PG 1, n PG i the number of eliible uil that belon to the uil rou nationally 24
n PG 1 i the um of the core of eliible uil that belon to the uil rou nationally Note a hrinkae factor i not alied to uil rou nationally. Worked examle 1 ( Bet 8 continuation) Let u then ay that Gillian i one of 30 diadvantaed uil (defined, for erformance table uroe, a uil who are either eliible for Free School Meal or are children who are looked after) amon the 100 uil in her chool KS4 cohort, who ain a rane of Bet 8 core: Diadvantaed uil # Diadvantaed uil name core 1 Gillian 26.90 2 Ro -16.44 30 Alion 12.16 Sum 347.41 We calculate the diadvantaed uil rou core for the chool,, by calculatin the averae core of the diadvantaed uil within the chool, a follow: 1000 1000 26.90 16.44 12.16 347.41 1000 1000 1011.580 (to 3 d..) 30 30 Note: We would ublih thi core a 1011.6, but retain the decimal lace for thi examle for illutrative uroe for the confidence interval calculation. n 1 n 25
SECTION E CALCULATING CONFIDENCE INTERLS A 95% confidence interval i calculated around the chool core, definin the rane of value within which we are tatitically confident that the true value of the chool core lie. Methodoloy for chool confidence interval calculation The confidence interval, denoted LowCI, UCI, i iven by the formula: LowCI UCI CI, CI,, where: LowCI i the lower confidence limit for the chool core UCI i the uer confidence limit for the chool core CI i the chool core i the ize of the confidence interval for the chool, iven by: CI 1. 96 B W B n W For each KS2-4 meaure, the national averae of all maintained maintream chool core i 1,000. When a chool ha LowCI > 1,000, the chool core i above averae and the reult i tatitically inificant (denoted Si+ ). When a chool ha UCI < 1,000, the chool core i below averae and the reult i tatitically inificant (denoted Si- ). In the other cae when LowCI < 1,000 < UCI, we cannot ay with confidence whether the chool core i above or below averae, and ay the reult i not tatitically inificant. See Section F for calculation of Secial chool confidence interval. Worked examle 1 ( Bet 8 continuation) Uin Bet 8 model value for model value for B (479.333821) and W (4153.461233), we can alo calculate the ize of the confidence interval for the chool Bet 8 core, a calculated on ae 18-19, baed on the 100 uil in Gillian chool KS4 cohort: CI 1. 96 BW B n W 26
466.331989 4080.673625 1.96 1.966.182443 12.006 466.331989 100 4080.673625 (3 d..) We derive the confidence interval for the chool core: LowCI, UCI CI, CI 1009.075 12.006, 1009.075 12.006 997.1, 1021.1 (1 d..) Hence, a LowCI < 1,000 < UCI, we cannot ay with confidence whether thi chool Bet 8 core i above or below averae, hence the chool core i not tatitically inificant either ide of the national averae. Methodoloy for uil rou confidence interval calculation A 95% confidence interval i calculated around each uil rou core for the chool, definin the rane of value within which we are tatitically confident that the true value of the uil rou core for the chool lie. The confidence interval, denotedlowci, UCI, i iven by the formula: where: where: LowCI UCI CI LowCI UCI CI, CI,, i the lower confidence limit for the uil rou core for the chool i the uer confidence limit for the uil rou core for the chool i the uil rou core for the chool i the ize of the confidence interval for the uil rou core for the chool, iven by: CI 1. 96 n N i the chool etimate for that uil rou i the tandard deviation of the core for all eliible N uil nationally; n i the number of eliible uil that belon to the uil rou within the chool; We are intereted in how the uil rou within the chool erform comared to all uil nationally; hence we tet for inificance by comarin the rane of the confidence interval to the national maintream chool uil KS2-4 27
