PLEPsychometric Assessment,Statistics andReport WritingAn introduction for psychologists, teachers and health professionalsSAMDr. Barry Johnson and Dr. Gareth Hagger-JohnsonStatistics 4.0.indd 112/02/2013 14:22

EPLMSACopyright 2013 Pearson Education, Ltd. or its affiliate(s).All rights reserved. This publication is protected by copyright and permission should be obtained from the publisher prior toany prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical,photocopying, recording, or likewise.Published byPearsonAssessment80 StrandLondon WC2R 0RLPearson is a trademark, in the U.S. and/or other countries, of Pearson Education, Inc. or its affiliate(s).Visit our website at in the United Kingdom978 0 749163 77 813 14 15 16 17 A B C D EStatistics 4.0.indd 212/02/2013 14:22

ContentsIntroductionAbout the CAL TERMS AND EQUATIONSBasic Statistical TermsTypes of Standard ScoresStandard Error of Measurement of the DifferenceStatistical and Clinical Differences Between Test ScoresSimple Regression to the MeanA Simple Regression TableStandard Error of the EstimateRegression and Confidence RangesTest-RetestGrowth Scale Values and Normal Curve EquivalentsCoefficient of DeterminationStandard Error of the MeanBinomial Distribution Probability and Multiple-Choice TestsMultiple RegressionSECTION 2Chapter 15Chapter 16Chapter 17REPORT WRITINGRange DescriptorsData Merging and Auto TextUsing Charts in ReportsPLMAppendix AAppendix BAppendix CAppendix DAppendix Ethe FUTUREThe Future: Trends and IssuesConversion Table for Standardised ScoresZ-P Conversion Table (Positive Z Scores)Z-P Conversion Table (Negative Z Scores)Percentile-Z Conversion TableAbility-Achievement Look-Up TableSASECTION 3Chapter 18ESECTION 1Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14ReferencesList of TablesTable 1.1Tests and their Standard Errors of MeasurementsTable 1.2Tests and their Confidence RangesTable 1.3The Null HypothesisTypes of Standardised Scores (i)Table 2.1Table 2.2Types of Standardised Scores (ii)Creating a Look-up TableTable 2.3Table 2.4Extract from a Z-P TableTable 2.5Extract from a Negative Z-P TableTable 2.6Converting Z Scores to PercentilesTable 2.7Types of Standardised Scores (iii)Table 2.8Stanines and RankingTable 2.9Frequency of Raw ScoresTable 2.10Converting Raw Scores to Percentile RanksTable 2.11Z Scores and Levels of 40iiiStatistics 4.0.indd 312/02/2013 14:22

P and Z Scores for One- and Two-Tailed Tests of SignificanceZ Values and Levels of ConfidenceKBIT-2 Composite IQ and Reading Comprehension ScoresPredicted Reading Comprehension Scores from KBIT-2 Composite IQ ScoresRaw and Standard Scores over TimeGrowth Scale Values over TimeTrends of Growth Scale Value and Standardised ScoresComparing IQ Scores on Two TestsTests’ Coefficients of Determination and Reliability CoefficientsStandard Error of the Mean – Spelling Scores for Two Groups of StudentsStandard and Scaled Scores for SubtestsStandard Scores for SubtestsRange Descriptors for Subtest ScoresReference Table for Tests’ Range DescriptorsWMS-IV Subtest Scaled ScoresCELF-4UK Subtest Scaled ScoresRaw Scores on Probe SheetRaw Scores on Probe Sheet – Preparation for Excel ChartETable 3.1Table 4.1Table 6.1Table 6.2Table 10.1Table 10.2Table 10.3Table 11.1Table 11.2Table 12.1Table 15.1Table 15.2Table 15.3Table 15.4Table 17.1Table 17.2Table 17.3Table 17.4SAMPLList of FiguresFigure 1.1Standard Deviation using Excel (i)Figure 1.2Standard Deviation using Excel (ii)Figure 1.3Standard Deviation using Excel (iii)Standard Normal DistributionFigure 1.4Figure 1.5Area Percentages within the Standard Deviations of a Standard Normal Distribution CurvePearson’s Product Moment Correlation using ExcelFigure 1.6Figure 1.7Scatter PlotFigure 1.8Overlapping Confidence RangesFigure 1.9Moderately Large Standard DeviationLarge Standard DeviationFigure 1.10Figure 1.11Standard Deviation of a Standard Normal Distribution CurveFigure 1.12Normal Distribution Curve in Excel – SD 15Figure 1.13Normal Distribution Curve in Excel – SD 20Figure 1.14Normal Distribution Curve in Excel – SD 10Figure 2.1Excel Conversion Table for Standardised ScoresExcel Conversion Table for Scaled ScoresFigure 2.2Figure 2.3Z Score of 1.5 on the Standard Normal Distribution CurveFilling Cells in ExcelFigure 2.4Figure 2.5Deriving Z Scores from Raw Scores via PercentilesFigure 2.6Deriving Standard Scores from Z ScoresFigure 2.7Deriving the Standard Error of MeasurementFigure 2.8Deriving Confidence RangesFigure 2.9Stanines and PercentilesFigure 2.10Standard Normal Distribution Curve and Standardised ScoresFigure 2.11Distribution of Raw Scores and their FrequenciesFigure 2.12Score Frequencies and Percentile RanksFigure 2.13Proportion of Unlikely Scores in the Normal Distribution CurveFigure 2.14Z Scores and Two-Tailed TestFigure 2.15Z Score and One-Tailed TestFigure 4.1Confidence Ranges – Levels of Confidence and Reliability Coefficients of 3946ivStatistics 4.0.indd 412/02/2013 14:22

