Contents目錄

Introduction 3 簡介

Why standards-referenced reporting? 4 為什麼要採用水平參照成績匯報？

Improving the current reporting system 5 改進現行成績匯報制度

Setting the standards 6 設定水平

Maintaining the standards 8 保持水平

Using the descriptors 9 等級描述的運用

Reporting the results 9 成績匯報

Recognition of the standards 11 水平認可

The future of standards-referenced reporting 12 水平參照成績匯報的未來發展

Appendix 1: Examples of the descriptors for 13 Chinese Language and English Language附錄一：中國語文科及英國語文科等級描述的例子

Appendix 2: Calibrating and equating the 15 examinations附錄二：考試的等值

Reference materials 17 參考資料

2

Hong Kong is not alone in pursuing standards-referenced reporting. It has been adopted by allmajor examining bodies in recent years, bynations such as the UK and the USA in theirschool testing programmes, and internationally,as for example in the OECD's Programme forInternational Student Assessment (PISA).

This has been in response to demands that resultsare reported with reference to standards that areworld-class, internationally recognized, transparent,explicit, and that remain constant over time.

Under 'standards-referenced' approaches, thestandards are held constant and the percentage ofstudents awarded a given grade or level can varyaccording to the proportion of the studentsmeeting the defined standard. There are no fixedpercentages -- these can go up or down -- but thereare fixed standards. This means that it is possibleto know how standards of students' performanceare changing over time.

In addition, under standards-referenced reporting,the standards are transparent. There are writtendescriptors of what the typical student who isawarded a particular grade/level knows and cando, and examples of student work and responsesto questions that illustrate the standards. Explicitstandards facilitate teaching and learning.Students can be shown what they have to do to beawarded higher grades or levels and teachersknow what they have to do to assist students to getbetter results. Explicit standards are also useful toemployers and tertiary institutions in makingselection decisions.

不獨是香港，世界各地的主要考試機構，近年均採用水平參照模式匯報成績，如英、美等

國的一些學校評核計劃，便是採用水平參照模

式。國際經濟合作與發展組織(OECD)主辦的「學

生能力國際評估計劃」，也採用水平參照模式。

採用水平參照模式乃是順應以下要求：成績

評級所參照的水平標準應符合世界水平、獲國

際認可、透明度高，並且明確而固定。

在水平參照模式下，預設的等級水平是維持不

變的，但每個等級的人數比例可以隨�考生所

達到的水平而變化。各等級的人數比例可升可

降，沒有預定的百分率，但等級水平是固定不

變的。由此可見，水平參照模式有助監察不同

年份考生的表現。

水平參照模式的另一個特點，是所預設的等級

水平透明度高。每個等級都有一套文字描述（簡

稱「等級描述」），說明達到該等級的典型學生

應具備的知識及能力水平。考評局亦會提供一

些學生答卷或作業樣本及示例，以說明各等級

水平的要求。明確清晰的等級水平可促進教與

學。一方面，學生知道該如何努力去獲取更高

的等級；另一方面，教師亦知道該如何協助學

生獲取更佳成績。明確的等級水平亦有助僱主

及大專院校作出甄選的決定。

Why standards-referenced reporting?為什麼要採用水平參照成績匯報？

4

Introduction簡介

With effect from 2007, standards-referenced reporting will be adopted for HKCE Chinese Language and English Language examinations. This is being done as part of a set of measures designed to ensure world-class educational assessment services for Hong Kong students.

Under the new system, Grades (A-F) will be replaced by Levels (1-5). The top-scoring students within Level 5 will be awarded a 5*. More importantly, each of the five levels will represent an explicit and fixed standard of performance.

The purpose of this booklet is to explain the rationale and key features of this new approach to reporting results.

由2007年開始，香港中學會考中國語文科及英國語文科將採用水平參照模式匯報考生的成績。

這是香港考試及評核局（簡稱考評局）致力為香

港學生提供國際級評核服務的其中一項措施。

在水平參照評級制度下，考生成績將由現時的

六個等級（A至F）變為五個等級（1至5）。在第5

等級內，成績最佳的考生可獲「5*」等級。此評

級模式的最大特點，是每個等級都代表明確而

固定的表現水平。

本小冊子旨在解釋水平參照成績匯報的理念及

主要特色，讓教師和公眾認識新的評級模式。

3

With effect from 2007, standards-referencedreporting will be adopted for HKCE ChineseLanguage and English Language examinations.This is being done as part of a set of measuresdesigned to ensure world-class educationalassessment services for Hong Kong students.

Under the new system, Grades (A-F) will bereplaced by Levels (1-5). The top-scoring studentswithin Level 5 will be awarded a 5*. Moreimportantly, each of the five levels will represent anexplicit and fixed standard of performance.

The purpose of this booklet is to explain therationale and key features of this new approach toreporting results.

由2007年開始，香港中學會考中國語文科及英國語文科將採用水平參照模式匯報考生的成績。

這是香港考試及評核局（簡稱考評局）致力為香

港學生提供國際級評核服務的其中一項措施。

在水平參照評級制度下，考生成績將由現時的

六個等級（A至F）變為五個等級（1至5）。在第5

等級內，成績最佳的考生可獲「5*」等級。此評

級模式的最大特點，是每個等級都代表明確而

固定的表現水平。

本小冊子旨在解釋水平參照成績匯報的理念及

主要特色，讓教師和公眾認識新的評級模式。

Introduction簡介

3

Why standards-referenced reporting?為什麼要採用水平參照成績匯報？

Hong Kong is not alone in pursuing standards-referenced reporting. It has been adopted by all major examining bodies in recent years, by nations such as the UK and the USA in their school testing programmes, and internationally, as for example in the OECD's Programme for International Student Assessment (PISA).

This has been in response to demands that results are reported with reference to standards that are world-class, internationally recognized, transparent, explicit, and that remain constant over time.

Under 'standards-referenced' approaches, the standards are held constant and the percentage of students awarded a given grade or level can vary according to the proportion of the students meeting the defined standard. There are no fixed percentages -- these can go up or down -- but there are fixed standards. This means that it is possible to know how standards of students' performance are changing over time.

In addition, under standards-referenced reporting, the standards are transparent. There are written descriptors of what the typical student who is awarded a particular grade/level knows and can do, and examples of student work and responses to questions that illustrate the standards. Explicit standards facilitate teaching and learning. Students can be shown what they have to do to be awarded higher grades or levels and teachers know what they have to do to assist students to get better results. Explicit standards are also useful to employers and tertiary institutions in making selection decisions.

