Schools Valueadded Information System Technical Manual


 Moris Edmund Malone
 3 years ago
 Views:
Transcription
1 Schools Valueadded Information System Technical Manual Quality Assurance & Schoolbased Support Division Education Bureau 2015
2 Contents Unit 1 Overview... 1 Unit 2 The Concept of VA... 2 Unit 3 Control Variables... 4 Unit 4 Interpreting VA Information... 5 Unit 5 Reporting VA Information Appendix: Calculating VA Scores... 18
3 Unit 1 Overview The Education Bureau (EDB) is committed to supporting schools to make use of data and evidence to conduct selfevaluation. The EDB also provides schools with different evaluation tools and data to meet their needs. Valueadded (VA) information is one of the selfevaluation tools provided by the EDB through the online platform, namely the Schools Valueadded Information System (SVAIS), since 2003 and it has been widely used by schools. The SVAIS provides schools with quantitative and objective data on students academic performance. In conjunction with other schoolbased data, VA information can facilitate schools to understand more clearly the academic performance of students. With the changes brought about by the implementation of the New Academic Structure (NAS), such as the phasingout of the Hong Kong Certificate of Education Examination and the Hong Kong Advanced Level Examination and the introduction of the Hong Kong Diploma of Secondary Education (HKDSE) Examination, the EDB has reviewed the VA model and the SVAIS. In the course of the revision, the EDB has sought advice from academic experts and maintained its communication with schools so as to enhance the transparency of the system and to have a better understanding of the schools needs. Under the NAS, the SVAIS has begun to provide VA information for the 2012 and 2013 S1/S6 cohort of students based on their HKDSE Examination results since Starting from 2015, two new control variables, namely nonchinese speaking (NCS) and special educational needs (SEN) have been added to enhance the reliability and validity of the VA model. VA information is rarely definitive and never explains why a school is performing better or worse. This can only be made clearer by conducting an indepth analysis of individual schools. Schools should make reference to other related evaluation data (for instance, students performance in the PreS1 Hong Kong Attainment Test, internal assessment results and among others) when examining the effectiveness of learning and teaching. In addition, VA information reflects only students academic performance. Schools should make use of other sources of information such as the Assessment Program for Affective and Social Outcomes (APASO), schoolbased questionnaires and teachers observation to understand the whole person development of students, in order to formulate and implement followup action plans for continuous improvement. 1
4 Unit 2 The Concept of VA In evaluating subject learning, public examination results are important indicators of absolute standards and can be helpful in identifying instances of unacceptably low standards. Nevertheless, they may not be good indicators of the extent to which schools have contributed to the levels of attainment of their students. When comparisons are made of the average results of students attending different schools, what is revealed often indicates more about the nature of the students attending those schools than the effectiveness of the schools. VA information, on the other hand, takes into account factors such as student ability and school characteristics and can better reflect the effectiveness of schools in improving the academic performance of their students. Therefore, schools are advised to refer to both the public examination results and the VA information in selfevaluation when evaluating the effectiveness of their learning and teaching strategies. The multilevel regression model used to compile VA scores can be described by the following formula: Student actual attainment in the HKDSE Examination (outcome variable) = Student predicted attainment (after adjusting for control variables) in the HKDSE Examination + school residual + student residual The formula shows that there is a difference between student actual attainment in the HKDSE Examination (outcome variable) and the statistically predicted attainment after taking into account student academic ability in S1 and other background characteristics (control variables). This difference the unexplained part or what is often called the residual can be further partitioned into two components, namely the schools attended by the students (school residual), and unexplained individual differences (student residual). It is through the estimation of the school residual that VA estimates can be obtained. For technical details of the multilevel regression model, please refer to the Appendix. 2
5 Other control variables e.g. School average AAI Gender All boys/ All girls school The logic behind this operational definition is as follows: given that examination scores have been adjusted statistically for the most important factors known to influence student performance, then if significant differences in examination scores among schools remain, it is reasonable to infer that these differences in scores reflect differences in the effectiveness of schools. 3
6 Unit 3 Control Variables An important issue in compiling VA estimates is to adjusting student predicted attainment by control variables. Since VA estimates are residuals, or what is left over after taking into account the effect of all the control variables, it is important to include control variables that are known to significantly affect student performance as far as practicable. The best predictor of student actual attainment is almost always student prior attainment. When a reliable and valid student prior attainment is available, this will explain a relatively large proportion of variance, while other control variables will only explain a small amount of variance. These other control variables may nonetheless still have a statistically significant but small influence on student actual attainment. The general advice in regression analysis is to strike a balance between maximising the percentage of variance explained while minimising the number of control variables. In the VA model, the student prior attainment and other control variables currently used are described below: Control variable Description of variable The AAI is the normalised scores of Secondary School Places Academic Ability Allocation (SSPA). It is a measure of the academic ability of Index (AAI) students on entry to Secondary One. It serves as the student prior attainment in the VA model. It is the average AAI score of all students within a school taking a School Average AAI given subject. It adjusts the peer AAI effect on student performance. Gender All Girls School All Boys School NonChinese Speaking (NCS) Special Educational Needs (SEN) It adjusts the different rates of progress made by boys and girls. It adjusts the effect of being in an all girls school. It adjusts the effect of being in an all boys school. It adjusts the effect of being a nonchinese speaking student. It adjusts the effect of being a student with special educational needs. 4
