What is a Z Score?

The State’s Waiver from NCLB All schools will achieve 85% proficiency for all students in all subjects (as measured on a statewide assessment) by Reward Schools ◦Highest Performing ◦Beating the Odds ◦Exceeding 85% ◦Highest Progress Focus Schools ◦The ten percent of schools with the largest gaps in student results (as identified by statewide assessments) between high and low-achieving students within a school. (Approximately 356 schools) Priority Schools ◦Schools in the bottom five percent on the state’s Top-to- Bottom list. These schools are placed under the jurisdiction of the School Reform Office and are required to rapidly turnaround, transform, restart or close. (Approximately 150 schools)

Ranking Schools Understanding the Use of Z-Scores in the Top to Bottom Ranking Selected Slides from Michigan Department of Education Materials provided by MDE

Thoughts on Ranking Schools To rank schools: – Have to compare them on a similar metric Example: MEAP Scale Score for 3 rd grade: 315 MME Scale Score for 11 th grade: 1100 How do you compare a school of 3 rd graders to a school of 11 th graders?

Example: Can’t add up all scale scores and divide by number of students, because the scores have different meanings Need to put all assessment scores on the same metric so that you can combine: ◦Across grades ◦Across test types ◦Across subjects

The answer: Z-scores! We can use z-scores to: ◦Level the playing field across grade levels and subjects ◦Talk about a student’s score in terms of distance from the statewide average for all similar students ◦Talk about a school value (such as average achievement or improvement) in terms of that school’s distance from the statewide average for all similar schools

Z-Score “Cheat Sheet” Z-scores are centered around zero Positive numbers mean the student or school is above the state average Negative numbers mean the student or school is below the state average State Average Better than state average….…Worse than state average

Z-Score Examples Your school has a z-score of 1.5. You are better than the state average State Average Better than state average….…Worse than state average Z-score of 1.5

Z-Score Examples Your school has a z-score of.2. You are better than the state average, but not by a lot State Average Better than state average….…Worse than state average Z-score of 1.5 Z-score of 0.2

Z-Score Examples Your school has a z-score of You are very far below state average State Average Better than state average….…Worse than state average Z-score of 1.5 Z-score of 0.2Z-score of -2.0

How do we use Z-Scores in the TTB? Understanding Z-Scores

Two main ways 1) To compare student test scores to other student test scores, and to combine all those test scores into school-level values 2) To compare school-level values (like school achievement, improvement, and gaps) to other schools

How do we get Standardized Scale Scores for Each Student? Step #1: Take each student’s score on the test they took and compare that score to the statewide average for students who took that same test in the same grade and year This creates a student-level z-score for each student in each content area – Compare MEAP to MEAP MEAP-Access to MEAP-Access MME to MME MI-Access – Participation to Participation – Supported Independence to Supported Independence – Functional Independence to Functional Independence

What do we do with those standardized scores? Step #2: Once each student has a z-score for each content area (based on the test they took), we take all of the students in a each school, and rank order the students within the school. – Z-scores will have come from different tests, and compare students to statewide average for that grade, test, and subject – But they can now be combined for the school Step #3: Add up all z-scores and take the average. This is now the average standardized student scale score. Step #4: Define the top and bottom 30% subgroups, based on that rank ordering.

StudentTest TakenZ-score TommyMi-Access, Participation 2.5 SallyMEAP2.0 MauraMI-Access, SI1.9 FredMEAP1.5 IchabodMEAP-Access1.0 FreudMEAP0.8 MaybelleMI-Access, FI0.7 DestinyMEAP0.5 HaroldMEAP-0.2 BickfordMI-Access, FI-0.5 TalledagaMEAP-Access-0.7 FrancineMEAP-1.2 JoeyMEAP-1.9 WilliamMEAP-2.2

StudentTest TakenZ-score TommyMi-Access, Participation 2.5 SallyMEAP2.0 MauraMI-Access, SI1.9 FredMEAP1.5 IchabodMEAP-Access1.0 FreudMEAP0.8 MaybelleMI-Access, FI0.7 DestinyMEAP0.5 HaroldMEAP-0.2 BickfordMI-Access, FI-0.5 TalledagaMEAP-Access-0.7 FrancineMEAP-1.2 JoeyMEAP-1.9 WilliamMEAP-2.2 Average Z-score (average standardized student scale score): 0.28 (sum all z-scores, divide by 15)

StudentTest TakenZ-score TommyMi-Access, Participation2.5 SallyMEAP2.0 MauraMI-Access, SI1.9 FredMEAP1.5 IchabodMEAP-Access1.0 FreudMEAP0.8 MaybelleMI-Access, FI0.7 DestinyMEAP0.5 HaroldMEAP-0.2 BickfordMI-Access, FI-0.5 TalledagaMEAP-Access-0.7 FrancineMEAP-1.2 JoeyMEAP-1.9 WilliamMEAP-2.2 Top 30% Bottom 30%

How do we compare school z- scores? We calculate school-level values for the following components in every subject: – Achievement – Improvement – Achievement gap Then we calculate overall values for each subject that combine those three components The school z-scores compare each school’s value to the average value for other similar schools

How is the TTB ranking calculated? Each subject area test is 20% If a building awards a diploma, the graduation rate is 10% and each of the five content areas are weighted at 18%. If a building doesn’t have a content area, the weight of the other content areas are modified equally to reach 100%. End of MDE Material

Z Scores and TTB Ranking: 2014 How does it look in a real Focus school?

Pleasantview Middle School Year Publicized Overall School Index TTB Percentile Rank Focus Year

Mathematics E/MS Math Yr Ave % Proficient: Achievement: Z: Improvement (PLC): Z: Index: Z: Achievement Gap: Z:

Reading E/MS Reading Yr Ave % Proficient: Achievement: Z: Improvement (PLC): Z: Index: Z: Achievement Gap: Z:

Science E/MS Science Yr Ave % Proficient: Achievement: Z: Improvement: Z: Index: Z: Achievement Gap: Z:

Social Studies E/MS Social Studies Yr Ave % Proficient: Achievement: Z: Improvement: Z: Index: Z: Achievement Gap: Z:

Writing E/MS Writing Yr Ave % Proficient: Achievement: Z: Improvement: Z: Index: Z: Achievement Gap: Z:

Trend Data TTB Rankings

Pleasantview Middle School School Z Score Analysis: ContentYearAchievementImprovementGap Mathematics Reading Science Social Studies Writing

Table Talk How would you explain your school’s TTB ranking to building administrators? Teachers? How might you assist your school in explaining these data to parents? School board? What further assistance or questions do you have around the Z score and the Top to Bottom Ranking?