不獨是香港，世界各地的主要考試機構，近年均採用水平參照模式匯報成績，如英、美等

國的一些學校評核計劃，便是採用水平參照模

式。國際經濟合作與發展組織(OECD)主辦的「學

生能力國際評估計劃」，也採用水平參照模式。

採用水平參照模式乃是順應以下要求：成績

評級所參照的水平標準應符合世界水平、獲國

際認可、透明度高，並且明確而固定。

在水平參照模式下，預設的等級水平是維持不

變的，但每個等級的人數比例可以隨�考生所

達到的水平而變化。各等級的人數比例可升可

降，沒有預定的百分率，但等級水平是固定不

變的。由此可見，水平參照模式有助監察不同

年份考生的表現。

水平參照模式的另一個特點，是所預設的等級

水平透明度高。每個等級都有一套文字描述（簡

稱「等級描述」），說明達到該等級的典型學生

應具備的知識及能力水平。考評局亦會提供一

些學生答卷或作業樣本及示例，以說明各等級

水平的要求。明確清晰的等級水平可促進教與

學。一方面，學生知道該如何努力去獲取更高

的等級；另一方面，教師亦知道該如何協助學

生獲取更佳成績。明確的等級水平亦有助僱主

及大專院校作出甄選的決定。

4

6

There are various methods that can be used to setstandards, but certain basic ideas are common toall. In particular, all standards-setting methodsinvolve a mechanism for deciding which score willbe used to determine whether or not a candidatehas attained a given standard.

In the case of the HKCEE, it has been determinedthat there will be five standards, which will belabelled Levels 1, 2, 3, 4, and 5, with Level 1being the lowest and Level 5 the highest. Thehighest scoring Level 5 candidates will beawarded a 5*.

Based on their examination performance andmoderated SBA results, candidates will beawarded a total score for Chinese Language andfor English Language. The task is thus to determinethe minimum scores a candidate must obtain inorder to meet various standards (i.e., Levels 1-5).These minimum scores are known as cut scores.This can be represented diagrammatically asshown below.

雖然設定水平的方法有很多，但都包含一些

共同的理念。其中，所有方法都牽涉制定一套

機制，以界定臨界得分，決定考生達到哪一個

水平。

以香港中學會考為例，五個等級水平分別以1、

2、3、4、5表示，其中第1等級為最低，而第

5等級為最高。在第5等級內，成績最佳的考生

可獲5*。

中學會考中國語文科及英國語文科的科目成績，

是由考生的公開考試成績及經調整的校本評

核分數組合而成。在設定水平時，首先要釐

訂不同等級水平（1-5）中，考生最少需要獲取

的分數。每個等級的最低分數稱為臨界得分，

如下圖所示：

Setting the standards設定水平

Cut scores臨界得分

� U� 1� 2� 3� 4� 5Level等級

Improving the current reporting system改進現行成績匯報制度

Currently in Hong Kong, candidates are awarded a grade on a scale ranging from A (high) to F (low) but there are no descriptors for the different grades and no samples of student work to illustrate the standards. In addition, the percentage of candidates awarded certain grades is determined by rules embedded in the policy for different subjects.

However, under the current grading policies, the allocation of grades is also guided by information on standards of performance. This information includes the results of annual monitoring of the performance of students in a control group of schools having stable patterns of enrolments and performance. It includes the administration of secure monitoring tests in the control group schools to measure standards of performance in Chinese, English and Mathematics. It also includes the results of benchmarking against British GCE standards. A sample of examination papers and scripts are sent to one of the British examining boards (Cambridge Assessment, formerly UCLES) each year. They vet the papers and scripts and provide a report on the standards. The HKEAA uses the information in adjusting grading standards in Hong Kong on an annual basis. In this respect, the current system for reporting results in Hong Kong has some of the features of a standards-referenced system.

The use of monitoring tests and benchmarking in collaboration with international examination boards will continue under the new system. Since each of the attainment levels will be accompanied by detailed information on what a typical student at a given level knows and is able to do, and since there will also be annotated samples of student work, the use of standards-referencing procedures will increase the community's confidence in the examination grading system. Tertiary institutions and employers will have a higher level of confidence in the reported standards of skills and knowledge of candidates. Teachers and students will be able to discuss the standards of performance expected at different levels and set learning goals and teaching strategies. Details of the standards-referencing procedures are described below.

現時是以A（最高）至F（最低）六個等級匯報香

港考生的公開考試成績。每個等級沒有文字描

述，亦沒有學生的答卷或作業樣本可供參考。

除此之外，每個等級的人數均根據各科的不同

要求而有預定的百分率。

不過，現行的評級制度也參考考生的表現以釐

定各個等級的人數比例。評級參考資料包括每

年參考組（control group）學校考生的表現（參考

組由過往數年收生情況及學生整體表現較穩定

的學校組成）。通過在參考組進行保密研究測

驗（secure monitoring tests），量度考生在中國

語文、英國語文及數學三科科目的表現水平。

此外，評級亦以英國普通教育文憑考試（GCE）

為基準。考評局每年抽取部分試題及答卷，送

交英國劍橋國際考試局委員會（Cambridge

Assessment），作局外審題及評級標準評鑑。

考評局利用以上的資料，調整每年的評級標準。

由此可見，現時採用的成績匯報方法已具備水

平參照的一些特徵。

新的水平參照評級制度會繼續沿用研究測驗及

海外評審的做法。由於各個等級都附有一套等

級描述及學生答卷或作業樣本，具體說明每個

等級的典型考生的知識及能力水平，新方法將

大大增加公眾對考試評級制度的信心，亦提高

大專院校及僱主對考生在知識及能力水平方面

的信心。教師及學生可相互討論不同等級的水

平要求，進而訂立學習目標及教學策略。下面

將詳細介紹設定水平的程序。

5

Improving the current reporting system改進現行成績匯報制度

5

Currently in Hong Kong, candidates are awardeda grade on a scale ranging from A (high) to F (low)but there are no descriptors for the different gradesand no samples of student work to illustrate thestandards. In addition, the percentage of candidatesawarded certain grades is determined by rulesembedded in the policy for different subjects.

However, under the current grading policies, theallocation of grades is also guided by informationon standards of performance. This informationincludes the results of annual monitoring of theperformance of students in a control group ofschools having stable patterns of enrolments andperformance. It includes the administration ofsecure monitoring tests in the control group schoolsto measure standards of performance in Chinese,English and Mathematics. It also includes the resultsof benchmarking against British GCE standards. Asample of examination papers and scripts are sentto one of the British examining boards (CambridgeAssessment, formerly UCLES) each year. They vetthe papers and scripts and provide a report on thestandards. The HKEAA uses the information inadjusting grading standards in Hong Kong on anannual basis. In this respect, the current system forreporting results in Hong Kong has some of thefeatures of a standards-referenced system.

The use of monitoring tests and benchmarking incollaboration with international examination boardswill continue under the new system. Since each ofthe attainment levels will be accompanied bydetailed information on what a typical student at agiven level knows and is able to do, and since therewill also be annotated samples of student work, theuse of standards-referencing procedures willincrease the community's confidence in theexamination grading system. Tertiary institutionsand employers will have a higher level ofconfidence in the reported standards of skills andknowledge of candidates. Teachers and studentswill be able to discuss the standards of performanceexpected at different levels and set learning goalsand teaching strategies. Details of the standards-referencing procedures are described below.

