A GUIDE TO LUE ADDED KEY STAGE 2 TO 4 IN 2011 SCHOOL & COLLEGE PERFORMANCE TABLES & RAISE ONLINE Content Pae No. Summary Interretin School Value Added Score 2 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 The 2011 KS2-4 Value Added Meaure 11 Chane Between 2010 and 2011 12 Technical Annex content 13 Guide to KS2-4 Value Added 2011 1
SUMMARY INTERPRETING SCHOOL LUE ADDED SCORES Examle of School information from Performance Table Dilayin a chool information viually on a chart How to interret the information and chart 1,028.6 meaure baed on rore between Key Stae 2 and Key Stae 4 Limit of Key Stae 2 to 4 Confidence Interval Intitution (centred around 1,000) Uer Lower Name 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] 1,019.9 1,011.1 School A core i inificantly above the national averae 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 Confidence interval then allow u ae whether the chool core i inificantly above or below the national averae School B 1,000 [NATIONAL AVERAGE SCHOOL SCORE] 1,008.1 998.8 989.4 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 KEY: Uer Confidence Limit School Score Lower Confidence Limit School C 1,000 [NATIONAL AVERAGE SCHOOL SCORE] 995.4 985.9 976.4 School C core i inificantly below the national averae 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. So a meaure i needed that 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 Stae 2 and the end of Key Stae 4). Thi i the uroe of Value Added (). Analyi how that there i a very tron relationhi between examination erformance of uil at a reviou Key Stae and their current Key Stae. A meaure ue thi relationhi to etimate how well all uil erform in their current Key Stae exam. In 2011, there are ix Key Stae 2 to Key Stae 4 (KS2-4) meaure, each etimatin a KS4 outcome for all uil nationally that are at the end of KS4. For the KS2-4 meaure, an individual uil etimated outcome at the end of KS4 i calculated by lookin at the actual KS4 erformance of all uil nationally that demontrated imilar ability in their exam at the end of KS2. More ecifically, we etimate a uil KS4 outcome a the averae KS4 oint achieved by uil nationally of imilar ability at 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 that are helin their uil make more rore or le rore than averae. The ummary diaram on ae 2 how how to interret thee core. The Performance 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 11 for further information on the ix meaure above. Guide to KS2-4 Value Added 2011 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 2011. 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 Subject 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 A 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 Puil Level Ready Reckoner which RAISEonline 1 uer can find in the Library at www.raieonline.or and it i alo on the Performance 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. Guide to KS2-4 Value Added 2011 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 School core (KS1-2 core are centred around 100). 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 B of the Technical Annex. Guide to KS2-4 Value Added 2011 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 bound i reater than 1,000), we can ay the chool core i inificantly above the national averae, 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 bound i le than 1,000), we can ay the chool core i inificantly below the national averae. 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. Guide to KS2-4 Value Added 2011 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 C of the Technical Annex. Another ueful reource i the KS2-4 School 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 Performance Table webite at www.education.ov.uk/chool/erformance. Comarion of Enlih Baccalaureate Subject 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 bound for Enlih i reater than the uer bound for humanitie), we can ay the chool Guide to KS2-4 Value Added 2011 7
Enlih core i inificantly above their humanitie core, 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 bound for Enlih i le than the lower bound for humanitie), we can ay the chool Enlih core i inificantly below their humanitie core, 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 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 bound for Enlih i reater than the uer bound 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. Guide to KS2-4 Value Added 2011 8
