1. Evaluating Pretest to Posttest Score Differences in CAP Science and Social Studies Assessments: How Much Growth is Enough? February 2014 Dale Whittington, Ph.D. – Shaker Heights Russ Brown, Ph.D – CMSD Denis Jarvinen, Ph.D. – Strategic Measurement and Evaluation, Inc.

2. Licensing Tests (e.g., Pharmacists) State Accountability Testing (e.g., Ohio OAA) CAP Foundation Science and Social Studies Assessments One Test and One Standard for Performance Pass or Fail One Test, Multiple Standards Below Basic, Basic, Proficient, Advanced Two Tests, One Standard Evaluating Growth (How Much?) Setting Standards for Performance

3. Looking at Performance Standards Content-Based Standards Goal of standard setting is to determine a level of knowledge and skill judged to be appropriate for test purpose Growth-Based Standards Goal of standard setting is to use common statistical feature(s) of the data to set a criteria for acceptable performance

4. Three Statistic-Based Approaches for Evaluating Growth of Student Scores Using Effect Size Using The Score Distribution Using the Standard Error of Measurement

5. Describing and Comparing Approaches Data Points Needed Calculations Required Outcomes Using a Common Set of Student Data Advantages and Disadvantages

6. The Common Data Set

11. Shaker Heights Schools Prepared by Dale Whittington Shaker Heights City School District Ohio Middle Level Annual Conference Columbus, Ohio February 21, 2014 Effect Size for SLO’s and Growth

12. What is effect size? In an educational setting, effect size is one way to measure the effectiveness of a particular intervention. Effect size enables us to measure both the improvement (gain) in learner achievement for a group of learners AND at the same time, take into account the variation of student performance. Adapted from Understanding, using and calculating effect size, Govt of South Australia, Department of Education & Child Development, http://www.decd.sa.gov.au/quality/files/links/WhatIsEffectSize.pdf

13. Practical Advantages Easy to calculate Easy to understand; makes intuitive sense Adaptable to different kinds of assessments Adaptable to different kinds of ways of considering growth and goals for SLO’s: –Shared attribution across the district –Shared attribution within a school –Attribution for a specific teacher or group of students

14. So how do you calculate effect sizes for SLO’s or growth? StudentPretestPosttest Denis4035 Donna2530 Dale4550 Russ3040 Difference (AKA Gain) -5 +5 +10 Start with a set of pretest scores and posttest scores for the same students Calculate the difference between the pretest & posttest for each student

15. Calculations Continued Pretest –Mean: 35.0 –SD: 9.1 Posttest –Mean: 38.8 –SD: 8.5 The average of 9.1 and 8.5 is 8.8 Calculate the means and standard deviations for both tests Average the Standard Deviations

16. How to adapt If your pretest and posttest are different lengths, convert to a similar scale, like percentages. Think about who you are basing your analysis on and use that to decide what standard deviation (SD) to use –Common attribution for district: District SD –Common attribution for school: School SD –Class: Class SD –Specific group, such as economically disadvantaged: the group’s SD

17. Use the average standard deviation and the gains to calculate the effect size: StudentPretestPosttestGainEffect Denis4035-5-.57 Donna2530+5+.57 Dale4550+5+.57 Russ3040+10+1.14 Effect Size=Gain/SD

18. Interpret your results: Common criteria Cohen (1969) ‘Small’ (.2) o real, but difficult to detect o difference between the heights of 15 year old and 16 year old girls in the US ‘Medium’ (.5) o ‘large enough to be visible to the naked eye’ o difference between the heights of 14 & 18 year old girls ‘Large’ (.8) o ‘grossly perceptible and therefore large’ o difference between the heights of 13 & 18 year old girls Hattie: “For students moving from one year to the next, the average effect size across all students is 0.40.”

19. How results differ, depending on attribution and how you tier students

20. Another Example based on OAA

22. Resources Understanding, using and calculating effect size. Government of South Australia, Department of Education & Child Development, http://www.decd.sa.gov.au/quality/files/links/WhatIsEffectSize.pdf Review Methods/Interpreting Effect Sizes. JHU: Best Evidence Encyclopedia. http://www.bestevidence.org/methods/effectsize.htm Calculating an effect size: a practical guide. Visible Learning Plus. http://visiblelearningplus.com/faqs/calculating-effect-size-practical-guide

23. Establishing Growth Targets with Limited Data Prepared by Russ Brown, Ph.D – CMSD

24. Design Principles for Student Growth Model work The PROBLEM! An Idea for a Solution Strengths/Weaknesses Overview

25. 1. Equity - like measures for like teachers, like expectations for like students. 2. Simplicity - Parsimony and transparency are critical. 3. Continuous improvement will be critical – It simply will not be perfect on the first try! Guiding Principles

26. The PROBLEM How much growth is enough? How do you estimate this when you don’t know the relationship between the two tests? ?

