
583 F.3d 1 (2009)
ANNA JAQUES HOSPITAL, Et Al., Appellees
v.
Kathleen SEBELIUS, In her Official Capacity as Secretary of the United States Department of Health and Human Services, Appellant.
Nos. 08-5407, 08-5529.
United States Court of Appeals, District of Columbia Circuit.
Argued May 8, 2009.
Decided September 11, 2009.
*2 Stephanie R. Marcus, Attorney, U.S. Department of Justice, argued the cause for appellant. With her on the briefs were Michael F. Hertz, Acting Assistant Attorney General, Jeffrey A. Taylor, U.S. Attorney, and Mark B. Stern, Attorney. R. Craig Lawrence, Assistant U.S. Attorney, entered an appearance.
Ankur J. Goel argued the cause for appellees. With him on the brief were M. Miller Baker and Kelly M. Falls.
Before: HENDERSON, TATEL, and GRIFFITH, Circuit Judges.
Opinion for the Court filed by Circuit Judge GRIFFITH.
GRIFFITH, Circuit Judge:
The Secretary of the Department of Health and Human Services appeals the decision of the district court that she improperly excluded the labor costs of certain types of hospitals from her calculation of Medicare reimbursements due to appellees. Because we conclude that the Secretary's exclusion of these costs was based on a reasonable interpretation of her statutory authority, we reverse the judgment of the district court.

I.
In 1983, Congress created the Prospective Payment System (PPS) as a new means to provide Medicare reimbursements to hospitals for medical care requiring at least one night's stay. See Social Security Amendments of 1983, Pub.L. No. 98-21, § 601, 97 Stat. 65, 149; see also Se. Ala. Med. Ctr. v. Sebelius, 572 F.3d 912, 914-15 (D.C.Cir.2009) (describing how the PPS works); Transitional Hosps. Corp. of La. v. Shalala, 222 F.3d 1019, 1020-21 (D.C.Cir.2000) (same). Hospitals that participate in the PPS are called "subsection (d) hospitals," named after the statutory provision that identifies them. See 42 U.S.C. § 1395ww(d)(1)(B) (2006). These facilities are best described as "short-term acute care general hospitals." Transitional Hosps., 222 F.3d at 1021 (quoting S.REP. No. 98-23, at 54 (1983), reprinted in 1983 U.S.C.C.A.N. 143, 194). Of relevance to this appeal, critical access hospitals, which are usually located in rural areas and have fewer than twenty-five beds, are excluded from subsection (d) and receive Medicare reimbursements under a payment scheme different from the PPS. See 42 U.S.C. § 1395x(e), (mm); Proposed Changes to the Hospital Inpatient Prospective Payment Systems and Fiscal Year 2004 Rates, 68 Fed.Reg. 27,154, 27,190 (May 19, 2003) [hereinafter Proposed FY 2004 Rates].
Under the PPS, a significant component of the Medicare payment subsection (d) hospitals receive is reimbursement for their "wages and wage-related costs." 42 U.S.C. § 1395ww(d)(3)(E)(i). Because these costs vary widely across the country, Congress requires the Secretary to adjust Medicare reimbursements according to "area differences in hospital wage[s]." Id. To do so, the Secretary calculates a wage index for each area (employing the area classification system used by the Office of *3 Management and Budget) by dividing the area's average hourly hospital wage by the national average. See id.; Changes to the Hospital Inpatient Prospective Systems and Fiscal Year 2004 Rates, 68 Fed.Reg. 45,346, 45,398-99 (Aug. 1, 2003) [hereinafter Final FY 2004 Rates]. She uses the wage indexreferred to as the "factor" by the statuteto adjust the labor cost component of Medicare reimbursements.