KS2-4 Bet 8 Value Added Percentile 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 1,032.9 and above To 5% of chool nationally 1,013.4 to 1,032.8 Next 20% of chool nationally 1,005.1 to 1,013.3 Next 15% of chool nationally 994.7 to 1,005.0 Middle 20% of chool nationally 986.3 to 994.6 Next 15% of chool nationally 967.7 to 986.2 Next 20% of chool nationally Below 967.6 Bottom 5% of chool nationally The ercentile for 2011 hown above are rovided for information only, and the band into which an individual chool fall will not be ublihed in School Performance Table. It i imortant to note that the ercentile are alicable to 2011 validated 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. Lowet 5% Next 20% Next 15% Middle 20% Next 15% Next 20% To 5% 1,100 1,075 1,050 KS2-4 'Bet 8' Meaure 1,025 1,000 975 950 925 900 Guide to KS2-4 Value Added 2011 9
CALCULATING PUPIL GROUP LUE ADDED SCORES The School and Collee Performance Table in 2011 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 Stae. For the Secondary School Performance 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 Performance Table for the Bet 8 lu Enlih and mathematic bonu meaure, and in the uortin dataet for the five Enlih Baccalaureate meaure. Thi information i available for individual chool. Similarly, the averae uil core for derived uil defined, for Performance Table uroe, a thoe who are either eliible for Free School Meal (FSM) or are Children Looked After (CLA) will be reented for each of the ix KS2-4 meaure in the Performance Table uortin dataet, 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. Guide to KS2-4 Value Added 2011 10
THE 2011 KS2-4 LUE ADDED MEASURES There are ix KS2-4 Value Added meaure ublihed in the 2011 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 Performance 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 Georahy and a C in GCSE Hitory then it i the GCSE Georahy 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 Guide to KS2-4 Value Added 2011 11
qualification at the end of KS4 are included in the cience, lanuae and humanitie ubject area meaure. CHANGES BETWEEN 2010 AND 2011 There have been a number of other chane to the 2011 KS2-4 meaure from the meaure ublihed in the 2010 Performance Table. Removal of Contextual Information The Government ha dicontinued the ue of Contextual Value Added meaure. While all ix of the KS2-4 meaure etimate uil outcome at KS4 uin their erformance at KS2, we no loner adjut uil KS4 etimate to take account of the characteritic of the uil nor the chool they attend. Calculation of Score for Secial School Previouly, the Deartment ublihed earate meaure for maintained Maintream chool and Secial chool. In other word, the rore of uil in Maintream chool wa comared aaint other Maintream chool uil only, and likewie the rore of uil in Secial chool wa comared aaint other Secial chool uil only. For 2011, the ix meaure no loner treat uil in maintained Maintream chool and uil in Secial chool earately. The new aroach for 2011 comare uil in Secial chool with uil who have the ame level of KS2 achievement in maintained Maintream chool. The Deartment i aware that Secial chool have a deire to ee a much data a oible and, in many cae, wih to comare the rore their children make relative to thoe in Maintream chool. The method decribed above will to enable uch comarion to be made. For more information on thi aroach to Secial chool calculation, leae ee Section D of the Technical Annex. Ue of Teacher Aement Outcome for Low Attainin Puil Another chane to the methodoloy i in the way that uil erformance at KS2 i calculated for the ix meaure. In reviou year, the calculation of the KS2 indicator ued for the meaure wa baed entirely on KS2 examination data. For 2011, KS2 Teacher Aement (TA) data will be ued intead of KS2 Tet data for uil with very low level of attainment in their KS2 tet. The intention i to better reflect how thee low attainin uil erformed at KS2, and ive chool and teacher much more realitic etimate of KS4 outcome for uil that had low attainment at KS2. ee Section E of the Technical Annex for a more detailed decrition. Guide to KS2-4 Value Added 2011 12
