A guide to value added key stage 1 to 2 in 2015 school performance tables

Transcription

1 A uide to value added key tae 1 to 2 in 2015 chool performance table February 2016

2 Content Summary Interpretin chool value added core 4 What i value added? 5 Calculatin pupil value added core 6 Calculatin chool value added core 7 Interpretin chool value added core 8 KS1-2 overall value added percentile 9 Calculatin pupil roup value added core 11 Interpretin pupil roup value added core 12 The 2015 amended KS1-2 value added meaure 13 KS1-2 overall meaure 13 KS1-2 readin meaure 13 KS1-2 writin meaure 13 KS1-2 mathematic meaure 14 Chane to KS1-2 meaure in Section A Interpretin chool core for pupil roup diadvantaed pupil 15 Section B Calculatin pupil value added core 16 Pupil eliibility for incluion in model 16 Methodoloy for pupil calculation 16 Worked example (referrin to KS1-2 overall meaure) 17 Section C Calculatin chool value added core 19 Methodoloy for chool calculation 19 Worked example (continuation) 20 Section D Calculatin pupil roup value added core 21 Methodoloy for pupil roup calculation 21 Methodoloy for national pupil roup calculation 21 Worked example 1 (KS1-2 overall meaure continuation) 22 Section E Calculatin confidence interval 23 Methodoloy for chool confidence interval calculation 23 Worked example (continuation) 23 Methodoloy for pupil roup confidence interval calculation 24 2

3 Worked example (continuation) 25 Section F Special chool value added core 27 Section G KS2 teacher aement adjutment 28 Section H Calculatin KS2 fine rade 30 Readin and mathematic 30 Writin 31 Overall 31 Section I KS1-2 model coefficient for

4 Summary Interpretin chool value added core 4

5 What i value added? When meaurin how effective a chool i, it i important to look at how well it pupil perform in their tet and examination. However, when evaluatin tet performance it i alo important to take into conideration that pupil movin from key tae 1 (KS1) to key tae 2 (KS2) have varyin level of ability, i.e. pupil at the beinnin of KS2 have many different tartin point. So a meaure i needed that look at how much prore pupil have made between the end of KS1 and the end of KS2. Thi i the purpoe of value added (). Analyi how that there i a very tron relationhip between performance of pupil at a previou key tae and their current key tae. A meaure ue thi relationhip to etimate how well all pupil perform in their current key tae aement. In 2015, there are four key tae 1 to key tae 2 (KS1-2) meaure, each etimatin a KS2 outcome for all pupil nationally that are at the end of KS2. For the KS1-2 meaure, an individual pupil etimated outcome at the end of KS2 i calculated by lookin at the actual KS2 performance of all pupil nationally that demontrated imilar ability in their aement at the end of KS1. More pecifically, we etimate a pupil KS2 outcome a the averae KS2 point achieved by pupil nationally of imilar ability at KS1. Thi KS2 etimated outcome can then be compared aaint what the pupil actually achieved in their KS2 tet, to ee whether or not they exceeded it. The difference between a pupil actual KS2 performance and their etimated KS2 performance ive the pupil their core. The averae core for all pupil in a chool can then be calculated to find a chool core, which help to identify chool that are helpin their pupil make more prore or le prore than averae. The ummary diaram on pae 2 and 14 how how to interpret thee core for chool and pupil roup. The performance table webite how chool core for the followin four KS1-2 meaure: KS1-2 overall meaure prore in readin, writin and mathematic combined. KS1-2 readin meaure prore in readin only. KS1-2 writin meaure prore in writin only. KS1-2 mathematic meaure prore in mathematic only. Pleae ee pae 13 for further information on the four meaure above. 5

