Use of Confidence Intervals in Performance Improvement Appeals. Performance Reporting Division Texas Education Agency. Overview of CI Process. Eligibility for application of CI Matched pairs of students Recalculate performance improvement Recalculate required improvement
Performance Reporting Division
Texas Education Agency
RI = 100 – ppy
UL = PI + [(z/sqrt(n))*sqrt((ppy*(1-ppy))+(pcy*(1-pcy))+(2*((ppy*pcy)-ppc))]
UL = Upper limit of the Wald confidence interval
PI = recalculated performance improvement rate (pcy - ppy)
z = z-score for selected confidence level (for a 68% CI, z = 0.47)
n = number of matched pairs
ppy = performance (passing rate) of matched pairs in prior year
pcy = performance (passing rate) of matched pairs in current year
ppc = performance (passing rate) of matched pairs in prior year and current year
We generate a range of potential PI values based on the recalculated PI and its standard error to get a normal curve.
Calculating the upper limit using the Wald formula gives us a range (or interval) of PI values we are confident the true PI value falls in (the green area).
If RI falls within CI (green area) then appeal for CI is granted!
If RI falls outside the CI, then appeal is denied.
NOTE: Because RI will never be less than zero, the real area of interest is the portion of the green area between 0 and the UL.
2005 Preliminary AYP a range (or interval) of PI values we are confident the true PI value falls in (the green area).
(Reading, Special Education group)
2005 Met Standard = 49%
2004 Met Standard = 44%
Change (PI) = 5%
RI = 6%
0.1% improvement on other measure
FAILS SAFE HARBORExample from an Actual Appeal
(Matched pair data)
NOW MEETS AYP