A GUIDE TO LUE ADDED KEY STAGE 2 TO 4 IN 2011 SCHOOL & COLLEGE PERFORMANCE TABLES & RAISE ONLINE TECHNICAL ANNEX Content Pae No. A. Calculatin Puil Value Added Score 14 B. Calculatin School Value Added Score 18 C. Calculatin Puil Grou Value Added Score 20 D. Calculatin Confidence Interval 22 E. Secial School Value Added Score 26 F. KS2 Teacher Aement Adjutment 26 G. Dicountin/cain rule for AS level / hiher corin qualification 27 Guide to KS2-4 Value Added 2011 13
SECTION A 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 math), 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 Stae 4 attainment can be matched to their attainment at Key Stae 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 E for calculation of Secial chool core. One further uil eliibility criteria exit in the cae of Enlih Baccalaureate cience, humanitie and lanuae meaure: they 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 Secial School will have a core for all ix KS2-4 meaure, rovided they have at leat one eliible uil for each meaure. Methodoloy for Puil calculation The model roduce coefficient to be alied to the uil level KS2 rior attainment variable decribed below. We ue the ame rior attainment variable for all ix KS2-4 meaure. Guide to KS2-4 Value Added 2011 14
For each meaure, the etimated KS4 attainment of the uil, where: 2 3 ( c KS2APS) + ( c KS2APS ) + ( c KS APS ) E = c + 1 2 3 2 + ( c 4 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 E, i iven by: Note that the value c i and c will be different for each of the ix KS2-4 meaure. 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 around 0. Worked examle 1 (referrin to Bet 8 meaure) A uil at the end of Key Stae 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 Guide to KS2-4 Value Added 2011 15
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 2011 Bet 8 model coefficient: Coefficient Alied to Coefficient c Contant alied to all uil 186.5064 c 1 KS2 APS 2.9213 2 c 2 KS 2APS 0.1167 c 3 3 KS 2APS 0.0030 c 4 ENGDEV 4.2628 c MATDEV 1.8879 5 Gillian etimated Bet 8 attainment, E, i then calculated a: 2 3 ( c KS2APS ) + ( c KS 2APS ) + ( c KS APS ) E = c + 1 2 3 2 + ( c 4 ENGDEV ) + ( c5 MATDEV ).5064 + ( 2.9213 31.54) + ( 0.1167 994.77) ( 0.0030 31375.10) + ( 4.2628 1.36) + ( 1.8879 0.10) = 186 + = 186.5064 + 92.1372 + 116.0454 + 95.2192 5.7975 0.1888 = 483.92 (to 2 decimal lace, or d..) Gillian actual Bet 8 attainment i iven by A = C8 + Be + Bm = 412 + 46 + 52 = 510. Therefore, her core i iven by: A E = 510 483.92 = 26.08 (to 2 d..). = Guide to KS2-4 Value Added 2011 16
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 14.7822 c 1 KS2 APS -1.1981 2 c 2 KS 2APS 0.106446 c 3 3 KS 2APS -0.001132 c 4 ENGDEV 0.0271 c 5 MATDEV 0.9785 Gillian etimated Enlih Baccalaureate mathematic attainment, then calculated a: 2 3 ( c KS2APS ) + ( c KS2APS ) + ( c KS APS ) E = c + 1 2 3 2 + ( c 4 ENGDEV ) + ( c5 MATDEV ) + ( 1.1981 31.54) + ( 0.106446 994.77) ( 0.001132 31375.10) + ( 0.0271 1.36) + ( 0.9785 0.10) = 14.7822 + = 14.7822 37.7890 + 105.8898 35.5137 0.0369 0.0978 = 47.23 (to 2 decimal lace, or d..) E, i Gillian actual Enlih Baccalaureate mathematic attainment i iven by A = 52. Therefore, her core i iven by: A E = 52 47.23 = 4.77 (to 2 d..). = Guide to KS2-4 Value Added 2011 17
SECTION B 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 School calculation The chool KS2-4 core, where: S, i iven by: ( S ) = 1000 +, 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. 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 26.08 2 Linday -2.04 Guide to KS2-4 Value Added 2011 18
M M M 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 ( 26.08 2.04 + + 32.75) = 1 L n = 100 = 986.35 = 9.864 100 (to 3 d..) We next calculate the hrinkae factor, uin Bet 8 amended model value for B (450.6903) and W (4705.5694): B 450.6903 S = = = 0.905 (to 3 d..) W 4705.5694 B + 450.6903 + n 100 Hence the final Bet 8 core for thi chool,, i iven by: ( S ) = 1000 + ( 0.905 9.864) 1008. 931 = 1000 + = (to 3 d..) Note: We would ublih thi core a 1008.9, 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 4.77 2 Linday -0.36 M M M 100 David 3.57 Sum 99.25 The next te in the calculation i to calculate, the averae Enlih Baccalaureate mathematic core for all eliible uil within the chool KS4 cohort: = n ( 4.77 0.36 + + 3.57) = 1 L n = 100 = 99.25 = 0.993 100 (to 3 d..) We next calculate the hrinkae factor, uin Enlih Baccalaureate mathematic model value for B (5.7538) and W (49.5400): Guide to KS2-4 Value Added 2011 19