6 Calculatin pupil value added core Individual pupil core need to be calculated before a chool core can be produced. The firt tep i to ue a tatitical model to calculate an etimated outcome for all pupil that are at the end of KS2 in Each pupil KS2 etimate i calculated baed on the actual KS2 outcome of all pupil nationally with the ame level of achievement at KS1. For example, calculation of an etimated outcome for a pupil who cored an averae of 15 point at KS1 will be baed on the actual KS2 outcome of all pupil nationally that alo cored an averae of 15 point at KS1. A pupil core i then calculated by ubtractin their etimated KS2 outcome from their actual KS2 outcome. Uin the KS1-2 mathematic meaure a an example, if a pupil attain a level 4 in KS2 mathematic (equivalent to 27 point) and they are etimated to attain a Level 3 (equivalent to 21 point) by the meaure, then the pupil ha a core of +6 point (27 point 21 point). The poitive core tell u that thi pupil ha exceeded their etimated KS2 outcome. If the core wa neative, then thi would tell u that the pupil cored le than their etimated KS2 outcome. The table below ummarie the calculation decribed above. Pupil' actual KS1 averae point core Performance of all pupil with an averae core of 15 at KS1 ued to etimate performance at KS2 Pupil' etimated KS2 math core Pupil' actual KS2 math core Difference (actual - etimate) 15 point Level 3 (21 point) Level 4 (27 point) +6 point (27-21) Section B of the technical annex provide a more detailed decription of how pupil etimated KS2 core and their core are calculated. If you wih to ue ome data to better undertand the pupil calculation, a ueful reource i the KS1-2 Pupil Level Ready Reckoner which RAISEonline 1 uer can find in the library on RAISEonline and it i alo on the performance table webite. 1 RAISEonline i an analytical tool ued by chool to analye chool and pupil performance data. 6

7 Calculatin chool value added core Once the pupil core have been calculated, we take the averae of all the pupil core within that chool. We then apply the hrinkae factor, an adjutment that provide a better etimate of core for chool with mall number of pupil. Finally, to differentiate between the KS1-2 and KS2-4 meaure, we centre by addin 100 to every KS1-2 chool core (KS2-4 core are centred on 1,000). The diaram below how an example of how a chool core i calculated from an example of five pupil core. STEP 1 - FIND THE AVERAGE OF PUPIL SCORES Pupil 1 Score Pupil 2 Score Pupil 3 Score Pupil 4 Score Pupil 5 Score Averae of the Pupil 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 = Centred Final School Score For more information on calculatin chool core, includin the application of hrinkae factor, pleae ee ection C of the technical annex. 7

8 Interpretin chool value added core 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 pupil' reult for a particular tet paper on a particular day. A chool could have been equally effective and yet the ame et of pupil miht have achieved lihtly different KS2 reult on the day. And the chool would almot certainly have hown lihtly different KS2 reult with a different et of pupil. Thi element of uncertainty need to be taken into account when interpretin 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 example, if a chool core i 101 and the ize of the chool confidence interval i 2 point, then the confidence interval rane between 99 and 103 (i.e. 2 point either ide of the chool core). The ize of the confidence interval i determined by the number of pupil in the chool at the end of KS2. Smaller chool have wider confidence interval becaue their core i baed on a maller number of pupil, 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 100 (i.e. the lower confidence limit i reater than 100), we can ay the chool core i above the national averae and i tatitically inificant, and we can be confident the chool i helpin it pupil make better than averae prore. An illutration of how to interpret chool core i iven on pae 2. Similarly, when the entire rane of the confidence interval i below 100 (i.e. the upper confidence limit i le than 100), we can ay the chool core i below the national averae and i tatitically inificant. Finally, if the confidence interval traddle the national averae of 100, then we can ay that the chool i not inificantly different from the national averae. In other word, we cannot ay with confidence 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 interpreted to reach one of the three definition above. School A i an example 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; 8

