Table Of ContentPISA 2003 Data Analysis Manual
SPSS® USERS
PISA 2003
The OECD Programme for International Student Assessment’s (PISA) 2003 survey collected data on students’
performances in reading, mathematics, science and problem solving, as well as contextual information on Data Analysis
students’ background, home characteristics and school factors which could infl uence performance. The fi rst
results were released in December 2004 and presented in two volumes: Learning for Tomorrow’s World –
First Results from PISA 2003 (OECD, 2004) and Problem Solving for Tomorrow’s World – First Measures Manual
of Cross-Curricular Competencies from PISA 2003 (OECD, 2004).
This publication is an essential tool for researchers, as it provides all the information required to understand
the PISA 2003 database and perform analyses in accordance with the complex methodologies used to
SPSS® USERS
collect and process the data. It includes detailed information on how to analyse the PISA 2003 data, enabling
researchers to both reproduce the initial results and to undertake further analyses. The publication includes:
(cid:129) Introductory chapters explaining the statistical theories and concepts required to analyse the PISA data,
including full chapters on how to apply replicate weights and undertake analyses using plausible values;
(cid:129) Worked examples providing full syntax in SPSS®; and
(cid:129) Comprehensive description of the OECD PISA 2003 international database.
The PISA 2003 database comprises micro-level data on student performance for 41 countries collected in
2003, together with students’ responses to the PISA 2003 questionnaires and the test questions. It can be
downloaded from www.pisa.oecd.org.
THE OECD PROGRAMME FOR INTERNATIONAL STUDENT ASSESSMENT (PISA)
PISA is a collaborative process among the 30 member countries of the OECD and nearly 30 partner countries.
It brings together scientifi c expertise from the participating countries and is steered by their governments
on the basis of shared, policy-driven interests. PISA is an unprecedented attempt to measure student
achievement, as is evident from some of its features:
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– The literacy approach: PISA aims to defi ne each assessment area (mathematics, science, reading and problem IS
solving) not mainly in terms of mastery of the school curriculum, but in terms of the knowledge and skills A
needed for full participation in society. 2
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– A long-term commitment: It will enable countries to monitor regularly and predictably their progress in meeting 3
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key learning objectives.
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– The age-group covered: By assessing 15-year-olds, i.e. young people near the end of their compulsory a
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education, PISA provides a signifi cant indication of the overall performance of school systems. n
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– The relevance to lifelong learning: PISA does not limit itself to assessing students’ knowledge and skills but ly
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also asks them to report on their own motivation to learn, their beliefs about themselves and their learning is
strategies. M
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OECD’s books, periodicals and statistical databases are now available via www.SourceOECD.org, our online library. u
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This book is available to subscribers to the following SourceOECD themes: l
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Education and Skills P
Emerging Economies SS
Transition Economies U®
Ask your librarian for more details on how to access OECD books on line, or write to us at: S
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[email protected] R
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www.oecd.org
Programme for International Student Assessment
ISBN 92-64-01065-3
www.pisa.oecd.org 98 2005 03 1 P
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Programme for International Student Assessment
PISA 2003
Data Analysis Manual
SPSS® Users
OECD
ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT
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Foreword
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The OECD’s Programme for International Student Assessment (PISA) surveys, which take place every
three years, have been designed to collect information about 15-year-old students in participating
countries. PISA examines how well students are prepared to meet the challenges of the future, rather than
how well they master particular curricula. The data collected during each PISA cycle are an extremely
valuable source of information for researchers, policy makers, educators, parents and students. It is now
recognised that the future economic and social well-being of countries is closely linked to the knowledge
and skills of their populations. The internationally comparable information provided by PISA allows
countries to assess how well their 15-year-old students are prepared for life in a larger context and to
compare their relative strengths and weaknesses.
The PISA 2003 database, on which this manual is focused, contains information on over a quarter of
a million students from 41 countries. It includes not only information on their performance in the
four main areas of assessment – reading, mathematics, science and problem solving – but also their
responses to the Student Questionnaire that they complete as part of the assessment. Data from the
school principals are also included.
The PISA 2003 Data Analysis Manual has evolved from the analytical workshops held in Sydney, Vienna,
Paris and Bratislava, which exposed participants to the various techniques needed to correctly analyse
the complex databases. It allows analysts to confi dently replicate procedures used for the production of
the PISA 2003 initial reports, Learning for Tomorrow’s World – First Results from PISA 2003 (OECD, 2004a)
and Problem Solving for Tomorrow’s World – First Measures of Cross-Curricular Competencies from PISA 2003
(OECD, 2004b), and to accurately undertake new analyses in areas of special interest. In addition to
the inclusion of the necessary techniques, the manual also includes a detailed account of the variables
constructed from the student and school questionnaires. This information was previously published in
the Manual for the PISA 2000 Database (OECD, 2002a).
