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Empirical Methods to Evaluate the Instructional Sensitivity of Accountability Tests Stephen C. Court Presented at Association of Educational Assessment - Europe 10th Annual Conference Innovation in Assessment to meet changing needs November 2009 Valletta, Malta

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Basic Assumption of Accountability Systems Student test scores accurately reflect instructional quality Higher scores = greater learning due to higher quality teaching Lower scores = less learning due to lower quality teaching In short, it is assumed, accountability tests are instructionally sensitive.

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Reality The assumption rarely holds. Most accountability tests are not sensitive to instruction because they simply were not constructed to be instructionally sensitive. The tests are built to the same general Army Alpha specifications - originally designed during the First World War – used to differentiate between officer candidates and enlisted personnel.

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Consequences of Instructional Insensitivity In principle: Lack of fairness Lack of fairness Lack of trustworthy evidence to support validity arguments Lack of trustworthy evidence to support validity arguments In practice Bad policy Bad evaluation Bad things happen in the classroom

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The situation in Kansas - SES SES disparities between districts

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The situation in Kansas - Test Scores Disparities in state assessment scores and proficiency rates

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The Situation in Kansas Can the instruction in high-poverty districts be so much worser than the instruction in low-poverty districts? Or, are construct-irrelevant factors (such as SES) masking the effects of instruction?

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The basic question: What methods can be employed to evaluate the instructional sensitivity of accountability tests?

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Definition Instructional Sensitivity the degree to which students performances on a test… accurately reflect the quality of instruction provided specifically to promote students mastery of the knowledge and skills being assessed. (Popham, 2008)

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Two-pronged Approach At last years AEA conference in Hissar, Popham (2008) advocated a two-pronged approach to evaluating instructional sensitivity: Judgmental strategies Judgmental strategies Empirical studies Empirical studies

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Empirical Study Following the guidance of Popham (2007)… three Kansas school districts conducted an empirical study of the Kansas assessments.

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Description of the Kansas Study Teachers were invited to complete a brief online rating form. Participation was voluntary. Each teacher identified the 3-4 indicators (curricular aims) he or she had taught best during the school year. Student results were matched to responding teachers.

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Study Participants Study Participants 575 teachers responded 320 teachers (grades 3-5 reading and math) 320 teachers (grades 3-5 reading and math) 129 reading teachers (grades 6-8) 129 reading teachers (grades 6-8) 126 math teachers (grades 6-8) 126 math teachers (grades 6-8) 14,000 students 14,000 students

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A Gold Standard Typically, test scores are used to confirm teacher perceptions…as if the test scores are infallible and the teachers are always suspect. In fact, for the first 40 years of inquiry into instructional sensitivity, teacher perceptions were never even part of the mix. Instructional sensitivity studies always contrasted two sets of scores – e.g. pre-test/post-test, not-taught/taught, etc. Asking teachers to identify their best-taught indicators has changed the instructional sensitivity issue both conceptually and operationally.

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Old and New Model Instructional Sensitivity A = Non-Learning B = Learning C = Slip D = Maintain A = True Fail B = False Pass C = False Fail D = True Pass

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Kansas Study Propensity Score Matching Propensity scores were generated from logistic regression: Several demographic and prior performance characteristics were regressed on overall proficiency rate. Probabilities were used to match Not-Best-Taught with Best-Taught students using nearest neighbor method. Purpose: to form quasi- random equivalent groups of similar size for each content area, grade level, and indicator configuration.

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Basic Contrast The basic contrast involved best-taught versus not-best- taught For example… Grade 3 Reading – Indicator 1… Grade 3 Reading – Indicator 1… Given average class size, 160 teachers responded 30 teachers identified Indicator 1 as one of their best-taught. From among the pool of other teachers and their students, the propensity score matching was used to form an equivalent group of 750 students from 30 teachers.

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Initial Analysis Scheme Conduct independent t-tests with mean indicator score as dependent variable mean indicator score as dependent variable Best-taught versus Other students as independent variable Best-taught versus Other students as independent variable

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Initial Analysis Scheme Initial logic: If best-taught students outperform other students, indicator is sensitive to instruction. If mean differences are small or in the wrong direction, indicator is insensitive to instruction.

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Problem But significant performance differences between best-taught and other students do not necessarily represent significant differences in instructional sensitivity. Instead, instructional sensitivity is about whether the indicator accurately distinguishes effective from ineffective instruction – without confounding from any form of construct irrelevant easiness or difficulty.

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Basic Concept In its simplest form, Pophams definition of instructional sensitivity can be depicted as a 2x2 contingency table.

