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Searching for DIF, Drift, and Growth Among the Deck Chairs -or- Why we cant make sense of measures of educational achievement Presentation at the 2008 Conference of The Fordham Council on Applied Psychometrics June 26, 2008 By Eliot R. Long Data Research Services Brooklyn, NY 11231 Copyright 2008 by Eliot R. Long. All rights reserved.

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Finding Meaning In the Difference Between Two Test Scores Exhibit 2. No Child Left Behind requires a reliable measurement of change through the comparison of test scores Yet, schools experience erratic, inexplicable variations in measures of achievement gains. This volatility results in some schools being recognized as outstanding and other schools identified as in need of improvement simply as the result of random fluctuations. Robert L. Linn and Carolyn Haug (Spring 2002) Stability of school-building accountability scores and gains. Educational Evaluation and Policy Analysis, 24(1), 29-36.

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Guessing on tests Exhibit 3. Findings from 90+ years of research on guessing - Guessing effects few test items - Modest effect on test score reliability - Encouraged guessing may improve fairness Text book recommendations - Encourage test-takers to guess, if necessary, to answer all questions e.g. Measurement and Evaluation in Education and Psychology Mehrens, W. A. & Lehmann, I. J. (1991), 464-465. School practice - Informal policy (not written) to encourage guessing If its blank, its wrong Are these research findings appropriate for current, high stakes testing? Is the informal practice of encouraged guessing consistent with standardized testing?

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A Norms Review Exhibit 4. The following exhibits are based on four separate research projects, each including the development of group response pattern norms -Classroom groups, grades 3-7 in a northeast urban school district 15,825 classrooms, 391,078 students - School groups, grade 3 statewide in Midwest 2,317 schools, 140,203 students -Nationwide sample, grade 4 A test section of the 2002 NAEP Reading 36,314 students -Job applicant groups across the U.S. 87 employers, 447 employer groups, 32,458 job applicants

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Percent Correct & Test Completion Exhibit 5. Teacher Administered Tests Non-teacher Administered Tests Pct. Pct. Attp. Pct. Pct. Attp. Test-Takers Correct All Questions Northeast1999-2001 Independent Proctor Administered Urban School District – Reading Tests NAEP Reading 2002 Grade 3 68.6% 97.4% Grade 4 67.6% 60.9% Grade 4 74.7% 96.7% Grade 5 65.5% 94.0% Employer Administered 1996-1999 Grade 6 67.4% 93.1% Verbal Skills Grade 7 71.0% 96.4% Job Applicants 82.0% 44.0% Midwest2001 Quantitative Skills Statewide – Math Test Job Applicants 75.2% 28.2% Grade 3 63.5% 97.4% If its blank, its wrong. No encouraged guessing

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Test Completion: A Teacher/Proctor Effect Exhibit 6. Answers left blank are concentrated by classroom 15.6% of all classrooms account for 77.6% of all answers left blank. 5.6% of all classrooms account for 48.0% of all answers left blank. Grade 5 Reading 45 items – 4 alternative, multiple-choice All Classes Low Blanks Classes High Blanks Classes < 26 Ans. Left Blank 26+ Ans. Left Blank Class Blanks Pct. Attp. Blanks Blanks Pct. of All Standing Classes Per Class All Ques. Classes Per Class Classes Per Class Classes Blanks 4 th Q.617 1.8 97.3% 613 1.6 4 34.3 0.6% 12.0% 3 rd Q.620 4.5 94.9% 599 3.2 21 43.3 3.4% 32.5% 2 nd Q.619 6.1 93.1% 580 3.7 39 42.0 6.3% 43.5% 1 st Q.619 10.4 90.1% 544 4.3 75 54.6 12.1% 63.8% All 2,475 5.7 94.0% 2,336 3.1 139 48.8 5.6% 48.0% -------------------------------------------------------------------------------------------------------- Pct. Correct 65.5% 65.9% 59.3% Pct. Attp. All 94.0% 95.1% 74.0%

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Tale of Two Classes Exhibit 7. Two classrooms at the same class average score with and without encouraged guessing. Class: n = 21, Blanks = 3 Class n = 21, Blanks = 199 RS Avg. = 19.4 SD = 4.3 RS Avg. = 19.4 SD = 7.9 KR-20 =.53 – Pct. Blank = 0.3% KR-20 =.89 – Pct. Blank = 21.1% The Norm of Classroom Test Administration The Exception

