2017 Concordance Study: Linking The Texas STAAR Scales To .
2017 Concordance Study: Linking the Texas STAARScales to the NWEA MAP Growth ScalesNovember 2017NWEA Psychometric Services:Sylvia Li, Research ScientistSarah Tran, Sr. Research Associate
2017 NWEA. All rights reserved. No part of this document may be modified or furtherdistributed without written permission from NWEA.MAP Growth is a registered trademark of NWEA.Disclaimer: This report is the product of research conducted by NWEA.
Table of Contents1. Introduction . 11.1. Purpose of the Study . 11.2. Assessment Overview . 11.2.1. State of Texas Assessments of Academic Readiness (STAAR) . 11.2.2. MAP Growth . 12. Data and Analysis . 22.1. Data . 22.2. Equipercentile Linking Procedure . 32.3. Consistency Rate of Classification . 32.4. Proficiency Projection . 43. Estimated MAP Growth Cut Scores Associated with STAAR Readiness Levels . 54. Consistency Rate of Classification . 105. Proficiency Projection . 116. Summary and Discussion . 237. References . 24List of TablesTable 2.1. Demographics of the Study Sample. 2Table 2.2. Descriptive Statistics of STAAR and MAP Growth Scores from the Study Sample . 3Table 2.3. Definition of Consistency Rate for STAAR to MAP Growth Concordance . 4Table 3.1. Concordance of Performance Level Score Ranges between STAAR and MAPGrowth when MAP Growth is taken in Spring—Reading . 5Table 3.2. Concordance of Performance Level Score Ranges between STAAR and MAPGrowth when MAP Growth is taken in Spring—Mathematics. 6Table 3.3. Concordance of Performance Level Score Ranges between STAAR and MAPGrowth when MAP Growth is taken in Spring—Science . 6Table 3.4. Concordance of Performance Level Score Ranges between STAAR and MAPGrowth when MAP Growth is taken in Fall or Winter—Reading . 7Table 3.5. Concordance of Performance Level Score Ranges between STAAR and MAPGrowth when MAP Growth is taken in Fall or Winter—Mathematics . 8Table 3.6. Concordance of Performance Level Score Ranges between STAAR and MAPGrowth when MAP Growth is taken in Fall or Winter—Science . 9Table 4.1. Consistency Rate of Classification for MAP Growth and STAAR Level 3Equipercentile Concordances . 10Table 5.1. Proficiency Projection and Probability for Passing STAAR Level 3 when MAP Growthis taken in the Spring . 11Table 5.2. Proficiency Projection and Probability for Passing STAAR Level 3 when MAP Growthis taken in the Fall or Winter—Reading . 15Table 5.3. Proficiency Projection and Probability for Passing STAAR Level 3 when MAP Growthis taken in the Fall or Winter—Mathematics . 18Table 5.4. Proficiency Projection and Probability for Passing STAAR Level 3 when MAP Growthis taken in the Fall or Winter—Science . 222017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage i
1. Introduction1.1. Purpose of the StudyNWEA is committed to providing partners with useful tools to help make inferences from theMAP Growth interim assessment scores. One important tool is the concordance tablebetween MAP Growth and state summative assessments. Concordance tables, typically derivedfrom statistical linking procedures, provide a direct link between scores on different tests thatmeasure similar but distinct constructs. Aside from describing how a score on one test relates toperformance on another test, these tables can also be used to identify benchmark scores onone test corresponding to performance categories on another test, or to maintain continuity ofscores on a test after the test is redesigned or changed. Concordance tables are helpful foreducators, parents, administrators, researchers, and policymakers to evaluate and formulateacademic standing and growth.This document presents the results of a concordance study conducted by NWEA in November2017 to connect the scales of the State of