
737 F.Supp. 120 (1990)
COMMONWEALTH OF MASSACHUSETTS, on behalf of the DEPARTMENT OF PUBLIC WELFARE OF the COMMONWEALTH, Plaintiff,
v.
UNITED STATES of America, Richard E. Lyng, Secretary of the United States Department of Agriculture, Orval Kerchner, George Marienthal, and Lawrence Slagle, members of the State Food Stamp Appeals Board, Robert E. Leard, Administrator of the Food and Nutrition Service, U.S. Department of Agriculture, and Harold T. McLean, Regional Administrator of the Northeastern Regional Office of the Food and Nutrition Service, U.S. Department of Agriculture, Defendants.
Civ. A. No. 86-2132-Y.
United States District Court, D. Massachusetts.
April 27, 1990.
*121 Douglas H. Wilkins, Asst. Atty. Gen., Boston, Mass., for plaintiff.
Asst. U.S. Atty. Jeffrey Martin, Steven Zelinger, U.S. Dept. of Justice, Washington, D.C., for defendants.

MEMORANDUM OF DECISION CONCERNING THE FOOD STAMP QUALITY CONTROL AND SANCTION PROCESS
YOUNG, District Judge.
The plaintiff Commonwealth of Massachusetts (the "Commonwealth" or "Massachusetts") has filed a motion for summary judgment to set aside a decision of the United States Department of Agriculture (the "Department") imposing a monetary sanction on Massachusetts for excessive errors in the Commonwealth's administration of the Food Stamp Program (or the "Program"). Specifically, Massachusetts claims that the sanction is void because the Department violated its own regulations and reviewed too many sample cases in determining the Commonwealth's error rate. In addition to arguing that the Commonwealth's motion should be denied, the United States maintains that it should be granted partial summary judgment on the issue of whether the monetary sanction is void because of the Department's oversampling.
The Food Stamp Program is administered at the national level by the Food and Nutrition Service ("Service" or "FNS") of the Department. At the state level, each participating state is responsible, through its agencies, for certifying applicant households and coordinating the distribution of monthly benefits. While the federal government reimburses the states for the full value of the food stamp benefits distributed, it pays only part of a state's administrative expenses associated with that distribution. 7 U.S.C. sec. 2025(a) (1982).[1] The Service may reduce the percentage of administrative expenses paid by the federal government upon finding that a state has failed to comply with a Program requirement. 7 C.F.R. sec. 275.25(d)(1) (1982). Noncompliance is reflected by the payment error rate assigned to each state agency by the Service.
One way that the Service may properly reduce federal funding is through application *122 of its quality control and sanction process (sometimes referred to as "QC"). 7 U.S.C. sec. 2025(d). Through its quality control procedures, the Service assigns to each state agency administering the Food Stamp Program a "target" payment error rate.[2] From time to time, the Service calculates an actual payment error rate that purports to reflect cases in which the state agency determined a family to be eligible for benefits when it was not, or authorized benefits in excess of those to which a family was entitled. To determine the actual error rate, the state agency is required to select a sample of all cases and review them to determine whether they were correctly decided by the case worker. 7 C.F.R. secs. 275.10-11 (1982). Based on the sample, the state agency makes a determination of how many cases were decided erroneously, counts those erroneous decisions as errors, and calculates an error rate for that state.
The Service then selects a subsample of the state agency's sample and reviews it for accuracy. 7 C.F.R. sec. 275.3 (1982). If the Service determines that a case which the state agency has found to be correct is in error, there is a "federal difference" which is resolved by an arbitration review procedure. 7 C.F.R. sec. 275.3(c)(3)-(4). Those "federal differences" that are upheld in arbitration are weighed and, along with the other errors, are computed through a regression formula in order to arrive at a state's error rate. 7 C.F.R. sec. 275.25. This error rate, expressed as a percentage, is an estimate of the total number of errors present in a state's entire Food Stamp case-load. If a state's error rate exceeds the target error rate, it receives a sanction in the form of reduced federal reimbursement of its expenses associated with administering the Program. 7 C.F.R. sec. 275.25.