現時是以A（最高）至F（最低）六個等級匯報香

港考生的公開考試成績。每個等級沒有文字描

述，亦沒有學生的答卷或作業樣本可供參考。

除此之外，每個等級的人數均根據各科的不同

要求而有預定的百分率。

不過，現行的評級制度也參考考生的表現以釐

定各個等級的人數比例。評級參考資料包括每

年參考組（control group）學校考生的表現（參考

組由過往數年收生情況及學生整體表現較穩定

的學校組成）。通過在參考組進行保密研究測

驗（secure monitoring tests），量度考生在中國

語文、英國語文及數學三科科目的表現水平。

此外，評級亦以英國普通教育文憑考試（GCE）

為基準。考評局每年抽取部分試題及答卷，送

交英國劍橋國際考試局委員會（Cambridge

Assessment），作局外審題及評級標準評鑑。

考評局利用以上的資料，調整每年的評級標準。

由此可見，現時採用的成績匯報方法已具備水

平參照的一些特徵。

新的水平參照評級制度會繼續沿用研究測驗及

海外評審的做法。由於各個等級都附有一套等

級描述及學生答卷或作業樣本，具體說明每個

等級的典型考生的知識及能力水平，新方法將

大大增加公眾對考試評級制度的信心，亦提高

大專院校及僱主對考生在知識及能力水平方面

的信心。教師及學生可相互討論不同等級的水

平要求，進而訂立學習目標及教學策略。下面

將詳細介紹設定水平的程序。

Setting the standards設定水平

There are various methods that can be used to set standards, but certain basic ideas are common to all. In particular, all standards-setting methods involve a mechanism for deciding which score will be used to determine whether or not a candidate has attained a given standard.

In the case of the HKCEE, it has been determined that there will be five standards, which will be labelled Levels 1, 2, 3, 4, and 5, with Level 1 being the lowest and Level 5 the highest. The highest scoring Level 5 candidates will be awarded a 5*.

Based on their examination performance and moderated SBA results, candidates will be awarded a total score for Chinese Language and for English Language. The task is thus to determine the minimum scores a candidate must obtain in order to meet various standards (i.e., Levels 1-5). These minimum scores are known as cut scores. This can be represented diagrammatically as shown below.

雖然設定水平的方法有很多，但都包含一些

共同的理念。其中，所有方法都牽涉制定一套

機制，以界定臨界得分，決定考生達到哪一個

水平。

以香港中學會考為例，五個等級水平分別以1、

2、3、4、5表示，其中第1等級為最低，而第

5等級為最高。在第5等級內，成績最佳的考生

可獲5*。

中學會考中國語文科及英國語文科的科目成績，

是由考生的公開考試成績及經調整的校本評

核分數組合而成。在設定水平時，首先要釐

訂不同等級水平（1-5）中，考生最少需要獲取

的分數。每個等級的最低分數稱為臨界得分，

如下圖所示：�

Cut scores臨界得分�

Level� U� 1� 2� 3� 4� 5 等級

6

8

Once set, the standards will be maintained byadministering secure monitoring tests annually tocarefully selected samples of candidates. Themonitoring test results will be used to equatesuccessive examinations. Equating means workingout what scores on the monitoring test areequivalent to what scores on the examination.

The cut scores established for the 2007examinations will be mapped onto the scaledefined by the monitoring tests. In subsequentyears, equating of successive examinations will becarried out and initial cut scores establishedempirically, although panels of judges willcontinue to fine-tune them through closeexamination of those scripts clustering aroundeach cut score.

Through this process, the public, tertiaryinstitutions both in Hong Kong and overseas,employers, and other users can be assured that thestandards have been held constant and that thereis no 'grade inflation' over time, as has occurredin some systems that do not use empirical methodsfor equating successive examinations.

For those interested in the technical details, a briefexplanation of the formulas to be used incalibrating and equating examinations is given inAppendix 2.

水平標準一經制訂，考評局每年都要小心選取一些樣本考生，進行保密研究測驗，以確保

每年的標準不變。研究測驗結果會用於不同年

度的考試成績的等值比較。通過等值比較，可

以找出研究測驗的某個分數與公開考試的哪個

分數等值。

通過等值方法，為2007年度會考設定的臨界

得分會對應到研究測驗的分數上，定出研究測

驗的臨界得分。在隨後數年，不同年度的考試

成績通過與研究測驗成績的等值比較，可以訂

定初步的臨界得分。專家小組會再仔細檢視與

臨界得分相同或貼近的答卷，進一步微調臨界

得分。

通過以上步驟，可以向公眾、香港及海外的大

專院校、僱主及其他使用者確保各等級的水平

標準是固定不變的；而不會像那些沒有作等值

比較的評級制度，在若干年後出現「等級膨脹」

的情況。

如有興趣深入了解水平參照的技術細節，可參

考附錄二。

Maintaining the standards保持水平

The method to be adopted by the HKEAA is a two-step process. The first step has already been completed. It involved the development of a set of descriptors that describe what it means to perform at each of the five levels. These descriptors were developed in conjunction with overseas as well as local experts and with close reference to samples of the actual performances of candidates in previous examinations. These descriptors have already been published, along with samples of student work that illustrate the relevant standards. By way of illustration, the descriptors for Levels 1, 3 and 5 in both Chinese Language and English Language are given in Appendix 1.

The descriptors provide a broad definition of the standards, but do not allow for a precise judgment to be made. This is achieved in the second step of the standards setting process. In this second step, cut scores for 2007 HKCEE Chinese Language and English Language will be determined by a panel of judges consisting of subject experts and experienced markers and teachers.

These panels will make a decision about cut scores based on past levels of performance in these subjects and the published descriptors for each of the five levels. It must be stressed, however, that it will not be possible to specify direct equivalences between the old system of Grades and the new system of Levels.

考評局設定水平的方法有兩個步驟。第一個步

驟現已完成，就是發展一套等級描述，說明各

個等級的知識及能力要求。這些等級描述是由

本地及海外的專家，根據過往公開考試考生的

實際表現制訂出來。有關等級描述及示例已編

輯成小冊子。附錄一具體展示中國語文科及英

國語文科其中第1、3及5級的等級描述。

等級描述提供了概括的水平表現，但還不能據

此作出準確的判斷。第二個步驟是由科目專家、

資深閱卷員及老師組成的專家小組，決定2007

年會考中國語文科及英國語文科的臨界得分。

專家小組會根據過往考生在該科目的表現與已

經公布的等級描述，決定各等級的臨界得分。

需要強調的是，舊制度的A至F級與新制度的

1至5級　　直接的等值關係。沒有

7

7

The method to be adopted by the HKEAA is a two-step process. The first step has already beencompleted. It involved the development of a set ofdescriptors that describe what it means to performat each of the five levels. These descriptors weredeveloped in conjunction with overseas as well aslocal experts and with close reference to samples ofthe actual performances of candidates in previousexaminations. These descriptors have already beenpublished, along with samples of student work thatillustrate the relevant standards. By way ofillustration, the descriptors for Levels 1, 3 and 5 inboth Chinese Language and English Language aregiven in Appendix 1.