Texas Assessments of Academic Readiness (STAAR ) assessments with those of the MAP Growth assessments. Specifically, this reportpresents the following: The cut scores on the MAP Growth Reading and Mathematics scales for grades 2–8 andon the Science scale for grades 5 and 8 that correspond to the benchmarks on theSTAAR Reading, Mathematics, and Science testsThe consistency rate of classification based on the estimated MAP Growth cut scoresThe probability of receiving a Level 3 (i.e., “meets” grade level) or higher performancedesignation on the STAAR assessments based on the observed MAP Growth scorestaken during the same school year1.2. Assessment Overview1.2.1. State of Texas Assessments of Academic Readiness (STAAR)STAAR includes a series of vertically scaled achievement tests aligned to the Texas statecurriculum, the Texas Essential Knowledge and Skills (TEKS), in Mathematics and Reading forgrades 3-8, Writing for grades 4 and 7, Science for grades 5 and 8, Social Science for grade 8,and end-of-course assessments for English I, English II, Algebra I, Biology, and U.S. History.STAAR tests can be delivered online and in paper-pencil form. For each grade and contentarea, there are three cut scores that distinguish between performance levels—Level 1: Did NotMeet Grade Level, Level 2: Approaches Grade Level, Level 3: Meets Grade Level, and Level 4:Masters Grade Level. The Level 3 cut score demarks the minimum level of performanceconsidered to be “proficient” for accountability purposes.1.2.2. MAP GrowthMAP Growth tests are adaptive interim assessments aligned to the TEKS standards. They areconstructed to measure student achievement from grades K–12 in Mathematics, Reading,Language Usage, and Science. MAP Growth scores are reported on a vertical Rasch Unit (RIT)scale with a range of 100 to 350. Each content area has its own RIT scale. To aid interpretationof MAP Growth scores, NWEA periodically conducts norming studies of student and schoolperformance on MAP Growth. For example, the 2015 RIT scale norming study by Thum &Hauser (2015) employed multi-level growth models on nearly 500,000 longitudinal test scoresfrom over 100,000 students that were weighted to create large, nationally representative norms.2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 1
2. Data and Analysis2.1. DataData used in this study were collected from 351 schools in Texas for students in grades 3–8.The sample contained 111,980 students for Reading, 112,322 students for Mathematics, and17,674 students for Science who took both the MAP Growth and STAAR tests in Spring 2017.Table 2.1 provides the demographics of the study sample. For all content areas, most studentswere Hispanic, followed by White, Black, and Asian/Pacific Islander (Asian/PI). Males made upslightly more of the study sample than females.To understand the statistical characteristics of the test scores, Table 2.2 provides descriptivestatistics, including the correlation coefficient (r), the mean, standard deviation (SD), minimum,and maximum. As shown in the table, the correlation coefficients between MAP Growth andSTAAR scores range from 0.73 – 0.80 for Reading, 0.73 – 0.84 for Mathematics, and 0.78 –0.79 for Science. In general, these correlations indicate a strong relationship between MAPGrowth and STAAR test scores.Table 2.1. Demographics of the Study 058.2%6.6%15.6%10.5%7.4%1.8%51.7%48.3%*Asian/PI Asian/Pacific Islander. AI/AN American Indian/Alaska Native.2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 2