9 School A School B School C School Score Upper Confidence Interval Lower Confidence Interval SCHOOL A IS ABOVE NATIONAL AVERAGE AND THIS IS STATISTICALLY SIGNIFICANT KEY: Upper Confidence Limit School Score Lower Confidence Limit NATIONAL AVERAGE SCORE = SCHOOL B IS NOT SIGNIFICANTLY DIFFERENT FROM NATIONAL AVERAGE SCHOOL C IS BELOW NATIONAL AVERAGE AND THIS IS STATISTICALLY SIGNIFICANT For more information on the calculation of confidence interval, pleae ee Section E of the technical annex. Another ueful reource i the KS1-2 School Level Ready Reckoner, which demontrate how the number of eliible pupil for a core in a chool i linked to the width of a chool confidence interval. RAISEonline uer can find thi in the Library on RAISEonline and it i alo on the performance table webite. KS1-2 overall value added percentile The KS1-2 overall core for maintream chool have been eparated into percentile, hown in the table below. The percentile illutrate the ditribution of KS1-2 overall core, and how where chool are placed nationally compared to other chool baed on their core. They are derived from national reult for maintream chool only. 9

10 KS1-2 overall meaure (centred on 100) All tate-funded maintream School Percentile and above Top 5% of chool nationally to Next 20% of chool nationally to Next 15% of chool nationally 99.8 to Middle 20% of chool nationally 99.4 to 99.7 Next 15% of chool nationally 98.4 to 99.3 Next 20% of chool nationally 98.3 and below Bottom 5% of chool nationally The percentile for 2015 hown above are provided for information only, and the band into which an individual chool fall will not be publihed in chool performance table. It i important to note that the percentile are applicable to 2015 amended data only. Snake plot are a ueful way of preentin percentile. The nake plot below imply repeat the information hown in the table above but in a way that enable the national ditribution to be more eaily undertood. 10

11 Calculatin pupil roup value added core The chool and collee performance table include information to hihliht how pupil of different tartin abilitie perform within each chool. Pupil are rouped baed on their performance at the end of an earlier key tae. For the primary chool performance table, pupil are rouped baed on their performance at KS1. The core will be hown for pupil previouly performin: Below the expected level (level 2) at KS1; At the expected level (level 2) at KS1; Above the expected level (level 2) at KS1. The averae pupil core for the three pupil roup decribed above will be preented for the KS1-2 overall meaure. Thi information i available for individual chool. Similarly, the averae pupil core for diadvantaed pupil defined, for performance table purpoe, a thoe who were either eliible for free chool meal (FSM) at any time in the previou 6 year or are looked-after children (CLA) will be preented for the KS1-2 overall meaure in the performance table upportin dataet, aain available for individual chool. The averae core for a particular pupil roup in a chool i calculated a the averae of the core for each individual pupil that belon to that pupil roup in the chool. A hrinkae factor i not applied to pupil roup within chool. A hrinkae factor i only applicable when calculatin chool core and i not appropriate for applyin to ubet of pupil within chool or to national level fiure. A a reult, for chool with all pupil belonin to one pupil roup (for example, all pupil were at the expected level at KS1), the pupil roup core will differ lihtly to the chool core. In thee cae the unhrunken (pupil roup) core hould be ued when comparin core for that pupil roup and the hrunken (chool) core hould be ued when comparin the chool to all pupil nationally. 11

12 Interpretin pupil roup value added core We can alo ue the chool pupil roup core a a meaure of chool effectivene for a particular pupil roup uin a imilar method a chool core. Similarly, it i important to note that thi core i baed on a iven et of pupil reult (who belon to a pupil roup) for a particular tet paper on a particular day. To compare pupil roup core, confidence interval are alo calculated to ive a rane of core within which we are tatitically confident that a chool pupil roup core will fall. There are two way in which a pupil roup core can be compared; to the national averae for all pupil (100) or to the national pupil roup averae. For an explanation of how to interpret confidence interval, pleae refer back to pae 6 (Interpretin chool value added core) and an illutration of how to interpret pupil roup core i alo iven on ection A of the technical annex. 12