averae, i.e. 1,000. When a uil rou within a chool ha LowCI > 1,000, the chool uil rou core i above the national uil core and the reult i tatitically inificant (denoted Si+ ). When a uil rou within a chool ha UCI < 1,000, the chool uil rou core i below the national uil core and the reult i tatitically inificant (denoted Si- ). In the other cae when LowCI < 1,000 < UCI, we cannot ay with confidence whether the chool uil rou core i above or below the national uil core, and ay the reult i not tatitically inificant. See Section F for calculation of ecial chool uil rou confidence interval and inificance tetin. Worked examle 1 ( Bet 8 diadvantaed uil rou continuation) Referrin back to the diadvantaed uil rou examle on ae 24, we can then calculate the ize of the confidence interval for the chool diadvantaed uil rou core uinci : CI N 67.120228 1.96 1.96 1.9612.25442 24.019 (to 3 d..) n 30 We derive the confidence interval for the chool diadvantaed uil rou core: LowCI, UCI CI, CI 1011.580 24.019, 1011.580 24.019 987.6, 1035.6 (to 1 d..) A LowCI < 1,000 < UCI, we cannot ay with confidence whether the chool diadvantaed uil rou core i above or below the national uil core, and ay thi reult i not tatitically inificant. We can alo tet for inificance by comarin the rane of the confidence interval to, the national core for the uil rou in Maintream G chool. The Bet 8 amended core for FSM uil nationally, G, ha been calculated to be 982.4. A LowCI > 982.4, we can ay with confidence that the chool FSM core i above the national FSM core, and thi reult i denoted Si+. However, a LowCI < 1000 < UCI, we cannot ay with confidence whether the chool FSM core i above or below the national uil core, and ay thi reult i not tatitically inificant. In other word, the chool FSM uil are erformin inificantly better than FSM uil nationally, but we cannot ay whether the chool FSM uil are 28
erformin better or wore than the averae uil nationally. 29
SECTION F SPECIAL SCHOOL LUE ADDED SCORES The etimated KS4 attainment ( E ) for uil in ecial chool i baed on comarion with uil of the ame rior attainment in maintream chool. Thi mean that their core are calculated baed on the model coefficient ( c i and c ) derived from maintream chool only. Similarly, confidence interval ecial chool and their uil rou are calculated uin the value from the maintream chool model. Comarion are then made to maintream chool national averae (1,000 for the chool core). SECTION G KS2 TEACHER ASSESSMENT ADJUSTMENT The followin table ummarie how teacher aement (TA) adjutment are alied to uil without a tet core in readin or mathematic or have a tet core at level 2 or below. The intention of the adjutment i to better reflect the attainment of low attainin uil by ubtitutin their readin and writin TA data if their correondin tet reult i any of the level how in the firt column of table 1. For examle, if a uil obtain a level 2 in their readin tet and their TA i a level 2, then the uil would be awarded 15 oint. If a uil i awarded level 2, B or N in one of their tet level or i lited a A, M, Q, S, T, X and no TA exit the uil i excluded from meaure a we have no mean of validatin the uil actual ability. Table 1 Teacher Aement Adjutment If tet core = 6 Puil fine rade core = 39 3-5 Ue uil fine rade core 2 If TA available Award: W = 3 Level 1 = 9 Level 2 = 15 Any hiher = ue uil fine rade core A,D,F,L,P,Z = Exclude uil If no TA available Exclude Puil 30
B, N If TA available Award: W = 3 Level 1 = 9 Level 2 = 15 Any hiher = 15 (caed) A,D,F,L,P,Z = Exclude uil A, M, Q, S, T, X If no TA available If TA available If no TA available Exclude Puil Award: W = 3 Level 1 = 9 Level 2 = 15 Level 3 = 21 Level 4 = 27 Level 5 = 33 Any hiher = 33 (caed) A,D,F,L,P,Z = Exclude uil Exclude Puil Note on rade code A Abent B Workin below the level of the tet D Dialied F KS2 uil not at end of KS2 and takin thi ubject in future year L Left N Not awarded a tet level M Miin P Reult for ubject found in reviou year dataet S Pendin maladminitration Q Maladminitration T Workin at the level of the tet but not able to acce them X Lot Z Ineliible SECTION H DISCOUNTING/CAPPING RULES FOR AS LEVELS / HIGHER SCORING QUALIFICATIONS The followin methodoloy decribe how AS level and other hiher corin qualification will be incororated in the Bet 8 includin Enlih and mathematic and Enlih Baccalaureate ubject area meaure erformance table from 2011, in term of dicountin (which qualification to include when both a GCSE and hiher corin qualification were taken) and cain of oint core for uil ittin hiher corin qualification. The table overleaf illutrate the GCSE equivalent oint awarded for AS level, and examle of other qualification which can be undertaken in Year 31
