The inappropriateness of using WADA to compare revenues between Texas’ charters and school districts: a mathematical analysis

Larry Toenjes^*

At the meeting of the Texas Senate Education Committee on December 7, 2015 several persons, senators as well as guests, said that evidence shows that Texas charters receive more maintenance and operations (M&O) revenues per students in average daily attendance (ADA) than do Texas’ independent school districts (ISDs).

But charter proponents, as well as Dr. Lisa Dawn-Fisher of the Texas Education Agency (TEA), said that when revenues are compared using weighted students (WADA), rather than ADA, as the divisor, charters receive less M&O revenue per WADA than do ISDs. Dr. Fisher said something to the effect that both methods are valid; they just give contradictory results!^[1]

This author testified to that committee, however, that comparisons between charters and ISDs made using WADA are invalid. This author also said that the current formula for charters that applies the arithmetic average of the adjusted allotments (AAs) of all individual ISDs, not only gives charters more M&O revenues per ADA than ISDs receive. But, in addition, the higher M&O amounts of necessity, by virtue of the structure embodied in the Texas school finance statutes, result in proportional inflation of charters’ calculated WADAs (see below). The consequence is that when the greater charter M&O amounts are divided by the inflated WADA numbers charters M&O revenues per WADA appear to be less than the M&O revenues for ISDs.

This conversion of M&O revenues to M&O revenues per WADA is central to charter proponents’ claims that charters suffer a $1,000 funding disadvantage relative to ISDs.

Simulation results

This author presented a four-page paper in writing to the Committee that clearly demonstrated these relationships, based on simulations for all charter systems in Texas, and the results aggregated across all charters. The following table is reproduced from that paper.

It can be seen from Table 1 that the $731 increase in the AA resulted in state aid increasing by 13 percent or $205 million, WADA increasing by 13 percent, and revenue per ADA increasing by 13 percent. But revenue per WADA decreased slightly, from $5,639 to $5,625. Charter proponents insist that dividing revenues by WADA is the “correct” way by which revenues per pupil between charters and ISDs should be compared^[2].

Table 1.

Relationships between AA, State Aid, WADA, and ADA for Texas Charter Schools as the AA is Increased from $5,534 to $6,265 (SY 2014-2015)

Adjusted Allotment (AA)	Revenue (State Aid)	WADA	Refined ADA	Revenue per ADA	Revenue per WADA	Ratio WADA/ADA

5,534	1,584,872,149	281,031	208,385	7,606	5,639	1.35
5,680	1,625,791,621	288,445	208,385	7,802	5,636	1.38
5,826	1,666,711,093	295,859	208,385	7,998	5,633	1.42
5,972	1,707,630,565	303,273	208,385	8,195	5,631	1.46
6,118	1,748,550,037	310,688	208,385	8,391	5,628	1.49
6,265	1,789,749,780	318,153	208,385	8,589	5,625	1.53

Data sources: Revenues and WADA calculated by author from TEA data for SY 2014-2015.

These results, shown in Table 1, are based on charter-by-charter calculations by the author of the 195 charter systems funded by the State of Texas during SY 2014-2015, using underlying data that TEA used in their own calculations on February 10, 2015.

Mathematical results

The examination of the relationships between AA, ADA, WADA, and M&O revenues for charters is repeated in this section but will be based on what might be called a mathematical approach.

This presentation is geared to readers with some acquaintance with Texas’ school funding mechanism and a familiarity with some of the commonly used terminology, such as AA, ADA, etc. Terms used explicitly in the following equations will first be described, after which the abbreviations will be used as if they were algebraic symbols, much as how y = 2x + 6 might be interpreted and manipulated if “y” and “x” are properly defined. The payoff of this approach is that the relationships for charters among the several concepts—AA, ADA, WADA, M&O revenues—can be unambiguously described and certain conclusions firmly drawn.

The analysis that follows is made possible by the fact that the critical calculations for all charters make use of identical values for 5 key parameters. This means, for example, that total state aid to charters can be described, and calculated, as a function of the adjusted allotment, making use of the values of the parameters which are based on the statewide arithmetic averages of the corresponding values that are actually calculated individually for each of these parameters for each ISD.

Definition of terms:

TSTAID: Total state aid to charters under the foundation support program, including grants in Tier 1, the two enrichment levels, and allotments for transportation, high school, and one other funding program referred to as “Rider 71”, more completely as TRS Employer Contribution Assistance. These latter 3 allotments do not depend upon specific values of the adjusted allotment.

TFTE: Total of number of weighted students across all FSP categorical programs.

TRAN: Sum of all payments to charters for transportation purposes.

HS: Total for all charters’ high school allotments.

R71: Total for all payments to charters under Rider 71.

The following five factors are the statewide arithmetic averages of the corresponding elements that are calculated individually for each ISD:

AA: Statewide average adjusted allotment (which is multiplied times each FTE in each categorical program in determining the entitlement amount for each program).