The PISA 2003 Data Analysis Manual is in four parts – the fi rst two sections give a detailed theoretical
background and instructions for analysing the data; the third section lists the program codes (syntaxes
and the macros), which are needed to carry out the analyses; and the fourth section contains a detailed
description of the database.
PISA is a collaborative effort by the participating countries, and guided by their governments on the
basis of shared policy-driven interests. Representatives of each country form the PISA Governing Board
which decides on the assessment and reporting of results in PISA.
There are two versions of this manual – one for SPSS® users and one for SAS® users. The OECD
recognises the creative work of Christian Monseur in preparing the text for both versions of the manual
in collaboration with Sheila Krawchuk and Keith Rust, as well as his preparation of the program coding
for the SAS® users’ manual. The coding for the SPSS® users’ manual was prepared by Wolfram Schulz and
Eveline Gebhardt. The main editorial work was completed at the OECD Secretariat by Miyako Ikeda,
Sophie Vayssettes, John Cresswell, Claire Shewbridge and Kate Lancaster. The PISA assessments
and the data underlying the manuals were prepared by the PISA Consortium under the direction of
Raymond Adams.
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Table of Contents
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Users’ Guide ..........................................................................................................................................................9
CHAPTER 1
The OECD’s Programme for International Student Assessment ......................................................11
An overview of PISA .................................................................................................................................12
What makes PISA unique? .......................................................................................................................13
How the assessment takes place .............................................................................................................15
About this manual ......................................................................................................................................16
CHAPTER 2
Sample Weights ................................................................................................................................................19
Introduction ................................................................................................................................................20
Weights for simple random samples .....................................................................................................21
Sampling designs for education surveys ...............................................................................................22
Why do the PISA weights vary? .............................................................................................................27
Conclusions .................................................................................................................................................30
CHAPTER 3
Replicate Weights .............................................................................................................................................31
Introduction ................................................................................................................................................32
Sampling variance for simple random sampling .................................................................................32
Sampling variance for two-stage sampling ...........................................................................................38
Replication methods for simple random samples ..............................................................................44
Resampling methods for two-stage samples ........................................................................................46
The Jackknife for unstratifi ed two-stage sample designs ..................................................................47
The Jackknife for stratifi ed two-stage sample designs .......................................................................48
The Balanced Repeated Replication method ......................................................................................49
Other procedures for accounting for clustered samples ..................................................................51
Conclusions .................................................................................................................................................51
CHAPTER 4
The Rasch Model ..............................................................................................................................................53
Introduction ................................................................................................................................................54
How can the information be summarised? ..........................................................................................54
The Rasch model for dichotomous items ............................................................................................56
Other Item Response Theory models ...................................................................................................69
Conclusions .................................................................................................................................................69
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s CHAPTER 5
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e Plausible Values .................................................................................................................................................71
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Comparison of the effi ciency of Warm Likelihood Estimates, Expected A Posteriori
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Conclusions .................................................................................................................................................80
CHAPTER 6
Computation of Standard Errors ................................................................................................................81
Introduction ................................................................................................................................................82
The standard error on univariate statistics for numerical variables ...............................................82
The SPSS® macro for computing the standard error on a mean ....................................................85
The standard error on percentages ........................................................................................................87
The standard error on regression coeffi cients ....................................................................................90
The standard error on correlation coeffi cients ...................................................................................92
Conclusions .................................................................................................................................................93
CHAPTER 7
Analyses with Plausible Values ....................................................................................................................95
Introduction ................................................................................................................................................96
Univariate statistics on plausible values ................................................................................................96
The standard error on percentages with plausible values ..............................................................101
The standard error on regression coeffi cients with plausible values ...........................................101
The standard error on correlation coeffi cients with plausible values ..........................................104
Correlation between two sets of plausible values ............................................................................104
A fatal error shortcut ..............................................................................................................................108
An unbiased shortcut ..............................................................................................................................109
Conclusions ...............................................................................................................................................110
CHAPTER 8
Use of Profi ciency Levels .............................................................................................................................111
Introduction ..............................................................................................................................................112
Generation of the profi ciency levels ....................................................................................................112
Other analyses with profi ciency levels ................................................................................................118
Conclusions ...............................................................................................................................................121
CHAPTER 9
Analyses with School Level Variables ......................................................................................................123