The Commonwealth here seeks further review of a $1,585,034 Food Stamp quality control penalty imposed upon it with respect to its 1982 administration of the Food Stamp Program. This appeal was first heard on March 27, 1986 by the State Food Stamp Appeals Board (the "Board"), the Department's administrative tribunal. In a decision dated June 23, 1986, the Board upheld $1,368,893 of the 1982 penalty.
Since that time, the Board has vacated penalties against other states on the grounds that the Service failed to comply with federal regulations and quality control manuals mandating the size of the federal subsample. According to the Board's more recent rulings, the federal subsample must be exactly one hundred and eighty (180) cases for the time period covered by the regulation relevant to that time period. The Board has held invalid and unenforceable quality control penalties based on more than 180 cases (oversampling)[3] as well as less than 180 cases (undersampling). In re: Louisiana, Administrative Review No. 5-87 (1988); In re: Pennsylvania, Administrative Review No. 8-87 (1988); In re: Utah, Administrative Review No. 21-85 (1986). In light of these favorable Board decisions, the Commonwealth prepared a motion to vacate a similar 1983 Food Stamp quality control penalty. That motion proved unnecessary because the Service voluntarily withdrew with prejudice the Commonwealth's 1983 penalty. With respect to the Commonwealth's 1982 penalty, however, the Service concedes that more than 180 cases were sampled, but now refuses to vacate the penalty, maintaining that it is valid and enforceable.
The Commonwealth here seeks to have the Board's 1986 decision reviewed, reversed, and the 1982 penalty vacated in its entirety.[4]
*123 The disputed regulation, 7 C.F.R. sec. 275.3(c)(1), provides:

Validation of States' Payment ... Error Rates. FNS shall validate each State's reported payment error rate during each 6-month quality control (QC) reporting period. Each validation review shall consist of the following actions.
(1) FNS will select a subsample of a State's completed sample. The Federal review sample size for completed active cases is determined by the following equation:
n1 = .14n + 50.31 where
n1 is the subsample size (maximum 180), and
n is the State's minimum required active sample size as determined by sec. 275.11(d)(1).
This number (n1) represents the minimum number of Federal review sample cases which must be selected and reviewed by a Regional office when conducting a validation review.
The dispute between the Commonwealth and the United States is over the numerical value to be assigned to n1. The position of the United States, as articulated by the Secretary of Agriculture (the "Secretary"), is that the regulation should be interpreted to mean that the Service need not review more than 180 cases in a sample (due to scarce resources), not that the agency is precluded from reviewing more than 180. On the other hand, both Massachusetts and the former Board maintain that the regulation requires that the Service select a subsample of exactly 180 cases.
The ultimate issue facing the Court is whether the 1982 penalty imposed on the Commonwealth is valid and enforceable, in light of the undisputed fact that the Service calculated the error rate from a subsample of greater than 180 cases. Before confronting that issue, however, the Court must work its way through a thicket of preliminary issues. First, the Court must determine whether there is an authoritative Departmental interpretation of the regulation concerned with subsample size. Second, if such an interpretation exists, the Court must determine how much deference to give it. It is only after making these determinations that the Court can determine the validity of the 1982 penalty imposed on the Commonwealth.
As to the first issue, the Court concludes that there is, in fact, an authoritative Departmental interpretation of 7 C.F.R. sec. 275.3(c)(1). That interpretation is the one initially accepted by the former Board: viz. that 7 C.F.R. sec. 275.3(c)(1) requires that the Service select subsamples of exactly 180 cases, neither more nor less. The former Board interpreted section 275.3(c)(1) pursuant to authority delegated to it by the Secretary of Agriculture in 7 C.F.R. sec. 276.7 (1982) and Departmental Regulation No. 1044-1 (September 18, 1981), which provides in relevant part that "the decision of the Appeals Board .... constitutes the final administrative determination of the Department of Agriculture and is binding on all parties." USDA Departmental Regulation No. 1044-1 at para. 7; see also 7 C.F.R. sec. 276.7. Because the Secretary delegated to the Board the final decision-making authority vested in him by the Food Stamp Act of 1977, 7 U.S.C. sec. 2023 (1982), including the duty to apply regulations defining the size of the Service's subsample, the interpretation of the former Board is in fact the final Departmental interpretation notwithstanding the Secretary's disavowal of it in this case.