DBA: Statewide average basic allotment, adjusted for the average amount by which districts’ compressed M&O tax rates fall below 1.00 per hundred dollars of assessed valuation.

CEIAdj: A factor that adjusts total level 1 entitlements, minus TRAN and HS, before dividing by the district basic allotment (DBA) to get WADA.

ET1: Amount a charter receives in tier 1 enrichment for each WADA pupil.

ET2: Amount a charter receives in tier 2 enrichment for each WADA pupil.

Several equations can now be developed which will express functions of interest.

(1) TSTAID = AA x TFTE +(ET1 + ET2) x WADA + (TRAN + HS + R71).

WADA is described by

(2) WADA = AA x TFTE x CEIAdj/DBA.

The expression for WADA in (2) is substituted into (1), and simplified, as follows:

TSTAID = AA x TFTE + (ET1 + ET2) x ((AA x TFTE x CEIAdj)/DBA) +C,

where C was substituted for the constant sum TRAN + HS + R71, and is equal to $33,818,232. Factoring AA x TFTE from the first two terms of the last equation results in

(3) TSTAID = AA x TFTE x (1 + ((ET1 + ET2) x CEIAdj/DBA) + C.

With all of the values in equation (3) other than AA determined, TSTAID can be calculated as a function of the adjusted allotment, AA. The following values, for SY 2014-2015, are known constants:

ET1 = 0.0535 x 100 x $61,86 = $330.951.

ET2 = 0.0502 x 100 x $31.95 = $160.389.

CEIAdj = 0.9732.

DBA = $4,893.

Substituting these last four values into equation (3) results in

(4) TSTAID = AA x TFTE x 1.097726 + C.

For SY 2014-2015 (as of Feb. 10, 2015) TFTE for charters was approximately 255,319, and C, as noted above, is equal to $33,818,232. While C is would not be affected by changes in AA, C is relatively small compared to the product of AA x TFTE x 1.097726. Consequently, if AA were increased TSTAID would increase nearly in direct proportion to the change in AA.

It can also be observed that since ADA would not be affected by any change in AA, if one were interested in TSTAID/ADA, this amount would also increase in almost exactly the same proportion as the change in AA. This can also be seen in the figures presented in Table 1, which were based on simulations for all charters.

Next, consider how TSTAID per WADA is related to the adjusted allotment, AA. Substituting the values for CEIAdj--0.9732--and for DBA--$4,893--in equation 2, we get the following expression for WADA:

(5) WADA = AA x TFTE x 0.0001989.

Dividing through equation (4) by WADA as expressed in equation (5) permits TSTAID per WADA to be written as

TSTAID/WADA = (AA x TFTE x 1.09772/WADA) + (C/WADA)

= (1.097726/0.0001989) + C/(AA x TFTE x 0.0001989).

Substituting values given previously for C and TFTE results in

(6) TSTAID/WADA = 5519 + 665,937/AA,

which gives TSTAID/WADA as function of the adjusted allotment, AA. This equation (valid for SY 2014-2015 only) demonstrates precisely why M&O revenues per WADA—designated as TSTAID/WADA in equation (6)—decrease slightly if AA is increased. If AA is larger, the ratio 665,937/AA becomes slightly smaller, so that when it is added to the constant 5519 the sum is slightly less.

To check the accuracy of equation (6) the largest and smallest values of AA used in developing Table 1 are substituted for AA, resulting in Table 2.

Table 2

Determining TSTAID per WADA using Equation (6)

Adjusted Allotment (AA)	TSTAID/WADA
$5,534	$5,639
$6,265	$5,625

As can be seen, the calculated amounts for TSTAID/WADA, which is labeled M&O per WADA in Table 1, are identical for the two values of AA for which they were calculated, using equation (6).

Conclusions

Based on the simulation results reported in Table 1 as well as the results based on the use of equation (6) above, an increase in the adjusted allotment of $731 actually caused a decrease in the M&O revenue per WADA, while the total M&O revenues to charters increased by $205 million. Relying upon such a measure—M&O revenue per WADA--to compare revenues per pupil between charters and ISDs is misleading, to say the least.

The minimum and maximum values of the adjusted allotment for which M&O state aid to charters were calculated were very specifically chosen. The value actually used in SY 2014-2015 by TEA, $6,265, was the actual arithmetic mean of all of the AA values for ISDs, determined individually, reflecting each district’s CEI and any scale adjustment to which each was entitled. The minimum value used, $5,534, was the weighted mean of the districts’ AAs, using ADA as the weights. Unweighted, the smallest district counts just as much as the largest in calculating the average. There are some 475 small districts enrolling just 4 percent of total ISD students, having very large scale adjustments, which inflated the average AA to the $6,265 value. The use of this value for the AA for charters results in charters receiving some $700 more per ADA than ISDs received, counting both state and local M&O revenues.