Introduction ..............................................................................................................................................124
Limits of the PISA school samples .......................................................................................................125
Merging the school and student data fi les ..........................................................................................126
Analyses of the school variables ...........................................................................................................126
Conclusions ...............................................................................................................................................128
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CHAPTER 10 s
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Standard Error on a Difference ..................................................................................................................129 e
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The standard error of a difference without plausible values .........................................................132
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The standard error of a difference with plausible values ................................................................137 e
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Multiple comparisons .............................................................................................................................140 b
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Conclusions ...............................................................................................................................................141
CHAPTER 11
OECD Average and OECD Total ................................................................................................................143
Introduction ..............................................................................................................................................144
Recoding of the database for the estimation of the OECD total and OECD average .............144
Duplication of the data for avoiding three runs of the procedure ................................................147
Comparisons between OECD average or OECD total estimates and a country estimate .........147
Conclusions ...............................................................................................................................................150
CHAPTER 12
Trends .................................................................................................................................................................153
Introduction ..............................................................................................................................................154
The computation of the standard error for trend indicators on variables other
than performance .....................................................................................................................................155
The computation of the standard error for trend indicators on performance variables .........158
Conclusions ...............................................................................................................................................164
CHAPTER 13
Multilevel Analyses .......................................................................................................................................165
Introduction ..............................................................................................................................................166
Simple linear regression .........................................................................................................................166
Simple linear versus multilevel regression analyses .........................................................................170
Fixed effect versus random effect ........................................................................................................173
Some examples with SPSS® ...................................................................................................................174
Limitations of the multilevel model in the PISA context ...............................................................190
Conclusions ...............................................................................................................................................192
CHAPTER 14
Other Statistical Issues ..................................................................................................................................193
Introduction ..............................................................................................................................................194
Analyses by quarters ...............................................................................................................................194
The concepts of relative risk and attributable risk ...........................................................................198
Instability of the relative and attributable risks .................................................................................200
Computation of the relative risk and attributable risk ....................................................................201
Conclusions ...............................................................................................................................................201
CHAPTER 15
SPSS® Macros ...................................................................................................................................................203
Introduction ..............................................................................................................................................204
Structure of the SPSS® macros .............................................................................................................204
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ts Appendix 1: PISA 2003 International Database ....................................................................................237
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te Appendix 2: Student Questionnaire ........................................................................................................251
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of Appendix 4: Information Communication Technology (ICT) Questionnaire ................................267
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Appendix 6: Student Questionnaire Data File Codebook ..................................................................285
Appendix 7: School Questionnaire Data File Codebook ....................................................................331
Appendix 8: Student Cognitive Test Data File Codebook ...................................................................345
Appendix 9: Student and School Questionnaire Indices .....................................................................375
Appendix 10: Scores Allocated to the Items ............................................................................................401
References .............................................................................................................................................................407
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Preparation of data fi les
All data fi les (in text format) and the SPSS® control fi les are available on the PISA Web site
(www.pisa.oecd.org).
SPSS® users
The PISA 2003 student data fi le and the PISA 2003 school data fi le need to be saved under
“c:\PISA\Data2003” before running the syntax in the following chapters.
Student data fi le: c:\PISA\Data2003\INT_stui_2003.sav
School data fi le: c:\PISA\Data2003\INT_schi_2003.sav
The SPSS® macros presented in Chapter 15 need to be saved under “c:\PISA\macros”.
SPSS® syntax and macros
All syntaxes and macros used in this manual can be copied from the PISA Web site (www.pisa.
oecd.org). Each chapter of the manual contains a complete set of syntaxes, which must be done
sequentially, for all of them to run correctly, within the chapter.
Rounding of fi gures
In the tables and formulas, fi gures were rounded to a convenient number of decimal places,
although calculations were always made with the full number of decimal places.
Country abbreviations used in this manual
AUS Australia FRA France KOR Korea PRT Portugal
AUT Austria GBR United Kingdom LIE Liechtenstein RUS Russian Federation
BEL Belgium GRC Greece LUX Luxembourg SVK Slovakia
BRA Brazil HKG Hong Kong-China LVA Latvia SWE Sweden
CAN Canada HUN Hungary MAC Macao-China THA Thailand
CHE Switzerland IDN Indonesia MEX Mexico TUN Tunisia
CZE Czech Republic IRL Ireland NLD Netherlands TUR Turkey
DEU Germany ISL Iceland NOR Norway URY Uruguay
DNK Denmark ITA Italy NZL New Zealand USA United States
ESP Spain JPN Japan POL Poland YUG Serbia
FIN Finland
Socio-economic status
The highest occupational status of parents (HISEI) is referred to as the socio-economic status
of the students throughout this manual. It should be noted that occupational status is only one
aspect of socio-economic status, which can also include education and wealth. The PISA 2003
database also includes a broader socio-economic measure called the index of Economic, Social
and Cultural Status (ESCS), which is derived from the highest occupational status of parents,
the highest educational level and an estimate related to household possessions.
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