Congress requires the Secretary "at least every 12 months . . . [to] update the factor . . . on the basis of a survey conducted by the Secretary (and updated as appropriate) of the wages and wage-related costs of subsection (d) hospitals in the United States." 42 U.S.C. § 1395ww(d)(3)(E)(i). The Secretary conducts this survey by compiling wage data from cost reports submitted annually by hospitals. See Changes to the Hospital Inpatient Prospective Payment Systems and Fiscal Year 2005 Rates, 69 Fed.Reg. 48,916, 49,049 (Aug. 11, 2004) [hereinafter Final FY 2005 Rates]. The Secretary removes data from this survey that fail to meet certain criteria for reasonableness, including data that are "incomplete[,] inaccurate. . ., or otherwise aberrant." Id. at 49,049-50; see also Final FY 2004 Rates, 68 Fed.Reg. at 45,397. From this scrubbed survey, the Secretary calculates each area's proposed wage index. Before putting the wage index in final form, she solicits comments from the public. See Publication of Schedules for Determining Prospective Payment Rates, 42 C.F.R. § 412.8 (2008). Because of the time required to scrub the data, the Secretary calculates each year's wage index using data from the survey conducted three years earlier. See Final FY 2005 Rates, 69 Fed.Reg. at 49,049; Final FY 2004 Rates, 68 Fed.Reg. at 45,397.
Prior to 2003, the Secretary included wage data for facilities that were subsection (d) hospitals during the survey year but were no longer classified as such by the time she calculated the wage index. In May 2003, the Secretary proposed a revision to this approach that would exclude wage data for hospitals that were subsection (d) hospitals during the survey year but became critical access hospitals before the year the index was actually calculated. See Proposed FY 2004 Rates, 68 Fed.Reg. at 27,190. Commenters generally supported removing data for critical access hospitals from the wage index, and the Secretary implemented the proposal. Final FY 2004 Rates, 68 Fed.Reg. at 45,397. One commenter raised the issue that is now the centerpiece of this appeal, arguing that the wage index should include data for facilities that qualified as subsection (d) hospitals at the time of the survey, including those later reclassified as critical access hospitals. Id. The Secretary concluded, however, that inclusion of data for these critical access hospitals has a "substantial negative impact" on the wage index for subsection (d) hospitals because they have "significantly different labor costs." Id. Specifically, "in 89 percent of all labor market areas with hospitals that converted to [critical access] status some time after FY 2000, the average hourly wage for [critical access hospitals] is lower than the average hourly wage for other [subsection (d)] hospitals in the area." Id. The Secretary continued to include wage data for other facilities that converted to non-subsection (d) status, as long as their data met her criteria for reasonableness. Id. She explained, "[W]age data for these hospitals, unlike CAHs, are not necessarily unique compared to other short-term hospitals, and these terminating or converting hospitals provide an accurate reflection of the labor market area." Id. at 45,398.
The Secretary first applied this policy when calculating the FY 2005 wage index. See Final FY 2005 Rates, 69 Fed.Reg. at *4 49,049. In calculating the wage index for Massachusetts, she excluded labor cost data from two facilities that had become critical access hospitals after 2001, the survey year: Nantucket Cottage Hospital and Martha's Vineyard Hospital. The Secretary also excluded the labor costs of these hospitals from the FY 2006 wage index. See Changes to the Hospital Inpatient Prospective Systems and Fiscal Year 2006 Rates, 70 Fed.Reg. 47,278 (Aug. 12, 2005).