11 and have a maximum oint core (on a GCSE bai) of more than 58 oint: Qualification Size Grade General/Alied General AS Free Standin Math Qualification at level 3 GCE AS level Double award Methodoloy Graded muic or dance Aet Lanuae Advanced (level 3) ½ A Level / 2 GCSE equivalent 2/3 GCSE equivalent 4 GCSE equivalent Variou ize deendin on rade ½ GCSE equivalent Point (GCSE equivalent bai) A 67.5 B 60 A 67.5 B 60 AA 67.5 AB 63.75 BB 60 Grade 6+ >58 Grade 11 62 Grade 12 70 (1) The uil actual oint core, A, to be ued in each EBacc ubject area model (e.. a uil bet oint core acro valid humanitie ubject) will be calculated a follow with reard to handlin hiher corin qualification: Aly dicountin rule to alway take the oint core from the hiher corin qualification over the uil relevant GCSE oint core; Ca the core at 58 oint. (2) The uil actual oint core, A, to be ued in the Bet 8 includin Enlih and mathematic model i the uil total oint core acro their bet 8 ubject, lu their Enlih and mathematic core added a bonu. Thi will be calculated a follow with reard to handlin hiher corin qualification: Aly dicountin rule to alway take the oint core from the hiher corin qualification over the uil relevant GCSE oint core for both the Bet 8 core and Enlih and mathematic bonu art; Ca core for individual hiher corin qualification contribution at 116 (2 x 58) toward the Bet 8 core art; Ca core for individual hiher corin qualification contribution at 58 toward each of Enlih or math in the Enlih and math bonu art. Note: The averae total oint core er uil (bet 8 qualification) indicator, to be ublihed at chool level erformance table from 2011, i marinally different to the Bet 8 core indicator ued in calculation, in that the 32
former alie the ame dicountin rule but doe not ca core from hiher corin qualification. The bai of the deciion to amend the dicountin/ cain methodoloy for the Bet 8 indicator wa to enure conitency acro all meaure. A imle uil examle Conider a uil ittin 11 GCSE and AS level in Enlih and mathematic, who attain the followin rade: ID Qualification Grade Point Incl. in Bet 8? Q1 GCSE Enlih (double award) A* 58 * Q2 GCSE Mathematic A 52 * Q3 GCSE Chemitry A 52 Q4 GCSE Phyic B 46 Q5 GCSE Sanih B 46 Q6 GCSE Georahy C 40 Q7 GCSE Art C 40 Q8 GCSE French C 40 Q9 GCSE Reliiou Studie D 34 Q10 GCSE Muic D 34 Q11 AS level Enlih A 67.5 Q12 AS level Mathematic D 45 * GCSE qualification dicounted a uil entered to AS level in the ubject. Referrin to the ID of qualification above, the followin illutrate the calculation of each indicator value for thi uil: (1) Bet 8 core for ue in Bet 8 incl. Enlih and mathematic = Q11 (2 GCSE equiv.) + Q3 + Q4 + Q5 + Q12 (2 GCSE equiv.) + Q6 = caed (67.5 x 2) + 52 + 46 + 46 + (45 x 2) + 40 = 116 + 52 + 46 + 46 + 90 + 40 = 390 Enlih and math bonu for ue in Bet 8 incl. Enlih and mathematic = Q11 + Q12 = caed (67.5) + 45 = 58 + 45 = 103 Combinin: Total oint core for Bet 8 meaure = Bet 8 core + Enlih and math bonu = 390 + 103 = 493 (2) Enlih Baccalaureate Enlih oint core = caed (Q11) = 58 Enlih Baccalaureate mathematic oint core = caed (Q12) = 45 Enlih Baccalaureate cience oint core = not alicable, a the uil ha not entered GCSE Bioloy Enlih Baccalaureate humanitie oint core = Q6 = 40 Enlih Baccalaureate lanuae oint core = bet core of Q5 and 33
Q8 = 46. 34
SECTION I KS2-4 AMENDED MODEL COEFFICIENTS FOR 2013 The table below ummarie the value added model coefficient, the variance term and tandard deviation ued to calculate the ix KS2-4 core and confidence interval for 2013. Thee value are ued to calculate a uil etimated KS4 outcome and the confidence interval around the uil core. KS2-4 Meaure Coefficient Alied to Bet 8 EBacc EBacc EBacc EBacc EBacc c Enlih mathematic cience humanitie lanuae Contant alied to all uil 118.148119 6.880080 8.511209 9.838114 51.286865 43.310749 c KS2 APS 17.754536 1.302028-0.798763 1.397555-4.962542 0.317852 1 2 c 2 2APS c 3 3 2APS 4 KS -0.651857-0.031531 0.105289-0.052840 0.215577-0.091733 KS 0.014643 0.000980-0.001276 0.001436-0.002000 0.002615 c ENGDEV 3.946191 0.862359-0.006707-0.253046 0.409679 0.625211 c MATDEV 1.843685-0.067341 1.046849-0.132213-0.214491 0.238140 5 W Within chool variance 4080.673625 47.780686 46.038763 33.139748 66.214008 57.594627 B Between chool variance 466.331989 7.013660 5.013297 7.146634 10.452611 14.734262 National tandard deviation 67.120228 7.291524 7.124942 6.293047 8.682884 8.405432 N 35