7 Unit 4 Interpreting VA Information Valueadded Scores Valueadded scores (VA scores) are normalised (so that they follow a normal distribution) and placed on a scale that ranges from 10 (the lowest score) to +10 (the highest scores), with an overall mean of zero (centred on zero). In other words, a score of zero does not imply that students in the school have made no progress, but rather that the progress of students in the school is average within the territory. VA scores are empirical Bayes estimates, which means that they are weighted to reflect the reliability of each school s score. In other words, the VA scores of a school with a small number of students analysed in a particular subject are biased towards the overall average. This means that for small schools that actually added high value, their true performance will not be reflected fully in their VA scores, which will instead be shrunk towards the average (zero). The same applies in the opposite direction to small schools that actually added low value. Their inferior performance will not be reflected fully in their VA scores. The VA scores compiled in such a way, on the one hand, is an advantage since they are conservative estimates. On the other hand, this shrinkage complicates the ranking of VA scores (i.e. Stanine), since highscoring small schools and lowscoring small schools may end up close together in rank. In this regard, schools are advised not to rely solely on VA scores or Stanine to make judgment on a school s VA performance, but also the confidence interval which is explained in the next section. Confidence Intervals All VA estimates are associated with a degree of uncertainty. In the SVAIS, this uncertainty is quantified and a 95% confidence interval is constructed around each VA score. A confidence interval is a range of values which contains the estimated parameter (i.e. the true VA score of a school) with a certain probability. A 95% confidence interval on a VA estimate can then be interpreted as an interval which contains the true VA score of a school with a 95% probability. A shorter 95% confidence interval implies that the corresponding VA estimates are more accurate. The 95% confidence interval of a VA estimate of a subject will usually be shorter if the percentage of variance explained by the control variables for that subject is 5
8 large, which is in turn affected by the predictive power of the control variables on student actual attainment in the HKDSE Examination, the number of students analysed for that subject and the variations among individual students, ceteris paribus. For example, as shown in the multisubject graph below, it can be observed that the 95% confidence interval of Liberal Studies is obviously shorter than that of Chinese Literature. One of the reasons is that the number of students available for analysis of Liberal Studies is much larger than that of Chinese Literature. On the other hand, given a similar number of students analysed in Chinese Language and English Language, the 95% confidence interval of English Language is slightly shorter than that of Chinese Language since a larger percentage of variance of English Language is explained by the control variables in the model than that of Chinese Language. 6
9 All regression analyses are carried out for each subject and each year separately. Hence, the confidence intervals of VA scores will differ across subjects and across years. This needs to be borne in mind when comparing VA performance across subjects and across years. Valueadded Performance There are three categories of valueadded (VA) performance: Below average: The VA score is significantly lower than the territory average. This happens when the whole length of the confidence interval is below the territory average (i.e. zero). If this happens, the text below average will be displayed under Valueadded performance in the VA reports. (See Subject A below) On a par with average: The VA score is not significantly different from the territory average. This happens when the confidence interval straddles the territory average (i.e. zero). If this happens, the text on a par with average will be displayed under Valueadded performance in the VA reports. (See Subject B below) Above average: The VA score is significantly higher than the territory average. This happens when the whole length of the confidence interval is above the territory average (i.e. zero). If this happens, the text Above average will be displayed under Valueadded performance in the VA reports. (See Subject C below) VA score Upper Confidence Bound Estimated VA Score Lower Confidence Bound 0 Subject C: VA is significantly above average Territory Average VA=0 = 0 Subject B: VA is not significantly different from average Subject A: VA is significantly below average 7
10 Stanines The VA scores of all schools in each subject are ranked in ascending order and subsequently transformed into nine groups (stanines). Distribution of schools by the nine groups (stanines) could be diagrammatically represented by the following figure. The stanine is a normalised standard score ranging from 1 to 9, with a mean of 5 and a standard deviation of 2. The stanine for each school provides a crude indication of the VA performance of the user s school relative to other schools. The stanine can be found in the All School Reports, All Years Report and the MultiSubject Table. Schools are advised not to rely solely on stanines to review their VA performance since stanines do not take into consideration the confidence interval, i.e. the accuracy of the VA estimates. Percentage of Students Analysed The percentage of students analysed is the ratio of the number of students included in VA analysis to the total number of students taking the examination of a particular subject in a school. For a student to be included in VA analysis, there should be HKDSE Examination results as well as his/her own Academic Ability Index (AAI) six years before the HKDSE Examination which can be matched with a personal identifier. Hence, students under the following circumstances cannot be included in VA analysis: 8