Confirming this analysis, the relevant case law is firmly settled that in a dispute such as this one between an agency head and an agency tribunal to which the agency head has delegated decision-making authority, such delegation precludes the agency head from exercising that authority independently of the tribunal. United States v. Nixon, 418 U.S. 683, 694-97, 94 S.Ct. 3090, 3100-102, 41 L.Ed.2d 1039 (1974); Vitarelli v. Seaton, 359 U.S. 535, 79 S.Ct. 968, 3 L.Ed.2d 1012 (1959); Service v. *124 Dulles, 354 U.S. 363, 77 S.Ct. 1152, 1 L.Ed.2d 1403 (1957); United States ex rel. Accardi v. Shaughnessy, 347 U.S. 260, 266, 74 S.Ct. 499, 502, 98 L.Ed. 681 (1954). In essence, the former Board's decisions with respect to the interpretation of section 275.3(c)(1) are binding upon the Secretary as the authoritative agency interpretation, regardless of whether he adopts a contrary position. GTE International, Inc. v. Hunter, 649 F.Supp. 139 (D.P.R.1986).
There is no evidence that the Secretary has rescinded his delegation of interpretative authority to the Board. While the Court expresses no opinion as to whether "it is theoretically possible for the [Secretary] to amend or revoke the [Board's] authority," it does point out that, in this instance, "he has not done so." Nixon, 418 U.S. at 696, 94 S.Ct. at 3101. Nor has the Secretary attempted to supplant the Board's interpretation of section 275.3(c)(1) through a rule-making proceeding in accordance with section 4(c) of the Food Stamp Act, 7 U.S.C. sec. 2013(c), and section 553 of the Administrative Procedure Act, 5 U.S.C. sec. 553, as was done when he revised the regulation pertaining to Federal Subsamples taken after 1983. Cf. Batterton v. Marshall, 648 F.2d 694, 705-06 (D.C. Cir.1980) (holding that notice and comment rulemaking are required when an agency adopts a statistical methodology that "prescribes the regulatory structure through which the critical variable in the [agency's program] formula is attained"). Because the Secretary has made no attempt to overturn the former Board's interpretation pursuant to the relevant statutes and regulations, the former Board's interpretation must stand as the authoritative Departmental interpretation of 7 C.F.R. sec. 275.3(c)(1).
Second, the court must determine how much deference to give the authoritative Departmental interpretation of the regulation it has just derived. Although this Court has held that the interpretation of the former Board is the authoritative agency construction, the Court is of course not unmindful of the fact that the Secretary's construction is now, and apparently always has been, diametrically opposed to that of the former Board. While this Court is not swayed by the Secretary's construction in determining what constitutes the authoritative Departmental interpretation, it acknowledges that the instant case is not one in which the agency speaks with a single voice. Therefore, in analyzing the case law to determine how much deference is to be given the authoritative Departmental interpretation, this case must be distinguished from those in which there was no dispute within the agency as to the interpretation of the regulation. Accordingly, the Court gives less deference to the authoritative Departmental interpretation than courts generally give to agency interpretations of their own agency regulations precisely because of this interpretative dispute between the Secretary and the former Board. See Immigration & Naturalization Service v. Cardoza-Fonseca, 480 U.S. 421, 446-47 n. 30, 107 S.Ct. 1207, 1221 n. 30, 94 L.Ed.2d 434 (1987) ("An agency interpretation ... which conflicts with the agency's earlier interpretation is `entitled to considerably less deference' than a consistently held agency view."); Massachusetts v. Secretary of Health and Human Services, 899 F.2d 53, 58 (1st Cir. March 19, 1990); Immigration and Naturalization Service v. Cardoza-Fonseca, 480 U.S. 421, 446-47, 107 S.Ct. 1207, 1221 n. 30, 94 L.Ed.2d 434 (1987); cf. Mayburg v. Secretary of Health & Human Services, 740 F.2d 100, 105 (1st Cir.1984) (holding that the decisions of the Supreme Court do not always compel deference to agency interpretations of statutes, and that "sometimes a different, and more independent judicial attitude is appropriate").[5]
*125 It is well recognized doctrine that deference is to be given to the statutory interpretation made by an agency charged with enforcement of a statute. E.g., Udall v. Tallman, 380 U.S. 1, 16, 85 S.Ct. 792, 801, 13 L.Ed.2d 616 (1965); cf. Wilcox v. Ives, 864 F.2d 915, 924-26 (1st Cir.1988) (validity of agency's statutory interpretation must be determined through analysis of language, purpose, and history of the statute).