On March 25, 2005, a group of subsection (d) hospitals in Massachusetts filed suit in the district court seeking, among other things, injunctive relief requiring the Secretary to recalculate the FY 2005 wage index using data from facilities that qualified as subsection (d) hospitals in 2001, including Nantucket Cottage Hospital, and to adjust Medicare reimbursements to the Massachusetts hospitals accordingly. The parties filed cross-motions for summary judgment. On February 27, 2008, the district court granted appellees' motion, concluding that the Secretary's interpretation of § 1395ww(d)(3)(E)(i) failed at Chevron step one because the statute requires that the wage index reflect the labor costs of all subsection (d) hospitals whose cost reports were used to conduct the annual survey, regardless of their status at the time the index is calculated. See Anna Jaques Hosp. v. Leavitt, 537 F.Supp.2d 24, 31 (D.D.C.2008). The court also rejected as arbitrary and capricious the Secretary's explanation that the wage data from critical access hospitals and subsection (d) hospitals were so different that they justified her new policy of excluding the former from the wage index. See id. at 34-35. As a remedy, the court ordered the Secretary to recalculate the FY 2005 wage index for Massachusetts using data from all facilities that qualified as subsection (d) hospitals in 2001, including data from Nantucket Cottage Hospital. See Anna Jaques Hosp. v. Leavitt, No. 05-625, at 2 (D.D.C. Feb. 27, 2008) (order accompanying opinion).[1] The Secretary filed a motion for reconsideration, which the district court denied. Anna Jaques Hosp. v. Leavitt, No. 05-625, at 4 (D.D.C. July 15, 2008). In a related lawsuit, appellees also challenged the Secretary's calculation of the FY 2006 wage index for Massachusetts on the same grounds. On November 13, 2008, the district court granted summary judgment for the hospitals in light of its previous decision. Anna Jaques Hosp. v. Leavitt, No. 06-767 (D.D.C. Nov. 13, 2008). The Secretary appealed each decision.
We have jurisdiction to consider this consolidated appeal under 28 U.S.C. § 1291 (2006). "Because the district court entered a summary judgment, we review its decision de novo and therefore, in effect, review directly the decision of the Secretary." St. Luke's Hosp. v. Thompson, 355 F.3d 690, 693 (D.C.Cir.2004) (quoting Lozowski v. Mineta, 292 F.3d 840, 845 (D.C.Cir.2002)).

II.
This appeal turns on three issues raised by the Secretary: (1) whether her interpretation of § 1395ww(d)(3)(E)(i), the statutory provision requiring annual calculation of the wage index, is permissible under Chevron; (2) whether she acted arbitrarily by failing to adequately explain her approach to calculating the wage index; and (3) whether she acted arbitrarily by treating data from similarly situated facilities differently. The Secretary raises a fourth issue, which we need not reach *5 because our resolution of the others renders it moot.
We review the Secretary's interpretation of § 1395ww(d)(3)(E)(i) under Chevron's two-step framework. When "Congress has directly spoken to the precise question at issue . . ., that is the end of the matter." Chevron U.S.A. Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 842-43, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). But if we determine the statute is "silent or ambiguous with respect to the specific issue," we will uphold the Secretary's interpretation so long as it is "based on a permissible construction of the statute." Id. at 843, 104 S.Ct. 2778. We begin with the statute's plain language. Congress directs the Secretary to "update the [wage index] . . . on the basis of a survey . . . of the wages and wage-related costs of subsection (d) hospitals in the United States." 42 U.S.C. § 1395ww(d)(3)(E)(i). This command requires the Secretary to adjust the wage index using data collected from subsection (d) hospitals. There is no question that the Secretary conducted a survey that gathered data from all subsection (d) hospitals, including those that later became critical access hospitals.
The dispute is over which data from the survey she must use to update the wage index. Appellees argue that the phrase "on the basis of a survey . . . of subsection (d) hospitals" means that the wage index must be calculated using all the survey data. In their view, the statute requires both the survey and the wage index to account for all facilities classified as subsection (d) hospitals at the time of the data collection, including those that later became critical access hospitals. Discarding data for a category of hospitals after having gathered it, so the argument goes, is no different from failing to gather it in the first place. The Secretary reads the statute differently. Rather than directing the inclusion of data collected from every subsection (d) hospital in the survey, she argues that the phrase "on the basis of" is ambiguous and gives her the discretion to remove data found wanting to the calculation of a meaningful wage index. According to the Secretary, such a reading is permissible at Chevron step two.