Table 2.2. Descriptive Statistics of STAAR and MAP Growth Scores from the Study SampleContentAreaReadingMathematicsScienceSTAARMAP 16.01532682.2. Equipercentile Linking ProcedureThe equipercentile procedure (e.g., Kolen & Brennan, 2004) was used to establish theconcordance relationship between STAAR and MAP Growth scores. This procedure matchesscores on the two scales that have the same percentile rank (i.e., the proportion of scores at orbelow each score).Consider the concorded scores between two tests. 𝑥 is a score on Test 𝑋 (e.g., STAAR). Itsequipercentile equivalent score on Test 𝑌 (e.g., MAP Growth), 𝑒𝑦 (𝑥), can be obtained through acumulative-distribution-based linking function defined in Equation 1:𝑒𝑦 (𝑥) 𝐺 1 [𝑃(𝑥)](1)where 𝑒𝑦 (𝑥) is the equipercentile equivalent of score on STAAR on the scale of MAP Growth,𝑃(𝑥) is the percentile rank of a given score on Test 𝑋, and 𝐺 1 is the inverse of the percentilerank function for Test 𝑌 that indicates the score on Test 𝑌 corresponding to a given percentile.Polynomial loglinear pre-smoothing was applied to reduce irregularities of the score distributionsand equipercentile linking curve.2.3. Consistency Rate of ClassificationConsistency rate of classification accuracy, expressed in the form of a rate between 0 and 1,measures the extent to which MAP Growth scores (and the estimated MAP Growth cut scores)accurately predicted whether students in the sample would pass (i.e., achieve Level 3 or higher)on STAAR tests.To calculate consistency rate of classification, sample students were designated “Below STAARcut” or “At or Above STAAR cut” based on their actual STAAR scores. Similarly, they were alsodesignated as “Below MAP Growth cut” or “At or Above MAP Growth cut” based on their actualMAP Growth scores. A two-way contingency table was then tabulated (see Table 2.3),2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 3
classifying students as “proficient” based on the STAAR cut score and concordant MAP Growthcut score. Students were classified as true positive (TP), true negative (TN), false positive (FP),or false negative (FN). The overall consistency rate of classification was computed as theproportion of correct classifications among the entire sample by (TP TN) / (TP TN FP FN). Students classified in the true positive (TP) category were those predicted to beproficient based on both the MAP Growth cut scores and STAAR cut scores.Students classified in the true negative (TN) category were those predicted to be notproficient based on both the MAP Growth cut scores and STAAR cut scores.Students classified in the false positive (FP) category were those predicted to beproficient based on the MAP Growth cut scores but were classified as not proficientbased on the STAAR cut scores.Students classified in the false negative (FN) category were those predicated to be notproficient based on the MAP Growth cut scores but were classified as proficient basedon the STAAR cut scores.Table 2.3. Definition of Consistency Rate for STAAR to MAP Growth ConcordanceBelow STAAR CutAt or Above STAAR CutBelow MAP Growth CutTrue Negative*False NegativeAt or Above MAP Growth CutFalse PositiveTrue Positive**Shaded cells are summed to compute the consistency rate.2.4. Proficiency ProjectionMAP Growth conditional growth norms provide students’ expected score gains across testingseasons (Thum & Hauser, 2015). This information is used to predict a student’s performance onSTAAR based on that student’s MAP Growth scores from prior seasons (e.g., fall and winter).The probability of a student achieving Level 3 (“meets” grade level) on STAAR based on his orher fall or winter MAP Growth score is given in Equation 2:𝑃𝑟(𝐴𝑐ℎ𝑖𝑒𝑣𝑖𝑛𝑔 𝐿𝑒𝑣𝑒𝑙 3 𝑖𝑛 𝑠𝑝𝑟𝑖𝑛𝑔 𝑎 𝑅𝐼𝑇 𝑠𝑐𝑜𝑟𝑒 𝑜𝑓 𝑥) Φ (𝑥 𝑔 𝑐)𝑆𝐷(2)where, Φ is a standardized normal cumulative distribution, 𝑥 is the student’s RIT score in fall orwinter, 𝑔 is the expected growth from fall or winter to spring corresponding to 𝑥, 𝑐 is the MAPGrowth cut score for spring, and 𝑆𝐷 is the conditional standard deviation of growth from fall orwinter to spring.The probability of a student achieving Level 3 on the STAAR test based on his or her springscore 𝑠 can be calculated by Equation 3:𝑃𝑟(𝐴𝑐ℎ𝑖𝑒𝑣𝑖𝑛𝑔 𝐿𝑒𝑣𝑒𝑙 3 𝑖𝑛 𝑠𝑝𝑟𝑖𝑛𝑔 𝑎 𝑅𝐼𝑇 𝑠𝑐𝑜𝑟𝑒 𝑜𝑓 𝑠 𝑖𝑛 𝑠𝑝𝑟𝑖𝑛𝑔) Φ (𝑠 𝑐)𝑆𝐸(3)where 𝑆𝐸 is the standard error of measurement for the MAP Growth test.2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 4