13 The 2015 amended KS1-2 value added meaure There are four KS1-2 meaure publihed in the 2015 performance table: KS1-2 overall meaure which look at prore in readin, writin and mathematic combined KS1-2 readin KS1-2 writin KS1-2 mathematic KS1-2 overall meaure The KS1-2 overall meaure i ued to ee how effective chool are in helpin their pupil prore from KS1 to KS2 in readin, writin and mathematic. The meaure etimate for each pupil their averae point core in KS2 readin, writin and mathematic. A pupil core i then calculated by findin the difference between the averae point core the pupil actually achieved in KS2 readin, writin and mathematic and the averae point core they were etimated to achieve. RAISEonline uer can find more information on convertin rade to point core in the library on RAISEonline, and thee can alo be found on the performance table webite. KS1-2 readin meaure The KS1-2 readin meaure i ued to ee how effective chool have been in helpin their pupil prore from KS1 to KS2 readin. The meaure etimate for each pupil their point core in KS2 readin. A pupil core i then calculated by findin the difference between the point core the pupil actually achieved in KS2 readin and the point core they were etimated to achieve. KS1-2 writin meaure The KS1-2 writin meaure i ued to ee how effective chool have been in helpin their pupil prore from KS1 to KS2 writin The meaure etimate for each pupil their point core in KS2 writin. A pupil core i then calculated by findin the difference between the point core the pupil actually achieved in KS2 writin and the point core they were etimated to achieve. 13

14 KS1-2 mathematic meaure The KS1-2 mathematic meaure i ued to ee how effective chool have been in helpin their pupil prore from KS1 to KS2 mathematic. The meaure etimate for each pupil their point core in KS2 mathematic. A pupil core i then calculated by findin the difference between the point core the pupil actually achieved in KS2 mathematic and the point core they were etimated to achieve by the meaure. Chane to KS1-2 meaure in 2015 In 2015 no chane to the KS1-2 meaure were made to the way in which pupil and chool are calculated. Since 2013, the department ha no loner produced Enlih prore meaure at key tae 2 - thi include the KS1-2 Enlih meaure. Thi ha been replaced by eparate meaure in readin and writin. For 2015 thi will remain the ame. The readin meaure i calculated in the ame manner a the mathematic meaure - each pupil tet mark are converted to fine rade and where neceary a teacher aement (TA) adjutment i applied (ee ection G and H of the technical annex). The writin meaure ue a pupil teacher aement level. Teacher aement level W throuh to 6 are converted to a fine rade then a point core (ee ection H of the technical annex). Detail of how the overall meaure i calculated are hown in ection H of the technical annex. 14

15 Section A Interpretin chool core for pupil roup diadvantaed pupil 15

16 Section B Calculatin pupil value added core Behind each KS1-2 meaure it a eparate tatitical model. The four model enerate an etimate of attainment for each pupil, repectively in KS2 readin, writin, mathematic and an overall etimate for KS2 readin, writin and mathematic combined. The etimated KS2 attainment outcome are expreed a a point core, and are baed on the performance nationally of all pupil with the ame KS1 prior attainment. The core for a pupil i then calculated a the difference (poitive or neative) between the model etimate for pupil like them nationally and their actual KS2 attainment. Pupil eliibility for incluion in model The ame cohort of pupil i included in all four KS1-2 model, namely if: their key tae 2 attainment in readin, writin and mathematic can be matched to their attainment at key tae 1; they have a KS1 averae point core that i reater than zero; they do not have a direarded outcome in either KS2 readin, writin or mathematic; they attend a tate-funded maintream chool (includin academie, free chool and city technoloy collee) ee ection F for calculation of pecial chool core. All tate-funded maintream and pecial chool will have a core for all four KS1-2 meaure, provided they have at leat one eliible pupil for each meaure. Methodoloy for pupil calculation The model produce coefficient to be applied to the pupil level KS1 prior attainment variable decribed below. We ue the ame prior attainment variable for all four KS1-2 meaure. For each KS1-2 meaure, the etimated KS2 attainment of the pupil E i iven by: where: 2 3 ( c KS1APS) + ( c KS1APS ) + ( c KS APS ) E p = c ( c READEV ) + ( c MATDEV ) p 16