11 1. Students who came from regions outside Hong Kong (including the Mainland and foreign countries) and joined local secondary schools directly; 2. Students repeated/suspended/skipped any levels in secondary school, leading to unmatched SSPA scores 6 years ago; or 3. Students who did not have SSPA scores 6 years ago as their primary schools did not participate in the SSPA scheme. The VA information should be interpreted with caution if the percentage of students analysed is low, since a large proportion of the school s students taking that subject have not been included in VA analysis. In that case, the school s VA information may not be representative enough to reflect the performance of all S6 students of the school. Nonetheless, the VA information is still useful for school development in the sense that it could reflect the performance of those students who are included in the analysis. In addition, since VA information based on a very small number of students is unreliable, if the number of students analysed in a particular subject of a school is fewer than ten, the VA information of that subject will not be released. 9
12 Unit 5 Reporting VA Information VA Information of Individual Subjects The standard marks of individual subjects compiled by the Hong Kong Examinations and Assessment Authority (HKEAA) are taken as the scores of student actual attainment and they are normalised before being included in VA analysis. In principle, VA analyses are conducted for all Category A subjects, but it does not follow that there is VA information for all HKDSE subjects. If the VA estimates of a particular subject are not accurate enough, such as English Literature, Visual Arts and Music, there will not be VA information for that subject. On the other hand, since there are no standard marks for Category B (Applied Learning) and Category C (Other Language) subjects, no VA information is provided for these subjects either. VA Information of Subject Groups The VA information of Core 4 and Best 5 subject groups may reflect the holistic VA performance of a school. Since the standard marks compiled by the HKEAA are taken as the scores of student actual attainment in the VA model, the scores of different Category A subjects are directly comparable. The Core 4 score is defined as the sum of the standard marks of Chinese Language, English Language, Mathematics (Compulsory Part) and Liberal Studies. The Best 5 score is defined as the sum of the five highest standard marks out of all the HKDSE subjects taken by a student (including Category A and Category B subjects). These five subjects may include or exclude the core subjects. When a student sits both the Mathematics (Compulsory Part) and the Mathematics (Extended Part) at the same time, the better of the two will be selected. Attained with Distinction and Attained in Category B subjects are deemed comparable to level 3 and level 2 in Category A subjects respectively. As there are no standard marks of Category C subjects, these subjects will not be included in the Best 5 calculation. In addition, if a student takes fewer than five HKDSE subjects, that student will not be included in the Best 5 VA analysis. Same as the standard marks of individual subjects, both Core 4 and Best 5 scores are normalised before being included in VA analysis. 10
13 School VA information is provided for individual subjects and for specific subject groups. So far there is no single VA score for summarising the VA performance of the whole school. SVAIS Reports In the SVAIS, each school is provided with a school account that allows users to access their own VA information as well as summary statistics for the territory. Five types of reports are provided through the SVAIS. 1. All Schools Report The All Schools Report shows the distribution of VA scores of all schools, schools with a similar intake of students and schools within the same district of a particular subject in a specific year as shown below. 11
14 The boxandwhisker plot of all schools displays the distribution of VA scores of all schools in the territory. As shown in the diagram below, the top whisker represents the 95th percentile, the top of the box represents the 75th percentile, the bold line in the middle of the box the 50th percentile (i.e. the median), the bottom of the box the 25th percentile, and the bottom whisker the 5th percentile. The red line indicates the VA score of the user s school. 95 th Percentile 75 th Percentile Your school 50 th Percentile 25 th Percentile 5 th Percentile The table below displays the distribution of VA scores of all schools in the territory and the position of the user s school. Valueadded Score Percentiles 5.50 or above Top 5% of schools in the territory (95th percentile or above) 2.25 to 5.50 Next 20% of all schools in the territory (75th percentile to 95th percentile) 0.84 to 2.25 Next 15% of all schools in the territory (60th percentile to 75th percentile) to 0.84 Middle 20% of all schools in the territory (40th percentile to 60th percentile) to Next 15% of all schools in the territory (25th percentile to 40th percentile) to Next 20% of all schools in the territory (5th percentile to 25th percentile) and below Bottom 5% of all schools in the territory (Below 5th percentile) The table below displays the detailed VA information of the user s school, including the VA score, the 95% confidence interval, the VA performance, the stanine, and the percentage of students analysed. 12