3. Estimated MAP Growth Cut Scores Associated with STAAR Readiness LevelsTable 3.1 –2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 5
Table 3.6 present the STAAR scale scores associated with each performance level, as well asthe estimated score range on the MAP Growth tests associated with each performance level.Specifically, Table 3.1 – Table 3.3 apply to MAP Growth scores obtained during the springtesting season for Reading, Mathematics, and Science, respectively. Table 3.4 –2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 6
Table 3.6 apply to MAP Growth tests taken in fall or winter prior to the testing season for eachcontent area.The tables also report the percentile rank (based on the NWEA 2015 MAP Growth norms)associated with each estimated MAP Growth cut score. These scores can be used to predictstudents’ most probable STAAR performance level. For example, a grade 6 student whoobtained a MAP Growth Mathematics score of 240 in the spring is likely to be at the high end ofLevel 3 (Meets) on the STAAR taken during that same testing season (see Table 3.2). Similarly,a grade 3 student who obtained a MAP Growth Reading score of 210 in the fall is likely to be atLevel 4 (Masters) on the STAAR taken in the spring of grade 3 (see Table 3.4).Table 3.1. Concordance of Performance Level Score Ranges between STAAR and MAP Growthwhen MAP Growth is taken in Spring—ReadingSTAAR ReadingGradeLevel 1: Did Not MeetLevel 2: ApproachesLevel 3: Meets*Level 4: 700–17821783–2153Level 1: Did Not MeetLevel 2: ApproachesLevel 3: MeetsLevel 4: MastersMAP Growth 33–35079–99*Bolded numbers indicate the cut scores considered to be at least “proficient” for accountability purposes (i.e.,“meets” grade level).**Highlighted text denotes grade 2 benchmarks are extrapolated from grade 3 cut scores.2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 7
Table 3.2. Concordance of Performance Level Score Ranges between STAAR and MAP Growthwhen MAP Growth is taken in Spring—MathematicsSTAAR MathematicsGradeLevel 1: Did Not MeetLevel 2: ApproachesLevel 3: Meets*Level 4: 00–18531854–2172MAP Growth MathematicsLevel 1: Did Not MeetGradeLevel 2: ApproachesLevel 3: MeetsLevel 4: 35084–99*Bolded numbers indicate the cut scores considered to be at least “proficient” for accountability purposes (i.e.,“meets” grade level).**Highlighted text denotes grade 2 benchmarks are extrapolated from grade 3 cut scores.Table 3.3. Concordance of Performance Level Score Ranges between STAAR and MAP Growthwhen MAP Growth is taken in Spring—ScienceSTAAR ScienceGradeLevel 1: Did Not MeetLevel 2: ApproachesLevel 3: Meets*Level 4: l 3: MeetsLevel 4: MastersMAP Growth ScienceLevel 1: Did Not MeetLevel 2: ded numbers indicate the cut scores considered to be at least “proficient” for accountability purposes (i.e.,“meets” grade level).2017 Concordance Study: Linking Texas STAAR to NWEA MAP GrowthPage 8
Table 3.4. Concordance of Performance Level Score Ranges between STAAR and MAP Growthwhen MAP Growth is taken in Fall or Winter—ReadingSTAAR ReadingGradeLevel 1: Did Not MeetLevel 2: ApproachesLevel 3: Meets*Level 4: 1517–16281629–17171718–20547969–15661
Dec 04, 2017 · 2017 Concordance Study: Linking Texas STAAR to NWEA MAP Growth Page 3 Table 2.2. Descriptive Statistics of STAAR and MAP Growth Scores from the Study Sample Content Area STAAR MAP Growth Grade N r Mean SD Min. Max. Mean SD Min. Max. Readi
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