When the construction of an administrative regulation rather than a statute is in issue, deference is even more clearly in order. `Since this involves an interpretation of an administrative regulation a court must necessarily look to the administrative construction of the regulation if the meaning of the words used is in doubt.... [T]he ultimate criterion is the administrative interpretation, which becomes of controlling weight unless it is plainly erroneous or inconsistent with the regulation.'

Tallman, 380 U.S. at 16-17, 85 S.Ct. at 801 (quoting Bowles v. Seminole Rock Co., 325 U.S. 410, 413-14, 65 S.Ct. 1215, 1217, 89 L.Ed. 1700 (1945) (emphasis added); Massachusetts v. Secretary of Health and Human Services, 899 F.2d at 61-64.
Analysis by the Court of the language of 7 C.F.R. sec. 275.3(c)(1) reveals that "the meaning of the words used is in doubt." Tallman, 380 U.S. at 16, 85 S.Ct. at 801. On the one hand, the regulation states that "n1 is the sample size (maximum 180)" and that "[t]his number (n1) represents the minimum number of Federal review sample cases which must be selected and reviewed by a Regional office when conducting a validation review." 7 C.F.R. sec. 275.3(c)(1) (emphasis added). Because of the use of "maximum" and "minimum," the above passage, standing alone, would appear capable of no interpretation other than that the federal subsample must be exactly 180 cases. On the other hand, the same regulation also states that
[t]he Federal review sample size for completed active cases is determined by the following equation:
n1 = .14n + 50.31 where ...
n is the State's minimum required active sample size as determined by sec. 275.11(d)(1).
7 C.F.R. sec. 275.3(c)(1).
According to sec. 275.11(d)(1), n, the sample size, is determined in the following manner:
(d) Sample Size. (1) The number of active cases to be selected and reviewed by each State agency during a six-month reporting period shall be determined by the average monthly caseload as follows:


    ---------------------------------------------------------------------
    Average monthly households      | Required semiannual
                                    |      sample size
    --------------------------------|------------------------------------
    60,000 and over ..............  | n = 1200
    10,000 to 59,999 .............  | n = 150 + 0.021(N - 10,000)
    Under 10,000 .................  | n = 150
    where . . .
    (ii) N is the anticipated average monthly participating caseload subject to quality
    control review . . . .

7 C.F.R. sec. 275.11(d)(1).
To the mathematically minded, the inconsistency may be obvious. It is the duty of this Court, however, to assay an explanation. The part of 7 C.F.R. sec. 275.3(c)(1) first discussed above appears to require that n1 equal exactly 180 cases, while the part of that same regulation discussed *126 thereafter states that n1 is determined by means of the provided formula after first determining the value for n. If the provided formula is applied after first determining n, however, then it is only by coincidence that n1 would equal 180. In fact, there is only one case in which application of the provided formula yields the result of n equal to 180. That result only occurs when n, the sample size, equals 926, and n will equal 926 only when the number of average monthly households equals 46,952. In any other situation where the number of average monthly households does not equal 46,952, application of the formula produces an n1 that does not equal 180.[6]
In sum, a common-sense, straightforward reading of 7 C.F.R. sec. 275.3(c)(1) reveals that it seems to state both that (a) the value of n1 must equal exactly 180 and (b) the value of n1 will vary as the value of n varies, as n is determined by the number of average monthly households for a state. Therefore, because the meaning of the language of the regulation is in doubt, the Court must next consider the "administrative interpretation, which becomes of controlling weight unless it is plainly erroneous or inconsistent with the regulation." Tallman, 380 U.S. at 16-17, 85 S.Ct. at 801 (emphasis added).