17 KS1APS KS1APS 2 KS1APS 3 READDEV MATDEV c i c i the pupil KS1 averae point core (APS) i the pupil KS1 APS quared i the pupil KS1 APS cubed i the difference between the pupil KS1 Readin core and their KS1 APS i the difference between the pupil KS1 mathematic core and their KS1 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 four KS1-2 meaure. The core of the pupil, p, i then calculated a the difference between their actual reult and their etimate (E p ), iven by: p = A E, p p where: A p i the pupil actual point core Note that p core are centred on 0. Worked example (referrin to KS1-2 overall meaure) A pupil at the end of key tae 2 ha the followin attainment: Surname Bibby Forename Bobbie KS1 readin 2B KS1 writin 2C KS1 mathematic 3 KS2 readin KS2 writin KS2 mathematic We convert level to point core a follow: KS1 readin = Level 2B = 15 point KS1 writin = Level 2C = 13 point KS1 mathematic = Level 3 = 21 point 17

18 KS1 APS = = point 3 KS2 APS = ( ) / = point 2 Bobbie etimated KS2 attainment i calculated by inertin the followin value, reflectin her KS1 outcome, into the formulae iven above for E p : Notation Decription Pupil value KS1APS KS1 APS KS1APS 2 KS1 APS quared KS1APS 3 KS1 APS cubed 4, READDEV KS1 readin minu KS1 APS MATDEV KS1 mathematic minu KS1 APS 4.67 The table below preent the 2015 amended overall KS1-2 model coefficient: Coefficient Applied to Coefficient c Contant applied to all pupil c 1 KS1APS c 2 KS1APS c 3 KS1APS c 4 READDEV c 5 MATDEV Bobbie etimated KS2 attainment, E p, i then calculated a: 2 3 ( c KS1APS) + ( c KS1APS ) + ( c KS APS ) E p = c ( c READEV ) + ( c MATDEV ) ( ) + ( ) + ( ) = ( ) + ( ) = = (2 decimal place, or d.p.) Bobbie actual KS2 APS A p = Therefore, her core i iven by: p = Ap E p = = 4.01 (2 d.p.) 18

19 Section C Calculatin chool value added core The core for a chool i then calculated a the averae core of all pupil in the chool, with an adjutment made by way of the application of a hrinkae factor for each chool. The hrinkae factor i ued to improve the accuracy of etimate of chool core by drawin them toward the national averae of 100. Each chool ha it own hrinkae factor, the ize of which depend on the variance within and between chool nationally, a well a the ize of the actual chool cohort. The effect of the hrinkae factor i reater for maller chool. Methodoloy for chool calculation The chool KS1-2 core,, i iven by: where: ( S ) =100 + p, S p i the hrinkae factor for the chool i the averae core for all eliible pupil within the chool, iven by: p = n p= 1 n p, where: n p= 1 N p i the number of eliible pupil in the chool i the um of the core of eliible pupil within the chool The hrinkae factor, S, i iven by: S = B W B + n where: B W i the national variance between chool i the national variance within chool Note each of the four KS1-2 meaure will have a eparate value for both B andw. 19

20 Worked example (continuation) Let u then ay that Bobbie i one of 100 pupil in her chool KS2 cohort, who ain a rane of KS1-2 core: Pupil # Pupil name core 1 Bobbie Carl Karolina 0.60 Sum The next tep in the calculation i to calculate p, the averae core for all eliible pupil within the chool KS2 cohort: p = n ( ) p p= 1 n = 100 = = (3 d.p.) We next calculate the hrinkae factor, uin 2015 overall KS1-2 model value for B ( ) and W ( ): B S = = = (3 d.p.) W B n 100 Hence the final KS1-2 Overall core for thi chool,, i iven by: ( S ) = ( ) = p = (3 d.p.) Note: We would publih thi core a 100.3, but retain the decimal place for thi example for illutrative purpoe later in confidence interval calculation. 20