27. What do we know? 1. Basic information about the distribution of scores. 2. The relative position of each student on the distribution. Can we leverage this to set targets? TimeMeanSD Pretest24.289.6

28. The Idea 1. Devoid of any way to estimate what growth “should be”… 2. Students of like ability (ie., same pretest scores) would typically be expected to make comparable growth over time. 3. Use Normal Curve Equivalents as a means to establish targets and relative growth.

29. How 1. Translate Pre-Test scores to NCEs Z= (Pretest Score - Mean Pretest Score) Standard Deviation of the Pretest NCE = (Z x 21.063)+ 50 (1-99 Interval) ClassPretest Pre- Mean SDPre-Z Pre- NCE Class18.024.39.6-1.714.2 Class19.024.39.6-1.616.4 Class19.024.39.6-1.616.4

30. Outcomes – What Threshold? Calculating whether the goal is obtained: Must make a judgment about the stringency of the goal/calculation Class Pre- NCE Post- NCE NCE Change Stringency of Goal 0-5-7.5 Stu 114.23.2-11.1No Stu 216.47.6-8.9No Stu 316.49.0-7.4No Yes Stu 418.611.9-6.7No Yes

31. Outcomes – What Performance Level? Percent of students achieving the Goal Teacher Growth Rating Translation 90- 100%5Above 80-89%4Met 70-79%3Met 60-69%2Met 0-59%1Below

32. Outcomes – What Performance Level? Group Percent of Students Reaching the Goal Mean Gain 0-5-7.5 Class 11- 12.0%1- 20.0%1- 52.0%24.04 Class 24- 84.0%5- 92.0% 37.88 Class 31- 44.0%1- 52.0%2- 60.0%34.44 Class 41- 44.0%1- 56.0%2- 64.0%34.76 Not surprisingly – outcomes vary by the stringency of the expectation…

33. Outcomes – Quick Comparison Group Percent of Students Reaching the Goal Mean Gain 0-5-7.5 Class 11- 12.0%1- 20.0%1- 52.0%24.04 Class 24- 84.0%5- 92.0% 37.88 Class 31- 44.0%1- 52.0%2- 60.0%34.44 Class 41- 44.0%1- 56.0%2- 64.0%34.76 Percent of Students Reaching the Goal (SEM) Group3 SE2 SE1 SEMean Gain Class 11- 44%4 -88%5- 100%24.04 Class 25- 96%5- 100% 37.88 Class 31- 52%1- 56%3- 76%34.44 Class 41- 48%2 – 60%3- 76%34.76

34. Outcomes – What about Real Data? Applied to 3 rd Grade OAA (Fall to Spring): Percent of students achieving the Goal Building Growth Rating TranslationIRN Count 90- 100%5Above0 60-89%2-4Met37 0-59%1Below36

35. Outcomes – What about Real Data? Applied to 4 th Grade Benchmark to OAA (Fall to Spring): Percent of students achieving the Goal Building Growth Rating TranslationIRN Count Mean Value Add Index 90- 100%5Above21.96 60-89%2-4Met50-.68 0-59%1Below13-1.56

36. Pros and Cons + Students with like scores have like expectations for growth + Relatively simple and relatively transparent - Must make a value judgment about the amount of error for which one wishes to compensate (not so transparent) -More adjustment = more bias at the bottom

37. Standard Error of Measurement All scores have a “true” score and “error” Error bands on score reports Standard Error quantifies degree of “error” in a test score Formula is: Standard Error of Measurement = Values needed: Mean, Standard Deviation, Reliability of the Test Assumptions that underlie this approach

38. Steps 1) For a set of data, calculate the mean and standard deviation 2) Calculate the reliability of the test 3) Use the formula to determine the Standard Error of Measurement (class level, school level) 4) Set a level for the growth standard (1 se, 2 se, etc.) 5) Add chosen level of standard error to raw score 6) Convert (raw score + standard error) to percent correct on pretest 7) Find corresponding percent correct/raw score on posttest (Note: Assumptions here not required once IRT equating is completed) 8) Compare actual student posttest score with target score 9) At or above target score = “Acceptable Progress”

39. Calculations for one student

40. Results

41. Observations High pretest scores can lead to out-of-range posttest score targets. Any modification to the sample that increases the Standard Deviation will increase the value of the Standard Error and therefore require more score growth to reach the target.