We agree with the Secretary. The statute is silent about whether she must use all of the survey data. It says only that her calculation of the wage index must be made "on the basis of" the survey. The dictionary defines "basis" to mean "the principal component of anything" or the "fundamental ingredient." WEBSTER'S THIRD NEW INTERNATIONAL DICTIONARY 182 (2d ed.1981). "Basis" does not mean "entire" or "only." Calculation "on the basis of a survey" does not require use of all the data collected. Because it may mean less than all, "on the basis of" could reasonably be interpreted to permit a variety of methods for using the survey data to calculate the wage indexhence, the ambiguity. Under the statute, the Secretary has the discretion to remove some data from the survey so long as the remaining data constitute the principal component of the final wage index calculation. And that is what the Secretary did here. She scrubbed from the survey data she determined would not reasonably help calculate a meaningful wage index. Applying her criteria for reasonableness, data that were "incomplete[,] inaccurate . . ., or otherwise aberrant" were not used to calculate the wage index. Final FY 2005 Rates, 69 Fed.Reg. at 49,049-50; see Final FY 2004 Rates, 68 Fed.Reg. at 45,397.
We faced similar arguments in Sierra Club v. EPA, 356 F.3d 296, 305-06 (D.C.Cir.2004), in which we parsed the phrase, "based on," and concluded it was ambiguous. Both phrases use a variant of the word "base," which means in this context "to use as a base or basis for." WEBSTER'S THIRD NEW INTERNATIONAL DICTIONARY *6 180 (2d ed.1981). In Sierra Club, Congress had directed EPA to determine state compliance with national ambient air quality standards "based on photochemical grid modeling or any other analytical method determined . . . to be at least as effective." 42 U.S.C. § 7511a(c)(2)(A) (emphasis added). The agency argued that the phrase "based on" was ambiguous and did not require EPA to rely "solely on" environmental modeling results. Sierra Club, 356 F.3d at 305-06. Instead, the phrase gave EPA the discretion to correct the mandated model's inaccurate projections of ozone levels by adjusting the results before making compliance decisions. The petitioners argued that "based on" required EPA to use only the results from the required environmental model. We agreed with EPA and held the agency's compliance determinations could still be "based on" the required modeling so long as EPA did "not wholly abandon" the modeling. Id. at 306. Here, there is no question that the Secretary did "not wholly abandon" the survey data. She merely refined it to arrive at a more accurate wage index.
Appellees next argue that the Secretary acted arbitrarily by failing to provide a reasoned explanation for her departure from the previous policy that used data for facilities that qualified as subsection (d) hospitals at the time of the survey. But appellees' argument is based on the flawed premise that it has been the Secretary's policy to use all of the subsection (d) hospital data to calculate the wage index. The Secretary has never done that. She has maintained a longstanding policy of scrubbing data that fail to meet her criteria for reasonableness, particularly those found to be aberrant. See Changes to the Hospital Inpatient Prospective Payment Systems and Fiscal Year 2003 Rates, 67 Fed.Reg. 49,982, 50,023 (Aug. 1, 2002) ("As in past years, we performed an intensive review of the wage data, mostly through the use of edits designed to identify aberrant data."). In 2004, the Secretary first removed critical access hospital data from the 2001 survey because she determined they have a "substantial negative impact" on the wage indexes for subsection (d) hospitals. Final FY 2004 Rates, 68 Fed. Reg. at 45,397. This was not a change in policy. Rather, it was a new application of her policy to remove aberrant data.
In any event, the Secretary has adequately explained her decision to exclude critical access hospital data from calculation of the wage index. "[A]n agency is free to change its mind so long as it supplies `a reasoned analysis.'" Nat'l Cable & Telecomms. Ass'n v. FCC, 567 F.3d 659, 667 (D.C.Cir.2009) (quoting Motor Vehicle Mfrs. Ass'n v. State Farm, 463 U.S. 29, 57, 103 S.Ct. 2856, 77 L.Ed.2d 443 (1983)). Explanation of a change in policy is not subject to a heightened standard of review. See FCC v. Fox Television Stations, Inc., ___ U.S. ___, 129 S.Ct. 1800, 1811, 173 L.Ed.2d 738 (2009). The Secretary found that critical access hospitals have significantly different labor costs from subsection (d) hospitals and concluded that including them in her calculations would skew wage indexes for subsection (d) hospitals. Such aberrational data fail to meet the Secretary's criteria for reasonableness. See Final FY 2004 Rates, 68 Fed.Reg. at 45,397. Excluding them, in the expert view of the Secretary, would "improve[] the overall equity of the wage index." Id. at 45,398. We believe this explanation is sufficient.