15 Valueadded Score 95% Confidence Interval Lower Bound Upper Bound Valueadded Performance Stanine (19) % of Students Analysed On a par with average (0) The boxandwhisker plot of similar intake schools displays the distribution of VA scores of the intake group which the user school belongs to for a particular subject. Similar intake schools are categorised by the School Average AAI. All School Average AAI of the same subject is ranked in ascending order and subsequently transformed into 9 groups with a mean of 5 and a standard deviation of 2. To avoid too few schools appearing in the highest and lowest groups, the highest two groups (Groups 8 and 9) are combined into one similar intake group. Likewise, the lowest two groups (Groups 1 and 2) are combined into one similar intake group. Altogether there are seven intake groups as shown in the diagram below. Combined into one intake group Combined into one intake group The boxandwhisker plot of schools from same district displays the distribution of VA scores of the District Council district which the user school belongs to for a particular subject. If there are fewer than three schools in a particular district for a particular subject, this plot will not be reported in the SVAIS to avoid the identification of individual schools. 13
16 2. Differential Effectiveness Report The SVAIS displays the differential effectiveness for students of different abilities in a statement. In the SVAIS, differential effectiveness refers to the extent to which a school is more or less effective for more or less able students. The following figures illustrate different cases of differential effectiveness in detail. The blue regression line in the graph summarises the relationship between the AAI (student prior attainment) and the HKDSE Examination scores in a hypothetical school, School A. The red regression line summarises the relationship between the AAI and the HKDSE Examination scores averaged across all schools. In the case of Panels 1 3, the line for School A is significantly steeper than the line for All Schools. This means that School A is relatively more effective for more able students and less effective for less able students. This may happen when the overall VA performance of the whole school is above average (Panel 1), on a par with average (Panel 2) or below average (Panel 3). In the case of Panels 4 6, the line for School A is significantly flatter than the line for All Schools. This means that School A is relatively more effective for less able students and less effective for more able students. This may happen when the overall VA performance of the whole school is above average (Panel 4), on a par with average (Panel 5) or below average (Panel 6). 14
17 In the case of Panels 7 9, the slope of the line for School A does not differ significantly from the slope of the line for All Schools. This means that School A is equally effective for students of different abilities. This may happen when the overall VA performance of the whole school is above average (Panel 7), on a par with average (Panel 8) or below average (Panel 9). 3. All Years Report Users may refer to this report for the VA trend of a particular subject. It consists of a chart and a table. The chart below provides a graphical display of VA scores and confidence intervals for all years for which VA information is available for that subject. 15
18 The table below displays the detailed VA information of the user s school of the same subject over the years, including the VA score, the 95% confidence interval, the VA performance and the stanine. Years Valueadded Scores 95% Confidence Interval Valueadded Lower Bound Upper Bound Performance Stanine (19) Above average (+) On a par with average (0) On a par with average (0) 5 This report is particularly useful for identifying consistently high or low performance over the years, but caution should be exercised to avoid reading too much into seemingly random fluctuations from year to year. 4. & 5. MultiSubject Graph and Table The MultiSubject Graph and Table display the VA information of all subjects in a single year. The MultiSubject Graph below provides a graphical display of VA scores and confidence intervals for all subjects with available VA information. 16
19 The MultiSubject Table below displays the detailed VA information of the user s school in all subjects, including the VA score, the 95% confidence interval, the VA performance, the stanine and the percentage of students analysed. Subject Name Valueadded Score 95% Confidence Interval Lower Bound Upper Bound Chinese Language Valueadded Performance On a par with average (0) Stanine (19) % of Students Analysed English Language Below average () Mathematics: Compulsory Part Above average (+) The table below displays the VA information of the user s school in each Key Learning Area (KLA). KLA Chinese Language Education English Language Education Mathematics Education No. of Subjects Offered No. of Subjects in Top 10% VA within KLA No. of Subjects in Top 50% VA within KLA It should be noted that in the table above, the number of subjects offered by the school within each KLA excludes any subjects with fewer than ten students available for VA analysis. In the SVAIS, three combinations under Combined Science (i.e. Biology/Chemistry, Biology/Physics and Chemistry/Physics) are counted as three individual subjects. Starting from 2015 HKDSE Examination, Accounting and Business Management are also counted as two individual subjects. 17
20 Appendix: Calculating VA Scores Multilevel Models The VA score refers to an estimate obtained using regression methods to make statistical adjustments to raw results to control for initial differences in the intake characteristics of students. Under the NAS, VA scores are calculated based on the HKDSE Examination results of students, their prior attainment (AAI) and other characteristics using multilevel models. To understand multilevel models, it is useful to begin with a simple (singlelevel) regression model. The formula for a simple regression model is given by equation (1) below: y i = β 0 + β 1 x i + e i (1) where subscript i takes values from 1 to n, where each value of i represents an individual student and n is the total number of students in all schools; y i is the actual examination score (say the normalised HKDSE Examination score) for student i; β 0 is the yintercept, or the examination score when variable x i equals zero; β 1 is the slope of the regression line, or the coefficient of variable x i ; x i is the control variable (say student prior attainment); and e i is the error term. The expected score of student i, E(y i ) is given by equation (2) below: E(y i ) = β 0 + β 1 x i (2) If we subtract equation (2) from equation (1), y i E(y i ) = β 0 + β 1 x i + e i ( β 0 + β 1 x i ) y i E(y i ) = e i It is observed that the difference between student i s actual examination score and the expected score is the error term, e i. It is referred to as a residual because it is the part 18