EPLMFigure 10.1Figure 10.2Figure 10.3Figure 12.1Figure 12.2Figure 12.3Figure 13.1Figure 13.2Figure 13.3Figure 13.4Figure 14.1Figure 14.2Figure 14.3Figure 14.4Figure 16.1Figure 16.2Figure 16.3Figure 16.4Figure 16.5Figure 16.6Figure 16.7Figure 16.8Figure 16.9Figure 16.10Figure 16.11Figure 16.12Figure 16.13Figure 16.14Figure 16.15Figure 16.16Tests’ Confidence RangesComparison of Multiple Test ScoresHighlighting Significant Test ScoresOptions for Highlighting Significant Test Scores‘Greater Than’ Option in ExcelReference Table for Significant Differences between Test ScoresTable of Correlation Coefficients for TestsTable of Severe Discrepancy Values Between TestsTable of Predicted Scores Using the Simple Regression FormulaRegression of Attainment Scores from AbilityRegressed ScoresPredicted Scores for a Range of Correlation CoefficientsAn Example of Looking Up a Regressed ScoreStoring Reliability and Validity Data in ExcelWorking across Worksheets in ExcelExcel and using Standard Error of the Estimate for Ability-Attainment ComparisonA Source of Standard Errors of the Estimates in ExcelAn Example – Comparing Billy’s ART Accuracy Score with his SPM ScoreComparing Confidence Ranges Derived from the Standard Error of Measurementand the Standard Error of the EstimateCharting Progress over Time Using Standard ScoresCharting Progress over Time Using Growth Scale ValuesNormal Curve Equivalents and Percentiles on a Standard Distribution CurveScatter Plot of ScoresStandard Deviation Calculations for Groups A and BSampling Numbers and the Standard Error of the MeanMultiple Choice Items – Obtaining Binomial Probability using Stat TrekMultiple Choice Items – Obtaining Binomial Probability using Excel (i)Multiple Choice Items – Obtaining Binomial Probability using Excel (ii)Probability (p) of Chance Successes on a Multiple-Choice TestMultiple Regression – Step 1Multiple Regression – Step 2Multiple Regression – Step 3Multiple Regression – Step 4Example 1 of Core TemplatesExample 2 of Core TemplatesPreparing a Template for Data MergingData File for MergingSelecting the Mail Merge Wizard in ExcelMail Merge Wizard – Step 1Mail Merge Wizard – Step 2Mail Merge Wizard – Selecting the ClientMail Merge Wizard – Step 3Mail Merge Wizard – Inserting Data FieldsMail Merge Wizard – Template with Data FieldsMail Merge Wizard – Step 4Mail Merge Wizard – Step 5Mail Merge Wizard – Step 6Final Mail Merged ReportMicrosoft’s Quick Access ToolbarSAFigure 4.2Figure 4.3Figure 4.4Figure 4.5Figure 4.6Figure 4.7Figure 4.8Figure 4.9Figure 5.1Figure 5.2Figure 6.1Figure 6.2Figure 6.3Figure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 15116116117117118119vStatistics 4.0.indd 512/02/2013 14:22

