# 1 Effective Use of Benchmark Test and Item Statistics and Considerations When Setting Performance Levels California Educational Research Association Anaheim,

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1 Effective Use of Benchmark Test and Item Statistics and Considerations When Setting Performance Levels California Educational Research Association Anaheim, California December 1, 2011

2 Review of Benchmark Test and Item Statistics Objective Extend knowledge of assessment team to: 1. Better understand test reliability and the influences of test composition and test length. 2. Better understand item statistics and use them to identify items in need of revision

Reliability is a measure of the consistency of the assessment Types of reliability coefficients (always range from 0 to 1) Test-retest Alternate forms Split-half Internal consistency (Cronbach’s Alpha/KR- 20) 3

Reliability Influenced by Test Length Spearman-Brown formula estimates reliabilities of shorter tests – Remember: The reliability of a score is an indication of how much an observed score can be expected to be the same if observed again. NOTE: See handout from STAR Technical Manual for exact cluster reliabilities. 4

Reliability Influenced by Test Length Example: given a 75 item test with r=.95 – 40 item test has r=.91 – 35 item test has r=.90 – 30 item test has r=.88 – 25 item test has r=.86 – 20 item test has r=.84 – 10 item test has r=.72 – 5 item test has r=.56 NOTE: See handout from STAR Technical Manual for exact cluster reliabilities. 5

Reliability Statistics for CST’s (see handout)  Note that CST reliabilities range from.90 to.95  Note that cluster reliabilities are consistent with those predicted by Spearman-Brown formula

Validity is the degree to which the test is measuring what was intended Types of test validity A.Predictive or Criterion (How does it correlate with other measures?) B.Content 1. How well does the test sample from the content domain? 2. How aligned are the items with regard to format and rigor 7

Validity Is Influenced by Reliability  Impact of Lower Reliability on Validity  Remember: Validity is the agreement between a test score and the quality it is believed to measure  Upper limit on validity coefficient is the square root of the reliability coefficient  75 item test = square root of.95 =.97 8

Validity Is Influenced by Reliability  Upper limit on validity coefficient is the square root of the reliability coefficient  75 item test =square root of.95=.97  30 item test= square root of.88=.94  20 item test= square root of.86=.93  10 item test = square root of.72=.85  5 item test = square root of.56=.75 9

Coefficient of Determination (R squared)  Square of validity coefficient gives “proportion of variance in the achievement construct accounted for by the test”  75 item test =.97 squared=.94  30 item test=.94 squared=.88  20 item test=.93 squared=.86  10 item test=.85 squared=.72  5 item test=.75 squared=.56 10

Using Item Statistics (p-value & point- biserials)  Apply item analysis statistics from assessment reporting system (e.g. Datadirector, Edusoft, OARS, EADMS, etc.)  P-values (percent of group getting item correct  Most should be between 30 and 80  Very high indicates it may be too easy; too low may indicate a problem item  Point-biserials (correlation of item with total score)  Most should be.30 or higher  Very low or negative generally indicates a problem with the item

Item statistics for CST’s (see handout)  Note that the range of P-values is consistent with most being between.30 and.80  Note that median point-biserials are generally in the 40’s

Algebra 1

Algebra 2

Geometry

18 Maximizing Predictive Accuracy of District Benchmarks Objective Extend knowledge of assessment team to: 1. Better understand how performance level setting is key to predictive validity. 2. Better understand how to create performance level bands based on equipercentile equating

19 Comparing District Benchmarks to CST Results Common Methods for Setting Cutoffs on District Benchmarks:  Use default settings on assessment platform (e.g. 20%, 40%, 60%, 80%)  Ask curriculum experts for their opinion of where cutoffs should be set  Determine percent correct corresponding to performance levels on CSTs and apply to benchmarks

20 Comparing District Benchmarks to CST Results There is a better way!

21 Comparing District Benchmarks to CST Results “Two scores, one on form X and the other on form Y, may be considered equivalent if their corresponding percentile ranks in any given group are equal.” (Educational Measurement-Second Edition, p. 563)