21 of the score that is not predicted by the fixed part of the model represented by equation (2). It is typically assumed that the residuals follow a normal distribution with a mean of zero and common variance, i.e. e i ~N(0, σ e 2 ). Proceeding now to a simple multilevel model, we can rewrite equation (1) as y ij = β 0 + β 1 x ij + (u j + e ij ) (3) where a new subscript j takes values from 1 to m, where each value of j represents an individual school and m is the total number of schools; y ij is the actual examination score (say the normalised HKDSE Examination score) for student i in school j; x ij is the control variable (say student prior attainment) of student i in school j; and u j is the difference between school j s actual intercept and the overall mean value β 0. The critical feature of equation (3) is the u j term which is known as a level 2 residual. It is the existence of the two residuals  the level 2 school residual, u j and the level 1 student residual, e ij  which identifies equation (3) as a multilevel model. Furthermore, it is through the estimation of level 2 residuals u j that school VA estimates can be obtained. The VA Model The VA model adopted under the NAS is very similar to equation (3). The only difference is that it includes more control variables on top of student prior attainment. A full list of control variables currently used is given in Unit 3. The VA model is represented in equation (4) below: y ij = β 0 + β 1 x 1ij + β 2 x 2ij + + β n x nij + (u j + e ij ) (4) where y ij is the normalised HKDSE Examination score for student i in school j; β 0 is a constant term, indicating the overall mean examination score when all control variables (x 1,...,x n ) included in the model equals zero; β 1 x 1ij is the coefficient and the value of student prior attainment (AAI) for student i in school j; 19
22 β 2 x 2ij,, β n x nij are the coefficients and the values of other control variables for student i in school j; u j is the level 2 residual term indicating school j s effect on student performance; and e ij is the level 1 residual term for student i in school j, indicating that part of the score that could not be explained by factors already included in the model. The model assumes that the outcome variable (y ij ) and the residuals (u j, e ij ) are normally distributed. In addition, it is assumed that level 1 and level 2 residuals are not correlated. The distributional assumptions of the model may be summarised as: u j ~N(0, σ u 2 ); e ij ~N(0, σ e 2 ) In the model represented by Equation (4), a school s VA score is obtained by estimating the school residual term u j, which is then normalised and placed on a scale that ranges from 10 to +10. Contact Us For enquiries about school VA information, please contact the Indicators Section of the Quality Assurance & Schoolbased Support Division at the EDB. Address: Room 1214, 12/F, Wu Chung House, 213 Queen s Road East, Wan Chai, Hong Kong Tel: (852) or (852) Fax: (852)
Tools and Data. for School Selfevaluation. For Secondary, Primary and Special Schools
Tools and Data for School Selfevaluation For Secondary, Primary and Special Schools Quality Assurance & Schoolbased Support Division Education Bureau 2015 Foreword In line with the implementation of
More informatione = random error, assumed to be normally distributed with mean 0 and standard deviation σ
1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More information1996 DfEE study of Value Added for 1618 year olds in England
1996 DfEE study of Value Added for 1618 year olds in England by Cathal O Donoghue (DfEE), Sally Thomas (IOE), Harvey Goldstein (IOE), and Trevor Knight (DfEE) 1 1. Introduction 1.1 This paper examines
More informationCurriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
More informationAn analysis of the 2003 HEFCE national student survey pilot data.
An analysis of the 2003 HEFCE national student survey pilot data. by Harvey Goldstein Institute of Education, University of London h.goldstein@ioe.ac.uk Abstract The summary report produced from the first
More informationThe Basic TwoLevel Regression Model
2 The Basic TwoLevel Regression Model The multilevel regression model has become known in the research literature under a variety of names, such as random coefficient model (de Leeuw & Kreft, 1986; Longford,
More informationNumerical Summarization of Data OPRE 6301
Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting
More informationReport on the Scaling of the 2014 NSW Higher School Certificate. NSW ViceChancellors Committee Technical Committee on Scaling
Report on the Scaling of the 2014 NSW Higher School Certificate NSW ViceChancellors Committee Technical Committee on Scaling Contents Preface Acknowledgements Definitions iii iv v 1 The Higher School
More informationReport on the Scaling of the 2012 NSW Higher School Certificate
Report on the Scaling of the 2012 NSW Higher School Certificate NSW ViceChancellors Committee Technical Committee on Scaling Universities Admissions Centre (NSW & ACT) Pty Ltd 2013 ACN 070 055 935 ABN
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGrawHill/Irwin, 2008, ISBN: 9780073319889. Required Computing
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationData Analysis, Statistics, and Probability
Chapter 6 Data Analysis, Statistics, and Probability Content Strand Description Questions in this content strand assessed students skills in collecting, organizing, reading, representing, and interpreting
More informationLocal outlier detection in data forensics: data mining approach to flag unusual schools
Local outlier detection in data forensics: data mining approach to flag unusual schools Mayuko Simon Data Recognition Corporation Paper presented at the 2012 Conference on Statistical Detection of Potential
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3 Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More information1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2
PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand
More informationThe test uses age norms (national) and grade norms (national) to calculate scores and compare students of the same age or grade.