Here, however, the authoritative Departmental interpretation derived from the decisions of the former Board (i.e., that n1 must equal exactly 180) is "plainly ... inconsistent with the regulation." Id. First, as already stated, that interpretation is inconsistent with the formula provided in 7 C.F.R. sections 275.3(c)(1) and 275.11(d)(1). See supra note 6. Second, that interpretation is inconsistent with the history of the regulation. While it may be true that the proposed initial rule on the Food Stamp error-rate sanction system did not provide a definition of the Federal subsample size, see 45 Fed.Reg. 65,932 (1980), and that the Service accepted the view of commenting states that "the Federal sample size ... should be valid and specified in the final regulations together with a description of the Federal review process," 46 Fed.Reg. 7,261 (1981), there is no evidence to suggest that the Service intended to limit itself to subsamples of exactly 180 cases. On the contrary, one of the statisticians who has been working with quality control in the Food Stamp Program since 1977 states:
If the formula resulted in sample sizes of more than 180 the formula was to be ignored and the minimum required sample size was to be 180 (thus the "maximum" 180). Our intentions in adding the word maximum was [sic] not to restrict the regions from selecting more than 180 cases but to keep them from being required to select more than 180 cases as the formula would have required if a "cap" was not imposed. We never intended nor gave out interpretations that said 180 was an absolute maximum not to be exceeded. At the time the regulations were being written this is what we wanted as the requirements for Federal subsampling.
Affidavit of Nicholas J. Manthos attached to Memorandum In Opposition to Louisiana's Motion to Vacate Sanction, In re Louisiana, Administrative Review No. 5-87 (1988).
Third, the authoritative Departmental interpretation is inconsistent with the purpose of the regulation. Because the federal government reimburses the states for up to half of the eligible state and local expenses associated with administering the Food Stamp Program, 7 U.S.C. sec. 2025, Congress, as an incentive to the states to administer the Food Stamp Program efficiently *127 and accurately, required the Department to impose monetary sanctions on states for excessive, erroneous payments of food stamp benefits.[7] The purpose of 7 C.F.R. sections 275.3(c)(1) and 275.11(d)(1) is to create a procedure by which the Service can determine each state's error rate efficiently and accurately. In this case, the Service appears to have selected a subsample of 194 cases[8] instead of 180 cases, a deviation of less than 10%. Therefore, the accuracy of the error rate determined from that subsample would theoretically be greaterand thus presumably more favorable to the Commonwealththan it would have been if the subsample size had been 180 cases.[9]
The selection by the Service of a subsample size of slightly more than 180 cases, of itself, was entirely consistent with the efficient and accurate determination of the Commonwealth's error rate.[10] Therefore, the authoritative Departmental interpretation, which would require dismissing a monetary sanction imposed by Congress in order to encourage accurate state administration of the Food Stamp Program solely on the grounds that the subsample size was greater than 180 cases without requiring a showing that a state had been prejudiced in some way by the inclusion of the additional cases, is inconsistent with the purpose of the regulation.

CONCLUSION
The Court holds that the interpretation of 7 C.F.R. sec. 275.3(c)(1) advanced by the Commonwealth is the authoritative Departmental interpretation, but that it is "plainly ... inconsistent with the regulation." Tallman at 16-17, 85 S.Ct. at 801. Because of this inconsistency, the Court gives little deference to the authoritative Departmental interpretation and instead concludes that 7 C.F.R. sec. 275.3(c)(1) does not require that the subsample to be reviewed by the Service contain exactly 180 cases. As a result, the Court denies the Commonwealth's motion for summary judgment and grants the United States' motion for partial summary judgment on the issue of whether the 1982 monetary sanction imposed on Massachusetts by the Service is invalid and unenforceable because the subsample reviewed by the Service exceeded 180 cases.
SO ORDERED.
NOTES
[1]  References to both the United States Code and the Code of Federal Regulations sections in this memorandum are to the statutes and regulations in effect for April-September 1982.
[2]  The target error rate is determined from estimates of the state error rate and the national error rate in the base period in a prior fiscal year. 7 C.F.R. sec. 275.25(d)(2) (1982).
[3]  In appealing its 1982 penalty to the Board, Massachusetts does not appear to have raised the oversampling issue. See Plaintiff's Statement of the Material Facts as to which There is No Genuine Issue to be Tried, paras. 14 and 18.