The descriptors provide a broad definition of thestandards, but do not allow for a precise judgmentto be made. This is achieved in the second step ofthe standards setting process. In this second step,cut scores for 2007 HKCEE Chinese Languageand English Language will be determined by apanel of judges consisting of subject experts andexperienced markers and teachers.

These panels will make a decision about cut scoresbased on past levels of performance in thesesubjects and the published descriptors for each ofthe five levels. It must be stressed, however, that itwill not be possible to specify direct equivalencesbetween the old system of Grades and the newsystem of Levels.

考評局設定水平的方法有兩個步驟。第一個步

驟現已完成，就是發展一套等級描述，說明各

個等級的知識及能力要求。這些等級描述是由

本地及海外的專家，根據過往公開考試考生的

實際表現制訂出來。有關等級描述及示例已編

輯成小冊子。附錄一具體展示中國語文科及英

國語文科其中第1、3及5級的等級描述。

等級描述提供了概括的水平表現，但還不能據

此作出準確的判斷。第二個步驟是由科目專家、

資深閱卷員及老師組成的專家小組，決定2007

年會考中國語文科及英國語文科的臨界得分。

專家小組會根據過往考生在該科目的表現與已

經公布的等級描述，決定各等級的臨界得分。

需要強調的是，舊制度的A至F級與新制度的

1至5級　　直接的等值關係。沒有

Maintaining the standards保持水平

Once set, the standards will be maintained by administering secure monitoring tests annually to carefully selected samples of candidates. The monitoring test results will be used to equate successive examinations. Equating means working out what scores on the monitoring test are equivalent to what scores on the examination.

The cut scores established for the 2007 examinations will be mapped onto the scale defined by the monitoring tests. In subsequent years, equating of successive examinations will be carried out and initial cut scores established empirically, although panels of judges will continue to fine-tune them through close examination of those scripts clustering around each cut score.

Through this process, the public, tertiary institutions both in Hong Kong and overseas, employers, and other users can be assured that the standards have been held constant and that there is no 'grade inflation' over time, as has occurred in some systems that do not use empirical methods for equating successive examinations.

For those interested in the technical details, a brief explanation of the formulas to be used in calibrating and equating examinations is given in Appendix 2.

水平標準一經制訂，考評局每年都要小心選取一些樣本考生，進行保密研究測驗，以確保

每年的標準不變。研究測驗結果會用於不同年

度的考試成績的等值比較。通過等值比較，可

以找出研究測驗的某個分數與公開考試的哪個

分數等值。

通過等值方法，為2007年度會考設定的臨界

得分會對應到研究測驗的分數上，定出研究測

驗的臨界得分。在隨後數年，不同年度的考試

成績通過與研究測驗成績的等值比較，可以訂

定初步的臨界得分。專家小組會再仔細檢視與

臨界得分相同或貼近的答卷，進一步微調臨界

得分。

通過以上步驟，可以向公眾、香港及海外的大

專院校、僱主及其他使用者確保各等級的水平

標準是固定不變的；而不會像那些沒有作等值

比較的評級制度，在若干年後出現「等級膨脹」

的情況。

如有興趣深入了解水平參照的技術細節，可參

考附錄二。

8

10

The Results Notice issued to candidates will follow a similar format.成績通知書會以類似的形式發放給考生。

香 港 考 試 及 評 核 局Hong Kong Examinations and Assessment Authority

香 港 中 學 會 考 證 書Hong Kong Certificate of Education Examination

茲證明This is to certify that

陳大文Chan Tai Man

參加2007年香港中學會考，成績如下：sat the 2007 Hong Kong Certificate of Education Examination and

achieved the following results:

� 科目� 科目等級� 分部等級

� Subject� Subject Grade/Level� Component� � � Grade/Level

中國語文� CHINESE LANGUAGE� 4 (Four)�• 閱讀� �• Reading� 5 (Five)• 寫作� �• Writing� 2 (Two)• 聆聽� �• Listening� 4 (Four)• 說話� �• Speaking� ABSENT• 綜合能力� �• Integrated Skills� 3 (Three)

英國語文� ENGLISH LANGUAGE� 3 (Three)• 閱讀� �• Reading� � 3 (Three)• 寫作� �• Writing� � 4 (Four)• 聆聽及綜合能力� �• Listening and Integrated Skills� � 3 (Three)• 說話� �• Speaking� � 2 (Two)

法文� FRENCH� A* (a*)

生物� BIOLOGY� E (e)�

化學� CHEMISTRY� D (d)

物理� PHYSICS� D (d)

數學� MATHEMATICS� B (b)

Using the descriptors等級描述的運用

The descriptors for Chinese Language and English Language (see examples in Appendix 1) provide important information about the performance typically exhibited by a candidate who achieves a certain level. This information can be of great value to teachers in communicating to students the standards and what they need to do in order to achieve a higher level of performance. They can also be very helpful to students in understanding the standards and knowing what they have to do in order to improve their marks.

The principle behind the descriptors is that they describe what typical candidates can do, not what they cannot do. In other words, they describe performance in positive rather than negative terms.

The descriptors, or summary versions of them, are also potentially useful to other users, including tertiary institutions and employers wishing to better understand the standards inherent in the new system of levels.

Reporting the results成績匯報

From 2007 onwards, the certificate awarded to HKCEE candidates will display levels for Chinese Language and English Language, and grades for all other subjects. In the case of the two language subjects, a level will be given for the subject as a whole, as well as for each of the components. An example of how results will be set out on the certificate is given below:

中國語文科及英國語文科的等級描述（見附錄一）

提供重要的資料，說明考生獲取某一等級的典

型表現。這些資料對教師而言是非常寶貴的。

教師可藉�與學生討論水平標準，協助他們知

道怎樣做才能達到更高的水平。對學生而言，

這些資料亦有很大幫助。等級描述讓他們明白

各個等級的要求，從而確定上進的目標，求取

更佳成績。

制訂等級描述的原則，是要描述各個等級的典

型學生所　做到的，而非他們　　做到的。換能 不能

言之，等級描述是正面而非負面地描述考生的

表現。

除了教師和學生，等級描述亦會對其他使用者

帶來幫助，例如大專院校和僱主可以此更清楚

了解新成績匯報制度下的考生水平。�

由2007年開始，香港中學會考成績證書將顯

示考生在中國語文科及英國語文科的表現水平，

其他科目的成績則仍然以六級表示。兩科語文

科均有科目的總等級及每一分部項目的等級。

考生成績證書的樣本如下：

9

9

Using the descriptors等級描述的運用

The descriptors for Chinese Language and EnglishLanguage (see examples in Appendix 1) provideimportant information about the performancetypically exhibited by a candidate who achieves acertain level. This information can be of great valueto teachers in communicating to students thestandards and what they need to do in order toachieve a higher level of performance. They canalso be very helpful to students in understanding thestandards and knowing what they have to do inorder to improve their marks.