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Correlation Number Correct - Number Attempted Exhibit 8. Teacher Administered All Students Students with Blanks =>5 Grade 5 Reading r =.153 n = 66,320 r =.527 n = 1,094 Grade 5 Math r =.110 n = 69,413 r =.549 n = 238 Grade 6 Reading r =.162 n = 62,524 r =.583 n = 658 Grade 7 Reading r =.202 n = 58,915 r =.597 n = 1,416 Independent Test Administrator NAEP Grade 4 Reading r =.608 n = 36,314 Employer Administered Job Applicants Test of Verbal Skills r =.717 n = 32,458 Test of Quantitative Skills r =.581 n = 31,629 Hovland and Wonderlic (1939) Adult workers & students Otis Test of Mental Ability 4 test forms & 2 time limits r =.608 to.723 n = 125 to 2,274

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Location of Answers Left Blank Exhibit 9. Recommendations to encourage guessing presume that most answers left blank are imbedded; that is, they represent questions that are addressed and, for some reason, skipped. Our norms reveal that most blanks are trailing; that is, they represent questions that are not reached during the time limit. Position of Blanks Imbedded Trailing Grade 5 Reading 22.3% 77.7% NAEP Grade 4 Reading 15.8% 84.2% Job Applicant Verbal Skills 5.2% 94.8% Teachers must significantly change students test work behavior to achieve answers to not reached questions. How?

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Test Score Reliability (KR-20) by Classroom Exhibit 10. Teacher involvement in their students test work behavior to encourage guessing is entrepreneurial, often undermining test score reliability. 50+ Answers Left Blank No Answers Left Blank 42 classrooms at and below average 330 classrooms at and below average likely to have little encouragement to guess likely to have extensive encouragement to guess

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The Volume of Teacher Encouraged Guessing Exhibit 11. Parsing Grade 5 number correct scores: The traditional correction-for-guessing: S = R – W/(n-1) For the number correct score at the minimum for Basic (R = 18): S = 18 – 27/(4-1) = 18 - 9 S = 9 Result: Half of the number correct score is due to random guessing. RS 18 = Min. Scale Score For Basic - just passing S = True Score R = Number Right W = Number Wrong n = Number of Answer Choices Grade 5 Reading: 45 items 4 ans. alternatives

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Success rate: A norms approach Exhibit 12. The traditional correction-for-guessing formula assumes that 100% of skills based answers are correct. A regression of median percent correct on number attempted for test-takers who leave 5+ answers blank finds a variable rate of success: Regression of Median Pct. Correct on Number Attempted Test-Takers Number Data Pts R squared Constant Slope Grade 5 Reading 1,449 7*.699 0.321 0.0091 Grade 6 Reading 1,486 7*.877 0.416 0.0065 Grade 7 Reading 1,269 7*.703 0.468 0.0040 Job Applicants 15,650 25**.905 0.465 0.0094 or Percent Correct = 0.465 + 0.0094*A s where A s represents the number of questions answered based on the test-takers skills. * Number attempted ranges: Up to 15, 16-20, 21-25, 26-30, 31-35, 36-40, 41-45 ** Number attempted: 21 through 45

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Add norms to The traditional formula = Empirical Approach Exhibit 13. Traditional formula: S = R – W/(n-1) orR = S + W/(n-1) skills + guessing Empirical formula: R = Pct. Correct*A s + (A t – A s )/n orR = 0.0094*A s 2 + 0.465*A s + (A t – A s )/n ---- skills ----- + guessing For a score of 18: 18 = (0.0094*17.7 2 ) + (0.465*17.7) + ((45-17.7)/4) = 2.945 + 8.23 + 6.825 18 = 11.175 + 6.825 skills + guessing Results:39% (17.7/45) of answers are attempted based on skills 61% of answers are guessed due to teacher encouragement 38% of the observed score is based on encouraged random guessing Note: W = (A t – A s )*((n-1)/n) A t = Total attempts = 45 A s = Skill based attempts Solution: Substitute 45 for A t and 18 for R, find A s = 17.7

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Observed and Estimated True Scores Exhibit 14. Grade 5 Reading Test: Distribution of Observed and Estimated True Skills Application of the empirical parsing formula to the full distribution of Grade 5 scores*. Student Distribution Mean SD Observed 29.1 7.8 Est. True 26.4 9.4 Change +10.2% -16.5% Classroom Distribution Avg. Mean Avg. SD Observed 29.1 5.9 Est. True 26.0 7.4 Change +11.6% -19.9% * Random guessing outcomes are forecast by the binomial distribution and moderated by the variation in the volume of guessing with student skill level. The actual percent guessed correct is lower than expected among lower observed scores and higher than expected among higher observed scores.