B 5.7538 S = = = 0.921 (to 3 d..) W 49.5400 B + 5.7538 + n 100 Hence the final Enlih Baccalaureate Mathematic core for thi chool,, i iven by: ( S ) = 1000 + ( 0.931 0.993) 1000. 914 = 1000 + = (to 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. SECTION C CALCULATING PUPIL GROUP LUE ADDED SCORES The core for any articular uil rou (e.. derived 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. Note that national uil rou core are not ublihed in Performance Table, and are dilayed in RAISEonline only. Methodoloy for Puil Grou 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 Puil Grou calculation Guide to KS2-4 Value Added 2011 20
The national KS2-4 core for a uil rou, G, i iven by: where: where: PG n PG n PG = 1 G = 1000 + PG, i the averae core for all eliible uil that belon to the uil rou nationally, iven by: PG = npg = 1 n PG i the number of eliible uil that belon to the uil rou nationally 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 derived uil (defined, for Performance 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: Derived uil # Derived uil name core 1 Gillian 26.08 2 Ro -16.44 M M M 30 Alion 12.16 Sum 48.69 Standard deviation 14.364 We calculate the derived uil rou core for the chool,, by calculatin the averae core of the derived uil within the chool, a follow: = 1000 + = 1000 + n = 1 n ( 26.08 16.44 + L + 12.16) 48.69 = 1000 + = 1000 + = 1001.623 (to 3 d..) 30 30 Note: We would ublih thi core a 1001.6, but retain the decimal lace for thi examle for illutrative uroe for the confidence interval calculation. Guide to KS2-4 Value Added 2011 21
SECTION D 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 School Confidence Interval calculation The confidence interval, denoted [ LowCI, UCI ] [ LowCI UCI ] = [ CI, + CI ], i iven by the formula:,, where: LowCI i the lower confidence limit for the chool core UCI i the uer confidence limit for the chool core i the chool core CI 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 E for calculation of Secial chool confidence interval. Worked examle 1 ( Bet 8 continuation) Uin Bet 8 model value for B (450.6903) and W (4705.5694), 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 B W ( B n ) + W 450.6903 4705.5694 = 1.96 = 1.96 6.527 = 12.794 (to 3 d..) + 4705.5694 ( 450.6903 100) Guide to KS2-4 Value Added 2011 22
We derive the confidence interval a follow: [ LowCI, UCI ] = [ CI, + CI ] [ 1008.931 12.794, 1008.931 + 12.794] = [ 996.1, 1021.7] = (to 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 Puil Grou 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, denoted [ LowCI, UCI ] [ LowCI UCI ] = [ CI, + CI ] where: LowCI where: UCI CI σ n t ( 1) n,,, i iven by the formula: 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 σ t( n ) n = 1 i the tandard deviation of the uil rou core for all eliible uil within the chool i the number of eliible uil that belon to the uil rou within the chool the value of the Student t-ditribution at 95% confidence with n 1 deree of freedom Puil rou confidence interval are not calculated when n = 1. 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 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+ ). Guide to KS2-4 Value Added 2011 23
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 E for calculation of Secial chool uil rou confidence interval and inificance tetin. Worked examle 1 ( Bet 8 derived uil rou continuation) Referrin back to the derived uil rou examle on ae 21, we can then calculate the ize of the confidence interval for the chool derived uil rou core, CI. We ue the tandard deviation of the individual core of the chool derived uil (14.364), and the value of the Student t- ditribution at 95% confidence with n 1 = 29 deree of freedom (2.045), a follow: σ 14.364 CI = t( n 1 ) = 2.045 = 2.045 2.622 = 5. 363 (to 3 d..) n 30 We derive the confidence interval for the chool derived uil rou core: [ LowCI, UCI ] = [ CI, + CI ] [ 1001.623 5.363, 1001.623 + 5.363] = [ 996.3, 1007.0] = (to 1 d..) A LowCI < 1,000 < UCI, we cannot ay with confidence whether the chool derived uil rou core i above or below the national uil core, and ay thi reult i not tatitically inificant. Additional comarion in RAISEonline of Puil Grou Confidence Interval with National Puil Grou core We can alo tet for inificance by comarin the rane of the confidence interval to G, the national core for the uil rou in Maintream chool. Thi comarion i made for chool in RAISEonline only When a uil rou within a chool ha LowCI > G, the chool uil rou core i above the national uil rou core and the reult i tatitically inificant (denoted Si+ ). Guide to KS2-4 Value Added 2011 24