The principle behind the descriptors is that theydescribe what typical candidates can do, not whatthey cannot do. In other words, they describeperformance in positive rather than negative terms.

The descriptors, or summary versions of them, arealso potentially useful to other users, includingtertiary institutions and employers wishing to betterunderstand the standards inherent in the new systemof levels.

中國語文科及英國語文科的等級描述（見附錄一）

提供重要的資料，說明考生獲取某一等級的典

型表現。這些資料對教師而言是非常寶貴的。

教師可藉�與學生討論水平標準，協助他們知

道怎樣做才能達到更高的水平。對學生而言，

這些資料亦有很大幫助。等級描述讓他們明白

各個等級的要求，從而確定上進的目標，求取

更佳成績。

制訂等級描述的原則，是要描述各個等級的典

型學生所　做到的，而非他們　　做到的。換

言之，等級描述是正面而非負面地描述考生的

表現。

除了教師和學生，等級描述亦會對其他使用者

帶來幫助，例如大專院校和僱主可以此更清楚

了解新成績匯報制度下的考生水平。

Reporting the results成績匯報

From 2007 onwards, the certificate awarded toHKCEE candidates will display levels for ChineseLanguage and English Language, and grades for allother subjects. In the case of the two languagesubjects, a level will be given for the subject as awhole, as well as for each of the components. Anexample of how results will be set out on thecertificate is given below:

由2007年開始，香港中學會考成績證書將顯

示考生在中國語文科及英國語文科的表現水平，

其他科目的成績則仍然以六級表示。兩科語文

科均有科目的總等級及每一分部項目的等級。

考生成績證書的樣本如下：

能 不能

香 港 考 試 及 評 核 局� Hong Kong Examinations and Assessment Authority

香 港 中 學 會 考 證 書� Hong Kong Certificate of Education Examination

茲證明� This is to certify that

陳大文� Chan Tai Man

參加2007年香港中學會考，成績如下：� sat the 2007 Hong Kong Certificate of Education Examination and

achieved the following results:

� 科目� 科目等級� 分部等級�

� Subject� Subject Grade/Level� Component � � � Grade/Level

中國語文� CHINESE LANGUAGE� 4 (Four)� • 閱讀� � • Reading� 5 (Five) • 寫作� � • Writing� 2 (Two) • 聆聽� � • Listening� 4 (Four) • 說話� � • Speaking� ABSENT • 綜合能力� � • Integrated Skills� 3 (Three)

英國語文� ENGLISH LANGUAGE� 3 (Three) • 閱讀� � • Reading� � 3 (Three) • 寫作� � • Writing� � 4 (Four) • 聆聽及綜合能力� � • Listening and Integrated Skills� � 3 (Three) • 說話� � • Speaking� � 2 (Two)

法文� FRENCH� A*�(a*)

生物� BIOLOGY� E� (e)�

化學� CHEMISTRY� D� (d)

物理� PHYSICS� D� (d)

數學� MATHEMATICS� B� (b)

The Results Notice issued to candidates will follow a similar format.成績通知書會以類似的形式發放給考生。

10

12

The future of standards-referenced reporting水平參照成績匯報的未來發展

The above arrangements will apply until the lastyear of the HKCEE. Standards-referenced reporting,along the lines described above, will be fullyimplemented in all subjects in the 2012 HKDSEexamination.

以上介紹的成績評級及匯報安排，將一直應用至最後一屆香港中學會考。在2012年，水

平參照成績匯報將全面應用於香港中學文憑考

試的所有科目。

Recognition of the standards水平認可

The Education and Manpower Bureau (EMB) hasconducted consultations on adjustments to the Secondary Six Admission Procedure (the Procedure) and has decided that Levels 1 to 5* for Chinese Language and English Language will be converted into points 0 to 5 respectively. The existing point system will continue to be adopted for the other subjects. The points for the two language subjects and for other subjects will be counted in the Procedure in the same way as in previous years. The points for admission to Secondary Six will continue to be printed on the S6 Admission Slip for 2007 and in subsequent years. Further details are available in EMB Circular Memorandum No. 194/2006 and at the EMB's website (http://www.emb.gov.hk/s6ap_e).

In order to sit for the HKALE, candidates have to meet specific requirements relating to performance in HKCEE subjects, including the two language subjects. For Chinese Language and English Language, candidates must obtain Level 2 or above in the 2007 HKCEE, or grade E or above in previous years. Further details can be found in the 2009 HKALE Regulations and Syllabuses.

In terms of international recognition, the 2007 HKCE Chinese Language and English Language examinations have been benchmarked against the International General Certificate of Secondary Education (IGCSE) by Cambridge Assessment. As a result, HKCEE results in these two language subjects are recognized as equivalent to the IGCSE as follows:

教育統籌局已就中六收生程序向各界諮詢，並決定將中國語文科及英國語文科的第1至5*

等級相應化為0至5積點；其他科目則繼續採用

現行的積點計算法。用水平參照匯報成績的科

目及其他科目的積點計算方法將與以往的中六

收生程序所採用的方法相同。2007年及以後的

中六入學取錄紙將會繼續印有入讀中六用途的

積點。有關收生程序的詳請已載於教育統籌局

通函第1 9 4 / 2 0 0 6號及教育統籌局網頁

(http://www.emb.gov.hk/s6ap)。

要符合參加香港高級程度會考的資格，考生必

須在香港中學會考中達到指定的成績要求，其

中包括兩科語文科的成績。考生必須在2007年

香港中學會考中國語文科及英國語文科考獲2

級或以上的成績，或在以往的香港中學會考考

獲E級或以上的成績。詳情請參閱2009年香港

高級程度會考考試規則及課程。

在國際認可方面，英國劍橋國際考試局委員會

已將2007年香港中學會考中國語文科及英國語

文科的成績等同於英國國際普通中學教育文憑

考試(IGCSE)的成績。下表列出兩試的成績等

值關係：

Levels attained in HKCEE香港中學會考等級 5* 5 4 3

Grades attained in IGCSEIGCSE等級 A* A B C

11

11

Recognition of the standards水平認可

The Education and Manpower Bureau (EMB) hasconducted consultations on adjustments to theSecondary Six Admission Procedure (the Procedure)and has decided that Levels 1 to 5* for ChineseLanguage and English Language will be convertedinto points 0 to 5 respectively. The existing pointsystem will continue to be adopted for the othersubjects. The points for the two language subjectsand for other subjects will be counted in theProcedure in the same way as in previous years.The points for admission to Secondary Six willcontinue to be printed on the S6 AdmissionSlip for 2007 and in subsequent years. Furtherdetails are available in EMB Circular MemorandumNo. 194/2006 and at the EMB's website(http://www.emb.gov.hk/s6ap_e).