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Volume of encouraged guessing By Performance Level Exhibit 15. Contribution of Encouraged Guessing To Student Scores Student Averages by Performance Level Grade 5 Reading Estimates for Random Guessing Average Average Pct. of Pct. of Student Pct. of Number Number Number All Performance Level Students Correct Attempted CorrectAnswers Level 4 Advanced 6.2% 42.1 45.0 0.0% 0.0% Level 3 Proficient 48.4% 34.1 44.9 5.3% 15.4% Level 2 Basic 37.1% 23.6 44.6 19.0% 42.8% Level 1 Below Basic 8.3% 14.4 44.1 44.1% 69.8% All Students 100.0% 29.1 44.8 10.2% 26.7%

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Gain in class average test score & Attenuation of class distribution due to guessing Exhibit 16. Encouraged guessing adds disproportionately to lower performing students scores, compressing the distribution of scores with respect to the distribution of achievement. Grade 5 Reading Classroom Averages___________ Quartile Standing Parsed for Guessing of Class Number of Observed Est. True Scores Pct. Pct. Average Score Classes RS Avg. SD Avg. RS Avg. SD Avg. RS Gain SD Atten. 4 th Q. 61935.7 4.8 34.3 6.0 4.0% -19.4% 3 rd Q. 620 30.6 6.2 27.9 7.7 9.5% -20.1% 2 nd Q. 61927.0 6.5 23.5 8.1 15.0% -20.2% 1 st Q. 61922.9 6.1 18.4 7.6 24.7% -19.6% All 2,47729.1 5.9 26.0 7.4 11.6% -19.9%

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Encouraged guessing Creates a test score modulator Exhibit 17. Changes in skill and guessing move in opposite direction, offsetting in the total score. Comparison of First Test and Second Test Scores Test Answers Test Observed Based on Based on Guessing Administration Total Skills Guessing Contribution 1 st Test Admin. Correct 18 11.2 6.8 37.8% Attempts 45 17.7 27.3 60.7% Pct. Correct 40.0% 63.3% 25.0% 2 nd Test Admin. Correct 20 13.8 6.2 31.0% Attempts 45 20.1 24.9 55.3% Pct. Correct 44.4% 68.7% 25.0% Gain 22.6 -0.6 Pct. Gain 11.1% 23.2% 52% of true gain masked by guessing

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Estimated Gain Masked by Guessing Exhibit 18. The empirical formula may be applied to first test and second tests at each score level. Hypothetical Gains Parsed for Guessing Effects Number Correct Pct. Pct. Pct. Percentile First SecondObserved Est. True True Gain Standing Score Score Gain Gain Masked_ 90% 39.0 42.9 10.0% 10.9% 8.3% 80% 36.0 39.6 10.0% 13.3% 24.9% 70% 34.0 37.4 10.0% 13.2% 24.2% 60% 32.0 35.2 10.0% 13.8% 27.3% 50% 30.0 33.0 10.0% 13.4% 25.6% 40% 27.0 29.7 10.0% 15.2% 34.1% 30% 25.0 27.5 10.0% 15.8% 36.7% 20% 22.0 24.2 10.0% 16.5% 39.2% 10% 18.0 19.8 10.0% 20.6% 51.5%

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Findings of a Norms Review Exhibit 19. The informal practice of teacher encouraged guessing to complete all test answers has the following effects: 1. High volume of non-skills based test answers The volume of test answers that result from teacher encouragement is very high: 26% of all answers for students at the school district average and 50% or more among students most at risk of failing. 2. Teacher involvement lowers test score reliability Teacher involvement is unstructured, varying from classroom to classroom and from student to student, creating widely varying and generally lower test score reliability. 3. Guessed correct answers reduce the range of measurement Added guessing increases among lower performing students, raising their scores more than higher performing students and therefore narrowing the range of measurement by ~20%.

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Findings of a Norms Review Continued Exhibit 19 cont. 4. Guessing creates a test score modulator Changes in student achievement will cause changes in the volume of guessing – in the opposite, offsetting direction - modulating observed scores. This modulating effect masks variations in gain, by as much as 50% or more among low performing students. Teacher encouraged guessing narrows the window onto student achievement gains, while reducing both the range and reliability of the measurement that can be observed. As a consequence, non-skills related variation may predominate, misdirecting test score interpretation and education policy.

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