21 Section D Calculatin pupil roup value added core The core for any particular pupil roup (e.. diadvantaed pupil, pupil previouly performin above level 2 at KS1 etc.) in a chool i calculated a the averae core of all pupil that belon to the pupil roup in the chool. Similarly, the core for a particular pupil roup nationally i calculated a the averae core of all pupil that belon to the pupil roup nationally. Methodoloy for pupil roup calculation The pupil roup KS1-2 core for any chool,, i iven by: where: =100 + p, p i the averae core for all eliible pupil that belon to the pupil roup within the chool, iven by: p np p p= = 1, n p where: n p p= 1 n p p i the number of eliible pupil that belon to the pupil roup within the chool i the um of the core of eliible pupil that belon to the pupil roup within the chool Note a hrinkae factor i not applied to pupil roup within chool. Methodoloy for national pupil roup calculation The national KS1-2 core for a pupil roup, G, i iven by: where: G =100 + PG, PG i the averae core for all eliible pupil that belon to the pupil roup nationally, iven by: 21

22 PG = n PG p= 1 n PG p, where: n PG p= 1 n PG p i the number of eliible pupil that belon to the pupil roup nationally i the um of the core of eliible pupil that belon to the pupil roup nationally Note a hrinkae factor i not applied to pupil roup nationally. Worked example 1 (KS1-2 overall meaure continuation) Let u then ay that Bobbie i one of 30 diadvantaed pupil amon the 100 pupil in her chool KS2 cohort, who ain a rane of KS1-2 overall core: Diadvantaed pupil # Diadvantaed pupil name core 1 Bobbie Roie Adam 1.75 Sum We calculate the diadvantaed pupil roup core for the chool,, by calculatin the averae core of the diadvantaed pupil within the chool, a follow: = p = n p p= 1 n p ( ) p = = = (3 d.p.) Note: We would publih thi core a 100.8, but retain the decimal place for thi example for illutrative purpoe for the confidence interval calculation. 22

23 Section E Calculatin confidence interval 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, UppCI ], i iven by the formula: [ LowCI UppCI ] = [ CI, + CI ],, where: LowCI i the lower confidence limit for the chool core UppCI i the upper confidence limit for the chool core i the chool core CI i the ize of the confidence interval for the chool, iven by: CI = B W ( B n ) + W For each KS1-2 meaure, the national averae of all tate-funded maintream chool core i 100. When a chool ha LowCI > 100, the chool core i above averae and the reult i tatitically inificant (denoted Si+ ). When a chool ha UppCI < 100, the chool core i below averae and the reult i tatitically inificant (denoted Si- ). In the other cae when LowCI < 100 < UppCI, we cannot ay with confidence whether the chool core i above or below averae, and ay the reult i not tatitically inificant. See ection F for calculation of pecial chool confidence interval. Worked example (continuation) Uin the 2015 KS1-2 overall model value for B ( ) and W ( ), We calculate the ize of the confidence interval for the chool core, CI, a follow: CI = B W ( B n ) + W 23

24 = 1.96 = = (3 d.p.) ( ) We derive the confidence interval for the chool core: [ LowCI, UppCI ] = [ CI, + CI ] [ , ] = [ 99.8,100.7] = (1 d.p.) Hence, a LowCI < 100 < UppCI, we cannot ay with confidence whether thi chool core i above or below averae, hence the chool core i not tatitically inificant either ide of the national averae. Methodoloy for pupil roup confidence interval calculation A 95% confidence interval i calculated around each pupil roup core for the chool, definin the rane of value within which we are tatitically confident that the true value of the pupil roup core for the chool lie. The confidence interval, denoted [ LowCI, UppCI ], i iven by the formula: [ LowCI, UppCI ] = [ CI, + CI ], where: LowCI UppCI CI i the lower confidence limit for the pupil roup core for the chool i the upper confidence limit for the pupil roup core for the chool i the pupil roup core for the chool i the ize of the confidence interval for the pupil roup core for the chool, iven by: CI = σ n N p where: σ N N p i the chool etimate for that pupil roup i the tandard deviation of the core for all eliible pupil nationally; i the number of eliible pupil that belon to the pupil roup within the chool; 24