In order to sit for the HKALE, candidates have tomeet specific requirements relating to performancein HKCEE subjects, including the two languagesubjects. For Chinese Language and EnglishLanguage, candidates must obtain Level 2 or abovein the 2007 HKCEE, or grade E or above inprevious years. Further details can be found in the2009 HKALE Regulations and Syllabuses.

In terms of international recognition, the 2007HKCE Chinese Language and English Languageexaminations have been benchmarked against theInternational General Certificate of SecondaryEducation (IGCSE) by Cambridge Assessment. Asa result, HKCEE results in these two new languagesubjects are recognized as equivalent to the IGCSEas follows:

教育統籌局已就中六收生程序向各界諮詢，並決定將中國語文科及英國語文科的第1至5*

等級相應化為0至5積點；其他科目則繼續採用

現行的積點計算法。用水平參照匯報成績的科

目及其他科目的積點計算方法將與以往的中六

收生程序所採用的方法相同。2007年及以後的

中六入學取錄紙將會繼續印有入讀中六用途的

積點。有關收生程序的詳請已載於教育統籌局

通函第1 9 4 / 2 0 0 6號及教育統籌局網頁

(http://www.emb.gov.hk/s6ap)。

要符合參加香港高級程度會考的資格，考生必

須在香港中學會考中達到指定的成績要求，其

中包括兩科語文科的成績。考生必須在2007年

香港中學會考中國語文科及英國語文科考獲2

級或以上的成績，或在以往的香港中學會考考

獲E級或以上的成績。詳情請參閱2009年香港

高級程度會考考試規則及課程。

在國際認可方面，英國劍橋國際考試局委員會

已將2007年香港中學會考中國語文科及英國語

文科的成績等同於英國國際普通中學教育文憑

考試(IGCSE)的成績。下表列出兩試的成績等

值關係：

5*� 5� 4� 3

A*� A� B� C

Levels attained in HKCEE香港中學會考等級

Grades attained in IGCSEIGCSE等級

The future of standards-referenced reporting水平參照成績匯報的未來發展

The above arrangements will apply until the last 以上介紹的成績評級及匯報安排，將一直應year of the HKCEE. Standards-referenced reporting, 用至最後一屆香港中學會考。在2012年，水along the lines described above, will be fully

平參照成績匯報將全面應用於香港中學文憑考implemented in all subjects in the 2012 HKDSE examination. 試的所有科目。

12

14

HKCEE English Language Subject DescriptorsA typical candidate at Level 5

Develops ideas well in writing, and generally writes in a way suitable for thepurpose in both style and content; uses accurate spelling and punctuation, andmainly correct grammar; uses a wide vocabulary, and appropriateparagraphing.Reads a range of texts with understanding; follows the development of argumentsin texts; has a wide vocabulary and is usually able to work out the meaning ofunfamiliar words; can follow detailed written instructions, and select appropriateinformation from texts to complete a task.Can understand spoken English at near-normal speed, in both familiar and someless familiar accents; interprets speakers' stress and intonation to identify theirattitudes and intentions; takes relevant notes while listening to a speaker.Expresses a range of ideas, in clear and well-pronounced English; can hold anextended conversation in most situations; participates actively and constructively indiscussions.

HKCEE English Language Subject DescriptorsA typical candidate at Level 3

Expresses straightforward ideas and information in writing with reasonableclarity; uses mainly accurate punctuation and spells common words correctly; usesmost basic grammatical structures correctly; uses appropriate paragraphing andstyle in short tasks of a familiar type.Understands most of what is read in simple texts, and understands some morecomplex texts when topics are familiar; identifies clearly expressed opinions; canwork out the meaning of some unfamiliar words with a very clear context; followsstraightforward written instructions; selects appropriate information to complete atask from simple texts and from more complex texts on familiar topics.Understands spoken English on familiar topics, at a moderate to slow pace, withfamiliar accents; identifies appropriate factual information while listening and isable to record this, especially when information is given clearly and slowly.Expresses familiar ideas and information clearly and comprehensibly, withaccurate pronunciation of most familiar words; takes part in short simpleconversational exchanges; makes occasional useful contributions to discussions.

HKCEE English Language Subject DescriptorsA typical candidate at Level 1

Writes simple sentences on familiar topics, with some accuracy in spelling,punctuation and grammar; attempts longer paragraphs or texts when guidance orstructure is given; completes forms and tables in written English; uses a smallrange of simple written vocabulary.Understands simple texts with mainly familiar vocabulary; uses headings or keywords to locate appropriate parts of text for a task; follows short, structuredwritten instructions; locates appropriate information for simple tasks, and transfersthis to tables or forms.Understands speakers who speak slowly and clearly on very familiar andpredictable topics; identifies some simple factual information, and recordsinformation such as names and addresses, numbers, and brief messages.Communicates some brief, factual information; takes part in very predictableshort conversational exchanges; makes brief contributions to discussions if giventime and support from others.

Level 5

Level 4

Level 3

Level 2

Level 1

Unclassified

e.g.

e.g.

e.g.

5*

●

●

●

●

●

●

●

●

●

●

●

●

Appendix 1: Examples of the descriptors for Chinese Language and English Language附錄一：中國語文科及英國語文科等級描述的例子