MPLECustomising the Quick Access Toolbar for Auto TextCreating a New Auto TextInserting an Auto TextInserting Auto Text as You Type – Step 1Inserting Auto Text as You Type – Step 2Inserting Auto Text as You Type – Step 3Creating a Table of Subtest Z Scores in ExcelCreating a Chart – Step 1Creating a Chart – Step 2Creating a Chart – Step 3Creating a Chart – Step 4Creating a Chart – Step 5Creating a Chart – Step 6Creating a Chart – Step 7Creating a Chart – Step 8Creating a Chart – Step 9Creating a Chart – Step 10Creating a Chart – Step 11Setting the Range of Scores in ExcelExample Chart of Scaled ScoresCreating a Stock Chart – Step 1Creating a Stock Chart – Step 2Creating a Stock Chart – Step 3Creating a Stock Chart – Step 4Creating a Stock Chart – Step 5An Alternative Way of Creating a Chart – Step 1An Alternative Way of Creating a Chart – Step 2An Alternative Way of Creating a Chart – Step 3An Alternative Way of Creating a Chart – Step 4An Alternative Way of Creating a Chart – Step 5An Alternative Way of Creating a Chart – Step 6An Alternative Way of Creating a Chart – Step 7An Alternative Way of Creating a Chart – Step 8An Alternative Way of Creating a Chart – Step 9Logarithmic Scale for a ChartCharting Probe Scores – Step 1Charting Probe Scores – Step 2Charting Probe Scores – Step 3Charting Probe Scores – Step 4Charting Probe Scores – Step 5Inserting a Trendline into a Chart – Step 1Inserting a Trendline into a Chart – Step 2Inserting a Trendline into a Chart – Step 3Inserting a Trendline into a Chart – Step 4Inserting a Trendline into a Chart – Step 5Inserting a Trendline into a Chart – Step 6Inserting a Trendline into a Chart – Step 7WAIS-IIIUK Mean Raw Scores for Age RangesSAFigure 16.17Figure 16.18Figure 16.19Figure 16.20Figure 16.21Figure 16.22Figure 17.1Figure 17.2Figure 17.3Figure 17.4Figure 17.5Figure 17.6Figure 17.7Figure 17.8Figure 17.9Figure 17.10Figure 17.11Figure 17.12Figure 17.13Figure 17.14Figure 17.15Figure 17.16Figure 17.17Figure 17.18Figure 17.19Figure 17.20Figure 17.21Figure 17.22Figure 17.23Figure 17.24Figure 17.25Figure 17.26Figure 17.27Figure 17.28Figure 17.29Figure 17.30Figure 17.31Figure 17.32Figure 17.33Figure 17.34Figure 17.35Figure 17.36Figure 17.37Figure 17.38Figure 17.39Figure 17.40Figure 17.41Figure Statistics 4.0.indd 612/02/2013 14:22

IntroductionThis book is designed primarily to support users of psychometric tests. It provides specialist teachers,psychologists and other health professionals with a practical reference book on basic statistical methods toaid them in their diagnostic interpretation of psychometric test scores when assessing children, young peopleand adults with special educational needs and specific learning difficulties. It offers a complementary resourceto published test scoring and reporting software. It acknowledges that assessors often need to have availablepractical guidance and references on a number of statistical matters, particularly as the range of available testsis now extremely wide.EThe level of statistical information provided is suitable for those UK teachers who are either training fortheir practising certificate in special education or seeking renewal of their certificate in order to be deemedas appropriately trained and safe to practice. It will also be helpful to experienced specialist teachers andpsychologists who are practising as diagnosticians but who feel that they need additional help with theirunderstanding and efficient application of a range of statistical concepts and approaches. Trainee andnewly qualified educational and clinical psychologists in the UK will also find the book useful as an aid totheir induction to fieldwork assessment practices and their CPD requirements for maintaining their HCPCprofessional registration. The book will be particularly relevant for those professionals involved in providingreports for clients who require assessments for consideration of eligibility for access arrangements for formalexaminations such as GCSE/GCE and Disabled Students’ Allowance (DSA).SAMPLThe book includes references to a range of contemporary psychometric tests. The examples are selectedpredominantly from tests published or distributed by Pearson Assessment. The book draws on the tests’standardisation data and encourages users to adopt a critical stance when selecting tests for diagnosticpurposes. It focuses on common mistakes and misunderstandings made by assessors when they attemptto interpret psychometric information for the purposes of providing diagnostic reports for their clients. Indoing so, it is likely to be of significant help by ensuring that these professionals can be confident that theirconclusions reflect sound principles of statistical interpretation and hypothesis-testing. Case examples andscenarios are given which are of the type commonly experienced by professionals, thereby making it relativelyeasy for them to be applied within their own contexts of need. Relatively simple Excel formulae and tablecreations are introduced to encourage professionals to establish incrementally a repertoire of referencesources, statistical tools and personal overview data relating to their assessment inputs. Tips are given on howto merge statistical data into reports and how to insert charts directly from data sources, thus making moreefficient the report writing process and the gathering of overview data across assessments.The book’s early chapters are arranged to give case examples with related summaries of the statistical issuesrelevant to the cases being investigated. As the case examples continue, the statistical issues are expandedand gradually covered in m