Reading the CogAT Report for Parents The CogAT Test measures the level and pattern of cognitive development of a student compared to age mates and grade mates. These general reasoning abilities, which
More information11. Analysis of Casecontrol Studies Logistic Regression
Research methods II 113 11. Analysis of Casecontrol Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationModule 3: Correlation and Covariance
Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis
More informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGrawHill/Irwin, 2010, ISBN: 9780077384470 [This
More informationA guide to level 3 value added in 2015 school and college performance tables
A guide to level 3 value added in 2015 school and college performance tables January 2015 Contents Summary interpreting level 3 value added 3 What is level 3 value added? 4 Which students are included
More informationSouth Carolina College and CareerReady (SCCCR) Probability and Statistics
South Carolina College and CareerReady (SCCCR) Probability and Statistics South Carolina College and CareerReady Mathematical Process Standards The South Carolina College and CareerReady (SCCCR)
More informationAN ILLUSTRATION OF COMPARATIVE QUANTITATIVE RESULTS USING ALTERNATIVE ANALYTICAL TECHNIQUES
CHAPTER 8. AN ILLUSTRATION OF COMPARATIVE QUANTITATIVE RESULTS USING ALTERNATIVE ANALYTICAL TECHNIQUES Based on TCRP B11 Field Test Results CTA CHICAGO, ILLINOIS RED LINE SERVICE: 8A. CTA Red Line  Computation
More informationRegression Analysis: Basic Concepts
The simple linear model Regression Analysis: Basic Concepts Allin Cottrell Represents the dependent variable, y i, as a linear function of one independent variable, x i, subject to a random disturbance
More informationCollege Readiness LINKING STUDY
College Readiness LINKING STUDY A Study of the Alignment of the RIT Scales of NWEA s MAP Assessments with the College Readiness Benchmarks of EXPLORE, PLAN, and ACT December 2011 (updated January 17, 2012)
More informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationMINITAB ASSISTANT WHITE PAPER
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. OneWay
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationWhat Does the Correlation Coefficient Really Tell Us About the Individual?
What Does the Correlation Coefficient Really Tell Us About the Individual? R. C. Gardner and R. W. J. Neufeld Department of Psychology University of Western Ontario ABSTRACT The Pearson product moment
More informationMATH THAT MAKES ENTS
The Bureau of Labor statistics share this data to describe the difference in earnings and unemployment rates by the amount of education attained. (1) Take a look at this table, describe what you notice
More informationLecture 4 Linear random coefficients models
Lecture 4 Linear random coefficients models Rats example 30 young rats, weights measured weekly for five weeks Dependent variable (Y ij ) is weight for rat i at week j Data: Multilevel: weights (observations)
More informationModule 2: Introduction to Quantitative Data Analysis
Module 2: Introduction to Quantitative Data Analysis Contents Antony Fielding 1 University of Birmingham & Centre for Multilevel Modelling Rebecca Pillinger Centre for Multilevel Modelling Introduction...
More informationCopyright 20102012 PEOPLECERT Int. Ltd and IASSC
PEOPLECERT  Personnel Certification Body 3 Korai st., 105 64 Athens, Greece, Tel.: +30 210 372 9100, Fax: +30 210 372 9101, email: info@peoplecert.org, www.peoplecert.org Copyright 20102012 PEOPLECERT
More informationCHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
More informationSection A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA  Part I
Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA  Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More information3: Summary Statistics
3: Summary Statistics Notation Let s start by introducing some notation. Consider the following small data set: 4 5 30 50 8 7 4 5 The symbol n represents the sample size (n = 0). The capital letter X denotes
More informationStatistical Rules of Thumb
Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN
More informationIn this chapter, you will learn to use moving averages to estimate and analyze estimates of contract cost and price.
6.0  Chapter Introduction In this chapter, you will learn to use moving averages to estimate and analyze estimates of contract cost and price. Single Moving Average. If you cannot identify or you cannot
More informationMAP Reports. Teacher Report (by Goal Descriptors) Displays teachers class data for current testing term sorted by RIT score.