However, as equation (5) above shows, any increase in AA will increase WADA in the same proportion as the increase in AA. The increase in WADA due to an increase in AA is not in any way a result of increases in the numbers of more costly to educate students, or increased costs of any other nature, but is solely a result of the increase in the adjusted allotment.

Whether by chance or design, the current statutory method of funding charters gives them substantially more M&O revenue per ADA than ISDs receive, and hence, as Judge Dietz concluded, charters have a significant amount of extra M&O revenues, on average, as compared to ISDs, that can be, and presumably are, used to help cover facilities costs^[3].

What should not occur is that the inflated WADA numbers for charters be used to effectively hide those extra M&O revenues, and therefore support charter proponents’ contention that they suffer a $1,000 funding gap as compared to ISDs. The view that the inflated WADA counts for charters are justified could not be further from the truth. It is no wonder that charter proponents are so adamant in insisting that the use of “weighted students”, i.e., WADA, provides the best and “undisputed” method of comparing per pupil revenues between charters and ISDs^[4]. This argument is based either on ignorance or a desire to obfuscate. The second option comes to mind when spokespersons for KIPP Inc, Houston, make the claim that a school district such as Alief ISD receives nearly $1,000 more in total funding “per weighted student” than does KIPP or any other charter school in the Houston area^[5]. In fact, based on TEA data for SY 2014-2015, there was only a $2 per ADA difference between KIPP Inc and Alief ISD, even including facilities money for Alief ISD. Compared to Houston ISD KIPP Inc received over $200 more per ADA than did Houston ISD, again, when including Houston’s facilities monies in the comparison.

It is also inexcusable when a senior employee of the Texas Education Agency tells members of the Senate Education Committee that comparisons of revenues between charters and ISDs can be made with either ADA or WADA—both are valid, but unfortunately they give conflicting results^[6]. There should at least be some effort in trying to explain why the two measures give conflicting results. With that understanding, the conclusion is inevitable: WADA should not be used in making comparisons of revenue per pupil between charters and ISDs. A recently-released study performed by the highly-respect Austin firm Moak, Casey and Associates for the organization Raise Your Hand Texas arrived at the same conclusion, namely “In the case of comparing charters to traditional ISDs, revenue or expenditures per WADA are not proper comparisons.”^[7]

Given the results above, and the conclusions reached in the Moak, Casey and Associates study, there will be no excuse for future considerations of State of Texas grants to charter schools to proceed on the basis of using WADA to assess the sufficiency and equity of those grants.

^* Toenjes may be reached at ltoenjes@aol.com .

^[1] Attempting to transcribe Dr. Fisher’s remarks beginning at approximately 1:39 on the recording of the meeting, she says: “David [Dunn] is talking about weighted students and the Judge [Dietz] is talking about unweighted students. Both of these statements are true…On an unweighted basis charters tend to have more money than an ISD does in operations. But when you look at that same funding on a weighted student basis it looks smaller.”

What Dr. Fisher fails to acknowledge is that the higher M&O revenues going to charters as a result of the effects of small districts’ scale adjustments increases also the WADA amounts, which then results in a deflation of the higher operations revenues. This failure is what this paper is concerned with.

David Dunn added comments to the effect that WADA analysis “takes into account the numbers of compensatory education students, etc.” Another of the myths asserted by charter advocates is that charters have a greater proportion of more costly to educate students than do ISDs. This assertion is not correct. For SY 2014-2015 charters had a greater proportion of FSP grants in regular student grants than did ISDs, meaning that ISDs therefore had a greater proportion of total grants in the non-regular, more costly categories, than did charters.

^[2] This insistence could be counter-productive, since these calculations demonstrate that charter revenues per WADA would increase when total funding is reduced!

^[3] In his ruling Judge Dietz drew the following conclusion [FOF 1505]:

“Charters accordingly have access to revenue in excess of what is available to school districts, and that revenue is available to meet charter schools’ facilities needs.”

The Texas Charter School Association (TCSA) and its supporters disagreed with Judge Dietz’s ruling. They filed a Brief with the Texas Supreme Court to try to get this part of his ruling reversed. In their Brief, the Charters’ attorneys asserted the following:

“First, it is undisputed that charter schools receive at least $1,000 less per student than other public schools.” [Brief, p. xii]

The Charters are so determined to convince the Supreme Court that this shortfall is a reality that they refer to it repeatedly throughout the Brief, asserting that the $1,000 gap is “undisputed” at least 18 times. This calls to mind Queen Gertrude’s line in Hamlet, namely “The lady doth protest too much, methinks.” [Hamlet Act 3, scene 2, 222-230]

^[5] “Charter school inequality?”, David Dunn and Mike Feinberg, Houston Chronicle, February 3, 2014.

^[6] This is reminiscent of a frequent statement by my original mentor in Texas school finance, Dr. Billy D. Walker, now deceased. Billy said he would always tell his high school geography class, at the beginning of each semester, “I can teach it round, or I can teach it flat.”