[4]  In view of the Service's concession that over-sampling is present here, one might have expected the Commonwealth tactically to have sought reconsideration of the imposition of the 1982 penalty from the Board itself in view of the above cited Board decisions condemning oversampling. It is perhaps a comment on the ever proliferating "judiciary" within the executive branch that the Departmentapparently stung by the reversals just citedhas replaced the Board wholesale with new personnel. See June 30, 1989 Memorandum of Acting Assistant Secretary for Food and Consumer Services, USDA ("Correction of SFSAB Erroneous Interpretation of 7 CFR Section 273.3(c)(1) 180-Case Subsample Regulation"), and letters from former Secretary Lyng and his successor, Secretary Yeutter, appointing new members of the Board.
[5]  In Mayburg, Judge Breyer makes two critical points with respect to the issue of whether a court should defer to an agency interpretation of a statute. First, "under Skidmore [v. Swift & Co., 323 U.S. 134, 65 S.Ct. 161, 89 L.Ed. 124 (1944)] the agency ultimately must depend upon the persuasive power of its argument. The simple fact that the agency has a position, in and of itself, is of only marginal significance." Id. at 106. Second, the less important the question of interpretation, the more likely that Congress would have intended that the courts defer to the agency's interpretation. Id.

In this case, because of the interpretive conflict between the Secretary and the former Board, and for the reasons detailed infra at 125-26, the Court finds little persuasive power in the position of the former Board. In addition, because the monetary sanction at issue here is in excess of one million dollars and embodies the congressional intent to spur accuracy in the administration of the Food Stamp Program, the Court is unable to conclude that this interpretive question is unimportant.
[6]  The equations which support these conclusions are as follows. First, we start with n1 equal to 180 and plug that value into the equation at 7 C.F.R. sec. 275.3(c)(1) in order to solve for n.
     n1 = .14n + 50.31
    180 = .14n + 50.31
  129.69 = .14n
       n = 926.35714 (approximately = 926)

The value for n just calculated is plugged into the equation at 7 C.F.R. sec. 275.11(d)(1) in order to solve for N, the number of average monthly households.
   926 = 150 + 0.021(N - 10,000)
0.021N = 926 - 150 + 210
0.021N = 986
     N = 46,952

[7]  See, e.g., Food Stamps Act Amendments of 1980, H.R.Rep. No. 788, 96th Cong., 2d Sess., reprinted in 1980 U.S.Code Cong. & Admin. News 843, 910-11; id., 1980 U.S.Code Cong. & Admin.News at 902 ("[T]he Committee would like to improve the management of the program and increase public confidence in its conduct both by rewarding those States that make acceptable efforts to reduce their error rates ... and by penalizing those States that fail to make satisfactory progress. The Committee is convinced that this combined approach will substantially improve program operations and will, therefore, considerably reduce the cost of errors to taxpayers as well as to participating households....").
[8]  See Defendant's Statement of Disputed Facts, para. 12.
[9]  Basic statistical theorywhich applies irrespective of the statistical model usedholds that the greater the subsample size, the smaller the variance, and the greater the precision of the statistical measurement. E.g., D. Harnett, Introduction to Statistical Methods 191 (2d ed. 1975) ("collecting a larger sample usually result[s] in a more representative sample"); D. Freedman, R. Pisani & R. Purves, Statistics 355 (1978) ("A large population is given. It is desired to estimate the percentage of people in the whole population who have a given quality.... The accuracy of this estimate depends mainly on the absolute size of the sample, larger samples being more accurate").
[10]  The Court takes issue with the Commonwealth's argument that the Service is not treating the states consistently unless it takes subsamples of exactly 180 cases for each state, regardless of the number of a state's average monthly households. On the contrary, the most consistent method for taking subsamples is to vary the size of the subsample with the size of the sample taken by each state (as is done by following the procedure set forth in 7 C.F.R. sections 275.3[c][1] and 275.11[d][1]), thus ensuring that the subsample is a fixed percentage of the sample. If the subsample always equals 180 cases, it would not remain a fixed percentage and, consequently, each state would be treated differently, depending on its number of average monthly households.