Goal Performance: These columns summarize the students performance in the goal strands tested in this subject. Data will display in these columns only if a student took a Survey w/ Goals test. Goal performance
More informationReport on the Scaling of the 2013 NSW Higher School Certificate. NSW ViceChancellors Committee Technical Committee on Scaling
Report on the Scaling of the 2013 NSW Higher School Certificate NSW ViceChancellors Committee Technical Committee on Scaling Universities Admissions Centre (NSW & ACT) Pty Ltd 2014 ACN 070 055 935 ABN
More informationStability of School Building Accountability Scores and Gains. CSE Technical Report 561. Robert L. Linn CRESST/University of Colorado at Boulder
Stability of School Building Accountability Scores and Gains CSE Technical Report 561 Robert L. Linn CRESST/University of Colorado at Boulder Carolyn Haug University of Colorado at Boulder April 2002 Center
More informationSection Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini
NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building
More informationAccurately and Efficiently Measuring Individual Account Credit Risk On Existing Portfolios
Accurately and Efficiently Measuring Individual Account Credit Risk On Existing Portfolios By: Michael Banasiak & By: Daniel Tantum, Ph.D. What Are Statistical Based Behavior Scoring Models And How Are
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationThe aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree
PS 511: Advanced Statistics for Psychological and Behavioral Research 1 Both examine linear (straight line) relationships Correlation works with a pair of scores One score on each of two variables ( and
More informationTIME SERIES ANALYSIS. A time series is essentially composed of the following four components:
TIME SERIES ANALYSIS A time series is a sequence of data indexed by time, often comprising uniformly spaced observations. It is formed by collecting data over a long range of time at a regular time interval
More informationDr. Peter Tröger Hasso Plattner Institute, University of Potsdam. Software Profiling Seminar, Statistics 101
Dr. Peter Tröger Hasso Plattner Institute, University of Potsdam Software Profiling Seminar, 2013 Statistics 101 Descriptive Statistics Population Object Object Object Sample numerical description Object
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationThe Big 50 Revision Guidelines for S1
The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand
More informationData Analysis: Describing Data  Descriptive Statistics
WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most
More informationSimple Random Sampling
Source: Frerichs, R.R. Rapid Surveys (unpublished), 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling, but few use this method for
More informationA Primer on Forecasting Business Performance
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
More informationPrimary school accountability in 2016. A technical guide for primary maintained schools, academies and free schools
Primary school accountability in 2016 A technical guide for primary maintained schools, academies and free schools January 2016 Contents Summary 3 About this guidance 3 Expiry or review date 4 Who is this
More informationStatistics courses often teach the twosample ttest, linear regression, and analysis of variance
2 Making Connections: The TwoSample ttest, Regression, and ANOVA In theory, there s no difference between theory and practice. In practice, there is. Yogi Berra 1 Statistics courses often teach the twosample
More informationAP Statistics 2001 Solutions and Scoring Guidelines
AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use
More information430 Statistics and Financial Mathematics for Business
Prescription: 430 Statistics and Financial Mathematics for Business Elective prescription Level 4 Credit 20 Version 2 Aim Students will be able to summarise, analyse, interpret and present data, make predictions
More informationGCSE Statistics Revision notes
GCSE Statistics Revision notes Collecting data Sample This is when data is collected from part of the population. There are different methods for sampling Random sampling, Stratified sampling, Systematic
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationLAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE
LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre
More informationA Correlation of. to the. South Carolina Data Analysis and Probability Standards
A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationCHINHOYI UNIVERSITY OF TECHNOLOGY
CHINHOYI UNIVERSITY OF TECHNOLOGY SCHOOL OF NATURAL SCIENCES AND MATHEMATICS DEPARTMENT OF MATHEMATICS MEASURES OF CENTRAL TENDENCY AND DISPERSION INTRODUCTION From the previous unit, the Graphical displays
More informationHow To Run Statistical Tests in Excel
How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting
More informationPrediction and Confidence Intervals in Regression
Fall Semester, 2001 Statistics 621 Lecture 3 Robert Stine 1 Prediction and Confidence Intervals in Regression Preliminaries Teaching assistants See them in Room 3009 SHDH. Hours are detailed in the syllabus.
More informationEducation Bureau Circular No. 8/2014. Enhanced Chinese Learning and Teaching for NonChinese Speaking Students
Ref: EDB(EC)5/2041/07 Government of the HKSAR Education Bureau 5 June 2014 Summary Education Bureau Circular No. 8/2014 Enhanced Chinese Learning and Teaching for NonChinese Speaking Students (Note:This
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationHandling attrition and nonresponse in longitudinal data
Longitudinal and Life Course Studies 2009 Volume 1 Issue 1 Pp 6372 Handling attrition and nonresponse in longitudinal data Harvey Goldstein University of Bristol Correspondence. Professor H. Goldstein
More informationINTRODUCTORY STATISTICS
INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
More informationCredit Card Market Study Interim Report: Annex 4 Switching Analysis
MS14/6.2: Annex 4 Market Study Interim Report: Annex 4 November 2015 This annex describes data analysis we carried out to improve our understanding of switching and shopping around behaviour in the UK
More information4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"
Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses
More informationGlossary of Terms Ability Accommodation Adjusted validity/reliability coefficient Alternate forms Analysis of work Assessment Battery Bias
Glossary of Terms Ability A defined domain of cognitive, perceptual, psychomotor, or physical functioning. Accommodation A change in the content, format, and/or administration of a selection procedure
More informationDirections for using SPSS
Directions for using SPSS Table of Contents Connecting and Working with Files 1. Accessing SPSS... 2 2. Transferring Files to N:\drive or your computer... 3 3. Importing Data from Another File Format...