第� 5等級

第� 4等級

第� 3等級

第� 2等級

第� 1等級

不予評級

5* 香港中學會考中國語文科整體等級描述第５等級●�

例子

聽說讀寫及綜合能力發展充分，具較高的語文駕馭能力；分析、比較、推理、論證、批判思維、創意等能力表現優異；語文理解深入，運用嫻熟；善用語言策略。

●� 透徹理解書面及口語材料；對作品內容及技巧評價鑒賞中肯允當，見解成熟、感受深切，並能深入拓展。

●� 書面及口語表達流暢、縝密、積極、靈活、自信，吸引讀者� / 聽眾，對討論活動有積極貢獻。

●� 能選擇與綜合多元信息，並結合相關經驗妥善完成工作。

香港中學會考中國語文科整體等級描述第３等級

例子 ●� 聽說讀寫能力發展尚佳；分析、比較、推理、論證、批判思維等能力表現中等；語文理解及運用一般。

●� 正確理解書面及口語材料；能作簡單評論及推論。

●� 書面及口語表達大體通順切題，有中心；能作必要的回應。

●� 能選擇並粗略綜合多元信息，基本完成工作。

香港中學會考中國語文科整體等級描述第１等級

●�

例子略具聽說讀寫能力；能進行最基本的辨認、分析及比較。

●� 能找出書面及口語材料中的明顯事實，了解口語大意。

●� 書面或口語表達能傳遞零碎意念，有時辭不達意。

●� 複述或概述部分信息，能作粗略回應。�

13

13

第5等級

第4等級

第3等級

第2等級

第1等級

不予評級

例子

香港中學會考中國語文科整體等級描述第５等級

聽說讀寫及綜合能力發展充分，具較高的語文駕馭能力；分析、比較、推理、論證、批判思維、創意等能力表現優異；語文理解深入，運用嫻熟；善用語言策略。

透徹理解書面及口語材料；對作品內容及技巧評價鑒賞中肯允當，見解成熟、感受深切，並能深入拓展。

書面及口語表達流暢、縝密、積極、靈活、自信，吸引讀者 / 聽眾，對討論活動有積極貢獻。

能選擇與綜合多元信息，並結合相關經驗妥善完成工作。

例子

香港中學會考中國語文科整體等級描述第３等級

聽說讀寫能力發展尚佳；分析、比較、推理、論證、批判思維等能力表現中等；語文理解及運用一般。

正確理解書面及口語材料；能作簡單評論及推論。

書面及口語表達大體通順切題，有中心；能作必要的回應。

能選擇並粗略綜合多元信息，基本完成工作。

例子

香港中學會考中國語文科整體等級描述第１等級

略具聽說讀寫能力；能進行最基本的辨認、分析及比較。

能找出書面及口語材料中的明顯事實，了解口語大意。

書面或口語表達能傳遞零碎意念，有時辭不達意。

複述或概述部分信息，能作粗略回應。

5*

Appendix 1: Examples of the descriptors forChinese Language and English Language附錄一：中國語文科及英國語文科等級描述的例子

●

●

●

●

●

●

●

●

●

●

●

●

Level 5

Level 4

Level 3

Level 2

Level 1

Unclassified

e.g.

5* HKCEE English Language Subject Descriptors A typical candidate at Level 5 ●� Develops ideas well in writing, and generally writes in a way suitable for the

purpose in both style and content; uses accurate spelling and punctuation, and mainly correct grammar; uses a wide vocabulary, and appropriate paragraphing.

●� Reads a range of texts with understanding; follows the development of arguments in texts; has a wide vocabulary and is usually able to work out the meaning of unfamiliar words; can follow detailed written instructions, and select appropriate information from texts to complete a task.

●� Can understand spoken English at near-normal speed, in both familiar and some less familiar accents; interprets speakers' stress and intonation to identify their attitudes and intentions; takes relevant notes while listening to a speaker.

●� Expresses a range of ideas, in clear and well-pronounced English; can hold an extended conversation in most situations; participates actively and constructively in discussions.

HKCEE English Language Subject Descriptors A typical candidate at Level 3 ●� Expresses straightforward ideas and information in writing with reasonable

clarity; uses mainly accurate punctuation and spells common words correctly; uses most basic grammatical structures correctly; uses appropriate paragraphing and style in short tasks of a familiar type.

●� Understands most of what is read in simple texts, and understands some more complex texts when topics are familiar; identifies clearly expressed opinions; can work out the meaning of some unfamiliar words with a very clear context; follows straightforward written instructions; selects appropriate information to complete a task from simple texts and from more complex texts on familiar topics.

●� Understands spoken English on familiar topics, at a moderate to slow pace, with familiar accents; identifies appropriate factual information while listening and is able to record this, especially when information is given clearly and slowly.

●� Expresses familiar ideas and information clearly and comprehensibly, with accurate pronunciation of most familiar words; takes part in short simple conversational exchanges; makes occasional useful contributions to discussions.

HKCEE English Language Subject Descriptors A typical candidate at Level 1 ● Writes simple sentences on familiar topics, with some accuracy in spelling,

punctuation and grammar; attempts longer paragraphs or texts when guidance or structure is given; completes forms and tables in written English; uses a small range of simple written vocabulary.

●� Understands simple texts with mainly familiar vocabulary; uses headings or key words to locate appropriate parts of text for a task; follows short, structured written instructions; locates appropriate information for simple tasks, and transfers this to tables or forms.

●� Understands speakers who speak slowly and clearly on very familiar and predictable topics; identifies some simple factual information, and records information such as names and addresses, numbers, and brief messages.

●� Communicates some brief, factual information; takes part in very predictable short conversational exchanges; makes brief contributions to discussions if given time and support from others.

e.g.

e.g.

14

16

現在，試想像以下的情境：科目考試包括T個獨立分部，每一分部有不同的比重。該比重是根據試卷結構及考生表現等資料計算出來的。若加入結構參數dt (t=1,2,...,T)，多級評分模型將變成：

其中{dt , t=1,2,...,T} 是已知的常數，而要估計的參數包括題目位置{ i}，題目閾值{ ik}和考生能力位置

（logits）{ßn}。

這是考評局將用於校定2007年公開考試題目與研究測驗的題目並做等值轉換的模型。

通過對每一份試卷與保密研究測驗的所有題目的同時校定，縱使不同考試分部有不同比重，仍可以用相同尺度估計每個考生的能力。尤其是當某一考生獲豁免不用參加某科部分考試時（如失聰人士免考聽說部分），便可以根據該考生參加了的部分考試成績，決定其能力位置（logit）。由於所有的能力位置都在相同的尺度上，該考生的能力位置仍然可與其他考生的能力位置互相比較。

(3)

Now, let us consider the situation in which theexamination is divided into T separate componentswith different weightings for the different components.These weightings are calculated based on thestructure of the examination papers and theperformance of the candidates in the examination.This can be modelled using a structure parameterdt (t=1,2,...,T) and the model for polytomousresponses becomes:

where {dt , t=1,2,...,T} are known constants and theparameters to be estimated are item locations { i},item thresholds { ik} and person locations/logits {ßn}.

This is the model that will be used to calibrate andequate the 2007 examinations and the monitoringtest results.

Calibration of all questions on each examinationpaper and on the secure monitoring tests enablesestimates of the ability of each candidate to begenerated that take into account the weightingsgiven to different components and that are on thesame scale. In particular, when a candidate isexempted from taking any part of the examination,the logit of the candidate will be determined basedon the performance on the parts that the candidatetook and this logit is also comparable with the logitsof other candidates as they are on the same scale.

Pr{Xni = xni} =exp{dt[xni (ßn- i) - � ik]}

xni

k=0

�exp{dt[l (ßn- i) - � ik]}l

k=0

m

l=0

(3)

Pr{Xni = xni} =exp{dt[xni (ßn- i) - � ik]}

xni

k=0

�exp{dt[l (ßn- i) - � ik]}l

k=0

m

l=0

Appendix 2: Calibrating and equating the examinations附錄二：考試的等值

In order to equate successive examinations and thus enable standards to be maintained from one year to the next, the HKEAA will make use of a latent trait model to calibrate responses to all questions on each examination paper and all questions on the secure monitoring tests. The model to be used to calibrate the examinations is based on the Rasch model, but includes a parameter to accommodate differences in the weightings to be applied to different parts of the examination.