25 We are intereted in how the pupil roup within the chool perform compared to all pupil nationally; hence we tet for inificance by comparin the rane of the confidence interval to the national maintream chool pupil KS1-2 averae, i.e When a pupil roup within a chool ha LowCI > 100, the chool pupil roup core i above the national pupil core and the reult i tatitically inificant (denoted Si+ ). When a pupil roup within a chool ha UppCI < 100, the chool pupil roup core i below the national pupil core and the reult i tatitically inificant (denoted Si- ). In the other cae when LowCI < 100 < UppCI, we cannot ay with confidence whether the chool pupil roup core i above or below the national pupil core, and ay the reult i not tatitically inificant. See ection F for calculation of pecial chool pupil roup confidence interval and inificance tetin. Worked example (continuation) Referrin back to the diadvantaed pupil roup example on pae 21, we can then calculate the ize of the confidence interval for the chool diadvantaed pupil roup core uin CI : CI σ N = 1.96 = 1.96 = = n 30 p (3 d.p.) We derive the confidence interval for the chool diadvantaed pupil roup core: [ LowCI, UppCI ] = [ CI, + CI ] [ , ] = [ 99.8, 101.7] = (1 d.p.) A LowCI < 100 < UppCI, we cannot ay with confidence whether the chool diadvantaed pupil roup core i above or below the national pupil core, and ay thi reult i not tatitically inificant. We can alo tet for inificance by comparin the rane of the confidence interval to G the national core for the pupil roup in maintream chool. When a pupil roup within a chool ha LowCI > G, the chool pupil roup core i above the national pupil roup core and the reult i tatitically inificant (denoted Si+ ). When a pupil roup within a chool ha UppCI < G, the chool pupil roup core i below the national pupil roup core and the reult i tatitically inificant (denoted Si- ). 25

26 In the other cae when LowCI < G < UppCI, we cannot ay with confidence whether the chool pupil roup core i above or below the national pupil roup core, and ay the reult i not tatitically inificant. When a pupil roup within a chool ha LowCI >100, the chool pupil roup core i above the national core for all pupil, and the reult i tatitically inificant (denoted Si+ ). When a pupil roup within a chool ha UppCI <100 the chool pupil roup core i below the national core for all pupil and the reult i tatitically inificant (denoted Si- ). In the other cae when LowCI < 100 < UppCI, we cannot ay with confidence whether the chool pupil roup core i above or below the national core for all pupil, and ay the reult i not tatitically inificant. When comparin a chool pupil roup core to the national pupil roup averae and the national averae for all pupil, It could be the cae that the core i tatitically inificant in one reult but not in the other, or indeed Si + in one and Si in the other. For example, a chool core for their diadvantaed pupil could be Si + compared with the national core for diadvantaed pupil but till Si- compared with the national core for all pupil. In other word, the chool diadvantaed pupil are makin prore above the national averae for diadvantaed pupil and thi i tatitically inificant, but are till performin below averae of all pupil nationally and thi i alo tatitically inificant. Pleae ee pae 12 for a further explanation of the interpretation of pupil roup core. 26

27 Section F Special chool value added core The etimated KS2 attainment (E p ) for pupil in pecial chool i baed on comparion with pupil of the ame prior 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 for pecial chool and their pupil roup are calculated uin the value from the maintream chool model. Comparion are then made to maintream chool national averae (100 for the chool core). 27