Among all the types of hospitals that lost their subsection (d) status, the Secretary excluded only the data from critical access hospitals. Appellees argue that singling out this data for exclusion was arbitrary because the Secretary treated data for similarly situated hospitals differently. To be consistent, they contend, the Secretary must treat the data from all *7 hospitals that no longer qualify as subsection (d) hospitals the same. "Where an agency applies different standards to similarly situated entities and fails to support this disparate treatment with a reasoned explanation and substantial evidence in the record, its action is arbitrary and capricious and cannot be upheld." Burlington N. & Santa Fe Ry. Co. v. Surface Transp. Bd., 403 F.3d 771, 777 (D.C.Cir.2005); see also 5 U.S.C. § 706(2)(A) (2006) (requiring a reviewing court to set aside agency action that is "arbitrary" or "capricious").
But appellees have failed to provide any support for their argument that critical access hospitals are similarly situated to other hospitals that have recently lost their subsection (d) status. Instead, they simply assert that other non-subsection (d) hospitals may have significantly different labor costs than those of subsection (d) hospitals. Appellees made no showing that hospitals that lost their subsection (d) status are, by reason of that change, outliers like critical access hospitals. Put simply, they have not demonstrated that other new non-subsection (d) hospitals are like the new critical access hospitals when it comes to labor costs. Unsupported allegations of arbitrary treatment are insufficient for us to render a judgment on the merits of such a claim. Federal Rule of Appellate Procedure 28(a)(9)(A) requires parties to provide "citations to the authorities and parts of the record on which [they] rel[y]" to bolster their arguments. We will not consider "asserted but unanalyzed" arguments because "appellate courts do not sit as self-directed boards of legal inquiry and research, but essentially as arbiters of legal questions presented and argued by the parties before them." Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983). In the absence of such a showing, we need not decide whether the Secretary acted arbitrarily by treating data from new non-subsection (d) hospitals differently.
Finally, our resolution of the case makes it unnecessary to reach the last issue raised by the Secretary on appeal. Under section 4410 of the Balanced Budget Act of 1997, Pub.L. No. 105-33, § 4410, 111 Stat. 251, 402 (codified at 42 U.S.C. § 1395ww note), the Secretary must calculate a "rural wage floor" for each state using data from its rural subsection (d) hospitals. The wage index for urban subsection (d) hospitals may not fall below the rural wage floor. See id. The Secretary has never read section 4410 as requiring her to calculate rural wage floors for states without rural subsection (d) hospitals. On appeal, the Secretary argues that even if we were to rule that she must include in the wage index called for by § 1395ww(d)(3)(E)(i) the labor costs of rural facilities that lost their subsection (d) status (Nantucket Cottage Hospital and Martha's Vineyard Hospital), she would not be required to calculate a rural wage floor for Massachusetts. Because section 4410, unlike § 1395ww(d)(3)(E)(i), makes no reference to "a survey," the Secretary maintains that she is free to use only data from facilities that are rural subsection (d) hospitals at the time she calculates the wage index. But the Secretary only raised this issue in anticipation of a holding that we have now decided against. Because we have ruled that the Secretary may exclude data from Nantucket Cottage Hospital and Martha's Vineyard Hospital, we need not consider an issue addressing a contingency that never materialized.

III.
For the foregoing reasons, the judgment of the district court is
Reversed.
NOTES
[1]  Although appellees did not challenge the exclusion of wage data from Martha's Vineyard Hospital, the Secretary included this data when recalculating the FY 2005 and FY 2006 wage indexes pursuant to the district court's orders.