22 Comparing District Benchmarks to CST Results  Equipercentile Method of Equating at the Performance Level Cut-points  Establishes cutoffs for benchmarks at equivalent local percentile ranks as cutoffs for CSTs  By applying same local percentile cutoffs to each trimester benchmark, comparisons across trimesters within a grade level are more defensible

23 Equipercentile Equating Method Step 1-Identify CST SS Cut-points

24 Equipercentile Equating Method Step 2 - Establish Local Percentiles at CST Performance Level Cutoffs (from scaled score frequency distribution)

25 Equipercentile Equating Method Step 3 – Locate Benchmark Raw Scores Corresponding to the CST Cutoff Percentiles (from benchmark raw score frequency distribution)

26 Equipercentile Equating Method Step 4 – Validate Classification Accuracy – Old Cutoffs

27 Equipercentile Equating Method Step 4 – Validate Classification Accuracy – Old Cutoffs

28 Equipercentile Equating Method Step 4 – Validate Classification Accuracy – Old Cutoffs

29 Equipercentile Equating Method Step 4 – Validate Classification Accuracy – New Cutoffs

30 Equipercentile Equating Method Step 4 – Validate Classification Accuracy – New Cutoffs

31 Equipercentile Equating Method Step 4 – Validate Classification Accuracy – New Cutoffs

32 Example: Classification Accuracy Biology OldNew 2 nd Semester Proficient or Advanced42%77% Each Level38%55% 1 st Semester Proficient or Advanced30%77% Each Level31%50%

33 Example: Classification Accuracy Biology OldNew 1 st Quarter Proficient or Advanced53%71% Each Level41%46%

34 Example: Classification Accuracy Chemistry OldNew 2 nd Semester: Prof. & Adv. 63%79% 2 nd Semester: Each Level 47%52% 1 st Semester: Prof. & Adv. 74% 1 st Semester: Each Level 49%50% 1 st Quarter: Prof. & Adv. 83%76% 1 st Quarter: Each Level 48%47%

35 Example: Classification Accuracy Earth Science OldNew 2 nd Semester: Prof. & Adv. 48%68% 2 nd Semester: Each Level 43%52% 1 st Semester: Prof. & Adv. 33%66% 1 st Semester: Each Level 38%47% 1 st Quarter: Prof. & Adv. 42%56% 1 st Quarter: Each Level 34%41%

36 Example: Classification Accuracy Physics OldNew 2 nd Semester: Prof. & Adv. 57%87% 2 nd Semester: Each Level 37%57% 1 st Semester: Prof. & Adv. 60%88% 1 st Semester: Each Level 42%50% 1 st Quarter: Prof. & Adv. 65%87% 1 st Quarter: Each Level 47%45%

37 Things to Consider Prior to Establishing the Benchmark Cutoffs  Will there be changes to the benchmarks after CST percentile cutoffs are established?  If NO then raw score benchmark cutoffs can be established by linking CST to same year benchmark administration (i.e. spring 2011 CST matched to 2010-11 benchmark raw scores)  If YES then wait until new benchmark is administered and then establish raw score cutoffs on benchmark  How many cases are available for establishing the CST percentiles? (too few cases could lead to unstable percentile distributions)

38 Things to Consider Prior to Establishing the Benchmark Cutoffs (Continued)  How many items comprise the benchmarks to be equated? (as test gets shorter it becomes more difficult to match the percentile cutpoints established on the CST’s)

39 Summary Equipercentile Equating Method  Method generally establishes a closer correspondence between the CST and Benchmarks  When benchmarks are tightly aligned with CSTs, the approach may be less advantageous (i.e. elementary math)  Comparisons between benchmark and CST performance can be made more confidently  Comparisons between benchmarks within the school year can be made more confidently

40 Coming Soon from Illuminate Education, Inc.! Reports using the equipercentile methodology are being programmed to: (1) establish benchmark cutoffs for performance bands (2) create validation tables showing improved classification accuracy based on the method

Contact: Tom Barrett, Ph.D. President, Barrett Enterprises, LLC Director, Owl Corps, School Wise Press 2173 Hackamore Place Riverside, CA 92506 951-905-5367 (office) 951-237-9452 (cell) 41

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