28 Section G KS2 teacher aement adjutment The followin table ummarie how TA adjutment are applied to pupil 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 pupil by ubtitutin their readin and mathematic TA data if their correpondin tet reult i any of the level hown in the firt column of table 1. For example, if a pupil obtain a level 2 in their readin tet and their TA i a level 2, then the pupil would be awarded 15 point. If a pupil 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 pupil i excluded from meaure a we have no mean of validatin the pupil actual ability. Table 1 Teacher aement adjutment If tet level = 6 Pupil fine rade core = Ue pupil fine rade core 2 If TA available Award: W = 3 Level 1 = 9 Level 2 = 15 Any hiher = ue pupil fine rade core A,D,F,L,P,Z = Exclude pupil If no TA available Exclude Pupil B, N If TA available Award: W = 3 Level 1 = 9 Level 2 = 15 Any hiher = 15 (capped) A,D,F,L,P,Z = Exclude pupil If no TA available Exclude Pupil A, M, Q, S, T, X If TA available Award: W = 3 Level 1 = 9 Level 2 = 15 Level 3 = 21 Level 4 = 27 Level 5 = 33 Any hiher = 33 (capped) A,D,F,L,P,Z = Exclude pupil If no TA available Exclude Pupil 28

29 Note on rade code A Abent B Workin below the level of the tet D Diapplied F KS2 pupil 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 previou 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 29

30 Section H Calculatin KS2 fine rade Key tae 2 point core are baed on the level that pupil achieved in their end of key tae aement. Fine rade ue the underlyin mark data to create a finer meaure. Readin and mathematic The followin et of rule i ued to convert tet mark to fine rade for readin and mathematic. Thee rule alo take into account ituation where a pupil ained level for their readin or mathematic tet i not conitent with the mark they receive. If tet level = 6 then: Fine Grade = 6.5 If tet level = 3, 4 or 5 then: If main tet mark exit and i conitent with level, then: mark level min Fine Grade = + level level max - level min + 1 If main tet mark exit and i not conitent with level: If the level i hiher than the mark then: Fine Grade = Tet level (3.0, 4.0 or 5.0). If the level i lower than the mark then the fine rade i obtained from the maximum mark in that level, then: level max level min Fine Grade = + level level max - level min + 1 If tet level = 2 and TA i 3+ then: If main tet mark exit and i conitent with level, then the difference in fine rade of one mark i extended from level 3 rane. Fine Grade = 3.0 min lev 3 mark mark max lev 3 mark min lev 3 mark + 1 If main tet mark doe not exit, then we ain the pupil the middle mark of the compenatory level 2 rane. If the main tet mark i lower than the minimum mark for the compenatory level 2 rane then we ain the minimum mark of the compenatory level 2 rane and if the main tet mark i hiher than the minimum mark for the compenatory level 2 rane then we ain the maximum of the compenatory level 2 rane. Then apply the above alorithm. 30

31 Writin A we only have teacher aement data for writin, the fine rade outcome are: Writin teacher aement level Fine rade W For readin, writin and mathematic, the point core i calculated a 6 * fine rade. Overall The KS2 averae point core (APS) for the overall meaure in 2015 i calculated uin the followin formula, KS2 APS = ((KS2 readin fine point + KS2 writin fine point)/2 + KS2 math fine point)/2 For example a pupil who receive 25.68, and point for readin, writin and mathematic repectively would have an APS core of KS2 APS = ( ) / =

32 Section I KS1-2 model coefficient for 2015 The table below ummarie the model coefficient, the variance term and tandard deviation ued to calculate the four KS1-2 core and confidence interval for 2015 amended data. Thee value are ued to calculate a pupil etimated KS2 outcome and the confidence interval around the pupil core. Coefficient Applied to KS1-2 overall meaure KS1-2 readin meaure KS1-2 writin meaure KS1-2 mathematic C Contant C1 KS2APS C2 KS2APS C3 KS2APS C4 READEV C5 MATDEV B Between chool variance W Within chool variance σ N National tandard deviation

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