More informationGuided Reading 9 th Edition. informed consent, protection from harm, deception, confidentiality, and anonymity.
Guided Reading Educational Research: Competencies for Analysis and Applications 9th Edition EDFS 635: Educational Research Chapter 1: Introduction to Educational Research 1. List and briefly describe the
More informationChapter 15 Multiple Choice Questions (The answers are provided after the last question.)
Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately
More informationInformation and Employee Evaluation: Evidence from a Randomized Intervention in Public Schools. Jonah E. Rockoff 1 Columbia Business School
Preliminary Draft, Please do not cite or circulate without authors permission Information and Employee Evaluation: Evidence from a Randomized Intervention in Public Schools Jonah E. Rockoff 1 Columbia
More informationInternational Statistical Institute, 56th Session, 2007: Phil Everson
Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA Email: peverso1@swarthmore.edu 1. Introduction
More informationHedonism example. Our questions in the last session. Our questions in this session
Random Slope Models Hedonism example Our questions in the last session Do differences between countries in hedonism remain after controlling for individual age? How much of the variation in hedonism is
More informationChapter 5: Analysis of The National Education Longitudinal Study (NELS:88)
Chapter 5: Analysis of The National Education Longitudinal Study (NELS:88) Introduction The National Educational Longitudinal Survey (NELS:88) followed students from 8 th grade in 1988 to 10 th grade in
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationChapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data
Chapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data Chapter Focus Questions What are the benefits of graphic display and visual analysis of behavioral data? What are the fundamental
More information2. A comparison of the current and the new academic structure is shown below. Undergraduate Degree Secondary 7
Purpose 1. The Chief Executive in his 2004 Policy Address set out the direction to develop a new senior secondary and university system that will effectively prepare our next generation to cope with the
More informationWHAT DO THEY KNOW? A summary of India s National Achievement Survey, Class V, Cycle 3, 2010/11. Supported by SSA TECHNICAL COOPERATION FUND
WHAT DO THEY KNOW? A summary of India s National Achievement Survey, Class V, Cycle 3, 2010/11 Supported by SSA TECHNICAL COOPERATION FUND Contents Introduction 3 States of change why we evaluate 4 The
More informationThe correlation coefficient
The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative
More information03 The full syllabus. 03 The full syllabus continued. For more information visit www.cimaglobal.com PAPER C03 FUNDAMENTALS OF BUSINESS MATHEMATICS
0 The full syllabus 0 The full syllabus continued PAPER C0 FUNDAMENTALS OF BUSINESS MATHEMATICS Syllabus overview This paper primarily deals with the tools and techniques to understand the mathematics
More informationLean Six Sigma Analyze Phase Introduction. TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY
TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY Before we begin: Turn on the sound on your computer. There is audio to accompany this presentation. Audio will accompany most of the online
More informationKEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007
KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 447) Surveys and
More informationRUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY
RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY I. INTRODUCTION According to the Common Core Standards (2010), Decisions or predictions are often based on data numbers
More informationThe importance of graphing the data: Anscombe s regression examples
The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 3031, 2008 B. Weaver, NHRC 2008 1 The Objective
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table covariation least squares
More informationUNIT 1: COLLECTING DATA
Core Probability and Statistics Probability and Statistics provides a curriculum focused on understanding key data analysis and probabilistic concepts, calculations, and relevance to realworld applications.
More informationImproving the Performance of Data Mining Models with Data Preparation Using SAS Enterprise Miner Ricardo Galante, SAS Institute Brasil, São Paulo, SP
Improving the Performance of Data Mining Models with Data Preparation Using SAS Enterprise Miner Ricardo Galante, SAS Institute Brasil, São Paulo, SP ABSTRACT In data mining modelling, data preparation
More informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More informationINTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA)
INTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the oneway ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of
More informationFORECASTING. Operations Management
2013 FORECASTING Brad Fink CIT 492 Operations Management Executive Summary Woodlawn hospital needs to forecast type A blood so there is no shortage for the week of 12 October, to correctly forecast, a
More informationKnowing Your School. A series of briefing notes for school governors from the National Governors Association produced in association with partners
Knowing Your School A series of briefing notes for school governors from the National Governors Association produced in association with partners RAISEonline for Governors of Primary Schools Briefing note
More informationAnalysing NAPLAN results using SMART. Version: 14 June 2012
Analysing NAPLAN results using SMART Version: 14 June 2012 TABLE OF CONTENTS INTRODUCTION 2 Undertaking NAPLAN Analysis 2 o SMART data login 3 o About the Reports tab 4 o About the Data Analysis tool 6
More information