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In Context

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Basic Concepts Mean Least effective = B/(A+B) Mean Most effective = D/(C+D) = D/(C+D)But Mean Least effective = False Pass/(True Fail + False Pass) makes no sense at all. In fact, it returns to the outcome as infallible and the teacher perceptions as suspect: If the pass-rate for the two groups are statistically similar, then the degree of difference between less and most effective must be questioned.

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Conceptually Correct Rather than comparing means, we instead need to look at the combined proportions of true fail and true pass. That is, (A + D) / (A + B + C + D) Which can be shortened to (A + D) / N

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Index 1 (A + D) / N Ranges from 0 to 1 (Completely Insensitive to Totally Sensitive) In practice: Values <.50 are worse than random guessing

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Totally Sensitive (A + D)/N = ( )/100 = 1.0 A totally sensitive test would cluster students into A or D.

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Totally Insensitive (A+D)/N = (0+0)/100 = 0.0 A totally insensitive test clusters students into B and C

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Useless (A+D)/N = (25+25)/100 = = mere chance Values < 0.50 are worse than chance.

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Index 1 Equivalents Index 1 is conceptually equivalent to: Mann-Whitney U Mann-Whitney U Wilcoxon statistic Wilcoxon statistic Transposing Cell A and Cell B, then running a t- test Transposing Cell A and Cell B, then running a t- test Area Under the Curve (AUC) in Receiver Operating Characteristic (ROC) curve analysis Area Under the Curve (AUC) in Receiver Operating Characteristic (ROC) curve analysis

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ROC Curve Analysis Has rarely been used in domain of educational research More commonly used in medicine and radiology medicine and radiology data mining (information retrieval) data mining (information retrieval) artificial intelligence (machine learning) artificial intelligence (machine learning) The use of ROC curves was first introduced during WWII in response to the challenge of how to accurately identify enemy planes on radar screens.

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AUC Context ROC Curve Analysis – especially the AUC - is more useful for several reasons: Easily computed Easily computed Easily interpreted Easily interpreted Decomposable into sensitivity and specificity Decomposable into sensitivity and specificity Sensitivity = D / (B+D) Specificity = C / (A+C) Easily graphed as (Sensitivity) versus (1 – Specificity) Easily graphed as (Sensitivity) versus (1 – Specificity) Readily expandable to polytomous situations Readily expandable to polytomous situations Multiple test items in a subscale Multiple subscales in a test Multiple groups being tested

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Basic Interpretation (Descriptive) Easy to compute: (A+D)/N Easy to interpret… = excellent (A) = excellent (A) = good (B) = good (B) = fair (C) = fair (C) = poor (D) = poor (D) = fail (F) = fail (F) Less than.50 is worse than guessing!

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Basic Interpretation Most statistical software packages – e.g., SAS, SPSS - include a ROC procedure. The area under the curve table displays estimates of the area, estimates of the area, standard error of the area, standard error of the area, confidence limits for the area, confidence limits for the area, and the p-value of a hypothesis test. and the p-value of a hypothesis test.

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ROC Hypothesis Test The null hypothesis: true AUC =.50. So, use of ROC Curve Analysis in this context would support rigorous psychometric inquiry into instructional sensitivity. Yet, the A, B, C, D, F system could be reported in ways that even the least experienced reporters or policy-makers can readily understand.

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Area Under Curve (AUC) - Graphed Curve 1 =.50 Pure chance…no better than random guess Curve 4 = 1.0 Totally Sensitive completely accurate discrimination between effective and less- effective instruction Curve 3 is better than Curve 2

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ROC Curve Interpretation Greater AUC values indicate greater separation between distributions e.g., Most effective versus less effective Best taught versus Not-best-taught 1.0 = complete separation – that is, total sensitivity

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ROC Curve Interpretation AUC values close to.50 indicate no separation between distributions. AUC =.50 indicates complete overlap No difference might as well guess

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Procedural Review Step 1: Cross-tabulate not/pass status with teacher identification of best-taught indicators Step 2:(Optional) Use logistic regression and propensity score matching to create randomly-equivalent groups – or, as close as you can get Step 3:Use (A+D)/N or formal ROC Curve Analysis to evaluate instructional sensitivity at the smallest grain-size possible – preferably, at the wrong/right level of individual items.

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In Closing The assumption that accountability tests are sensitive to instruction rarely holds. Inferences drawn from test scores about school quality and teaching effectiveness must be validated before action is taken. The empirical approaches presented here should prove helpful in determining if the inference that a test is instructionally sensitive is indeed warranted.

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Presenters address: Questions, comments, or suggestions are welcome

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