When a uil rou within a chool ha UCI < G, the chool uil rou core i below the national uil rou core and the reult i tatitically inificant (denoted Si- ). In the other cae when LowCI < G < UCI, we cannot ay with confidence whether the chool uil rou core i above or below the national uil rou core, and ay the reult i not tatitically inificant. It could be the cae that a chool uil rou core i tatitically inificant in one tet but not in the other, or indeed Si + in one and Si in the other. For examle, a chool core for their FSM uil could be Si + comared with the national FSM core but till Si- comared with the national core for all uil. In other word, the chool FSM uil are erformin inificantly better than FSM uil nationally, but are till erformin inificantly wore than the averae uil nationally. Guide to KS2-4 Value Added 2011 25
SECTION E SPECIAL SCHOOL LUE ADDED SCORES The etimated KS4 attainment ( E ) for uil in Secial 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 F KS2 TEACHER ASSESSMENT ADJUSTMENT In reviou year, in calculation of KS2 variable for ue in meaure, a uil awarded a B ( Below the level of the KS2 Tet ) or an N ( Not awarded a Tet level ) in any tet are aumed to be at the equivalent of Level 2 and awarded 15 oint. For 2011, it ha been decided to ubtitute Teacher Aement (TA) data (caed at 15 oint) for thee uil. The intention i to better reflect the attainment of thee low attainin uil, and to remain a conitent a oible with the methodoloy ued in meaure of exected rore. TA data i alo ubtituted for any tet in which a uil i awarded Level 2. The aroach retain the tet fine rade core for uil who ain a TA of Level 3 or above (on the aumtion that thee uil are workin at a hiher level, were correctly entered to the tet, but didn t erform a well a exected on the day), and dicount the fine rade core for thoe who ain a TA of Level 2 or below. If a uil i awarded a Level 2, B or N in the tet and no TA exit, the uil i excluded from meaure, a we have no mean of validatin the uil actual ability. The table below illutrate the full rane of adjutment made to KS2 tet core uin Teacher Aement to define the KS2 inut variable for modellin. If tet core = 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 Guide to KS2-4 Value Added 2011 26
B, N A, M, Q, T, X If no TA available If TA available If no TA available If TA available If no TA available Exclude Puil Award: W = 3 Level 1 = 9 Level 2 = 15 Any hiher = 15 (caed) A,D,F,L,P,Z = Exclude uil 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 Q Maladminitration T Workin at the level of the tet but not able to acce them X Lot Z Ineliible SECTION G 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 in 2011 Performance Table, 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 11 and have a maximum oint core (on a GCSE bai) of more than 58 oint: Guide to KS2-4 Value Added 2011 27
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) Point (GCSE equivalent bai) ½ A Level / 2 A 67.5 GCSE equivalent B 60 2/3 GCSE A 67.5 equivalent B 60 AA 67.5 4 GCSE AB 63.75 equivalent BB 60 Variou ize deendin on Grade 6+ >58 rade ½ GCSE Grade 11 62 equivalent 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 math 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 math 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 in 2011 Performance Table, i marinally different to the Bet 8 core indicator ued in calculation, in that the 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. Guide to KS2-4 Value Added 2011 28
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 = 104 Combinin: Total oint core for Bet 8 meaure = Bet 8 core + Enlih and math bonu = 390 + 104 = 494 (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 Q8 = 46. Guide to KS2-4 Value Added 2011 29