The simple Rasch model for dichotomous responses is:

exp(ßn­ i) (1) pni = Pr{Xni = 1} = 1 + exp(ßn­ i)

However, most examinations contain questions that are not simply right or wrong, and for which more than one mark may be awarded. The model for polytomous responses is:

xni

exp{xni (ßn- i) - � ik} Pr{Xni = xni} = m

k=0 (2) �exp{l (ßn- i) - �

l

ik}l=0 k=0

where is the ability of the person n, is the difficulty of the item i, { ik} are the centralized thresholds and � ik =0. and are generally called

0

k=0

the locations (logits).

為要將連續多個年度的考試等值以維持每年的等級水平，考評局將採用潛在特性模型（latent trait model)去校定公開考試每份試卷中所有題目與保密研究測驗中所有題目的參數。題目校定採用的潛在特性模型是根據Rasch模型發展出來的，但包含多一個參數，以調節每個考試不同分部的不同比重。

簡單的二值反應Rasch模型如下：�

exp(ßn­ i)pni = Pr{Xni = 1} = (1) 1 + exp(ßn­ i)

但是，大部分考試題目都不是簡單的只有「對」或「錯」兩個答案的問題，每題答對的得分亦可能多於1分。這時，需要下面的多級評分模型：

exp{xni (ßn­Pr{Xni = xni} = m

�exp{l (ßn­l=0

xni

i) - � ik}k=0 (2) l

i) - � ik}k=0

其中 是考生� n 的能力， 是題目� i 的難度，{ ik}是已經中心化的閾值（centralized thresholds）， 而� � ik =0。 與 則統稱為位置參數（logits）� .

0

k=0

15

15

為要將連續多個年度的考試等值以維持每年的等級水平，考評局將採用潛在特性模型（latent trait model)去校定公開考試每份試卷中所有題目與保密研究測驗中所有題目的參數。題目校定採用的潛在特性模型是根據Rasch模型發展出來的，但包含多一個參數，以調節每個考試不同分部的不同比重。

簡單的二值反應Rasch模型如下：

In order to equate successive examinations andthus enable standards to be maintained from oneyear to the next, the HKEAA will make use of alatent trait model to calibrate responses to allquestions on each examination paper and allquestions on the secure monitoring tests. The modelto be used to calibrate the examinations is basedon the Rasch model, but includes a parameter toaccommodate differences in the weightings to beapplied to different parts of the examination.

The simple Rasch model for dichotomous responsesis:

但是，大部分考試題目都不是簡單的只有「對」或「錯」兩個答案的問題，每題答對的得分亦可能多於1分。這時，需要下面的多級評分模型：

其中 是考生 n 的能力， 是題目 i 的難度，{ ik}是已經中心化的閾值（centralized thresholds）， 而� ik =0。 與 則統稱為位置參數（logits）.

(1)

(2)

0

k=0

pni = Pr{Xni = 1} =exp(ßn- i)

1 + exp(ßn- i)

Pr{Xni = xni} =exp{xni (ßn- i) - � ik}

xni

k=0

�exp{l (ßn- i) - � ik}l

k=0

m

l=0

However, most examinations contain questions thatare not simply right or wrong, and for which morethan one mark may be awarded. The model forpolytomous responses is:

where is the ability of the person n, is thedifficulty of the item i, { ik} are the centralizedthresholds and � ik =0. and are generally calledthe locations (logits).

(1)

(2)

0

k=0

pni = Pr{Xni = 1} =exp(ßn- i)

1 + exp(ßn- i)

Pr{Xni = xni} =exp{xni (ßn- i) - � ik}

xni

k=0

�exp{l (ßn- i) - � ik}l

k=0

m

l=0

Appendix 2: Calibrating and equating theexaminations附錄二：考試的等值

Now, let us consider the situation in which the examination is divided into T separate components with different weightings for the different components. These weightings are calculated based on the structure of the examination papers and the performance of the candidates in the examination. This can be modelled using a structure parameter dt (t=1,2,...,T) and the model for polytomous responses becomes:

xni

exp{dt[xni (ßn­ i) - � ik]} Pr{Xni = xni} = k=0

l (3) �m

exp{dt[l (ßn­ i) - � ik]} l=0 k=0

where {dt , t=1,2,...,T} are known constants and the parameters to be estimated are item locations { i}, item thresholds { ik} and person locations/logits {ßn}.

This is the model that will be used to calibrate and equate the 2007 examinations and the monitoring test results.

Calibration of all questions on each examination paper and on the secure monitoring tests enables estimates of the ability of each candidate to be generated that take into account the weightings given to different components and that are on the same scale. In particular, when a candidate is exempted from taking any part of the examination, the logit of the candidate will be determined based on the performance on the parts that the candidate took and this logit is also comparable with the logits of other candidates as they are on the same scale.

現在，試想像以下的情境：科目考試包括� T個獨立分部，每一分部有不同的比重。該比重是根據試卷結構及考生表現等資料計算出來的。若加入結構參數� dt (t=1,2,...,T)，多級評分模型將變成：

xni

exp{dt[xni (ßn­ i) - � ik]} Pr{Xni = xni} = k=0

l (3) �m

exp{dt[l (ßn­ i) - � ik]} l=0 k=0

其中{ dt , t=1,2,...,T} 是已知的常數，而要估計的參數包括題目位置{ }，題目閾值{ ik}和考生能力位置

（logits）� {ßn}。i

這是考評局將用於校定2007年公開考試題目與研究測驗的題目並做等值轉換的模型。

通過對每一份試卷與保密研究測驗的所有題目的同時校定，縱使不同考試分部有不同比重，仍可以用相同尺度估計每個考生的能力。尤其是當某一考生獲豁免不用參加某科部分考試時（如失聰人士免考聽說部分），便可以根據該考生參加了的部分考試成績，決定其能力位置（logit）。由於所有的能力位置都在相同的尺度上，該考生的能力位置仍然可與其他考生的能力位置互相比較。�

16

Reference materials參考資料

The full set of Chinese Language and EnglishLanguage descriptors can be downloaded from the HKEAA's website (www.hkeaa.edu.hk). Other reference materials can be found in the following publications:

-� 2007 Hong Kong Certificate of Education Examination English Language Sample Papers and Information on Standards-referenced Assessment

-� 2007年香港中學會考中國語文科水平參照等級描述及示例�

整套中國語文科與英國語文科等級描述可於考評局網頁� (www.hkeaa.edu.hk)中下載，而其他參考資料可見於：�

-� 2007 Hong Kong Certificate of Education Examination English Language Sample Papers and Information on Standards-referenced Assessment

-� 2007年香港中學會考中國語文科水平參照等級描述及示例�

Enquiries can be directed to:

如有查詢，請聯絡：

Hong Kong Examinations and Assessment Authority

香港考試及評核局

13/F, Southorn Centre, 130 Hennessy Road

Wan Chai, Hong Kong

香港灣仔軒尼詩道一百三十號修頓中心十三樓

Telephone電話 �：� 3628 8833 （852）

Fax傳真 � ：� 3628 8088 （852）

E-mail電郵 � ：� ce@hkeaa.edu.hk

17