Howard Hogan, J.
Under attack in the second phase of this long involved joint trial on the separate issue of ratio for the tax years 1965-1966 through 1973-1974 is the methodology utilized by the State Board of Equalization and Assessment (SBEA) by which this board arrives at the State equalization rate for respondent, Nassau County.
A State equalization rate is defined as: "The percentage of full value at which taxable real property in a county, city, town or village is assessed as determined by the state board”. (Real Property Tax Law, § 102, subd 19.)
The State equalization rate serves primarily to apportion the allocation of tax benefits and burdens throughout the tax districts. A State equalization rate seeks to establish a just relationship between the valuations of all the tax districts [527]*527within the county. Litigation to establish ratio of assessment to full value of all other properties within the tax districts has long been known to be burdensome, costly and unwieldy (People ex rel. Yaras v Kinnaw, 303 NY 224, 231; People ex rel. Stewart v Feitner, 53 Misc 334). In an inequality case the task is to make a comparison between the rate of assessment of subject property, i.e., the proportion of its assessed value to its full value with the rates of assessment of the selected sample parcels within the tax district. This requires proof of full market value of all selected sample parcels. The purpose of an inequality proceeding is to eliminate discrimination in assessment so that one taxpayer pays no more than his proportionate share of the aggregate tax levied in the district (Matter of Wolf v Assessors of Town of Hanover, 308 NY 416, 421). Sample parcels should represent a fair cross section of the tax district and should not be chosen for their similarity to the subject (People ex rel. Hagy v Lewis, 280 NY 184).
To date, this litigation has consumed many months. At present there are in excess of 7,000 pages of testimony and some 293 exhibits. In the first phase of this trial the court heard evidence as to valuation of the 33 selected sample parcels pursuant to subdivision 3 of section 720 of the Real Property Tax Law. In this, the second phase, among the witnesses were three distinguished university professors well versed in statistics and a recognized real estate appraiser who have analyzed SBEA’s techniques and methods in arriving at the State equalization rate for respondent county.
In terms of trial logistics, the preparation by both sides may be the equivalent of Sherman’s march through Georgia, but unlike Sherman, counsel left little to chance and almost nothing overlooked. The trial carried with it the impression nothing was to be left undone. During the course of the litigation lasting nearly two years, there have been innumerable motions, orders to show cause, and at least one intermediate appeal.
Respondent, County of Nassau, has a population approximating 1,500,000 with more than 400,000 parcels of real property subject to taxation. Better to understand the complexities of this litigation within Nassau there are 2 cities, 3 towns and 62 incorporated villages. The cities, villages and county have their own assessors; the towns do not.
The last time respondent, County of Nassau, had reassessment was nearly 40 years ago (1938) when the late J. Russell [528]*528Sprague was county executive. Since then real property values have increased manyfold. However, the proportionate increase in real property taxes has far exceeded the rate of increase in actual market values during the past decade. The time has come for a total reassessment. This, perhaps, may remedy some of the inequality found from the evidence in this trial. For example, the range in values as established from the list of sales used by SBEA in the 1968 survey for the Town of Oyster Bay reflect a range in ratio from 8.02% to 142.84% of true value, a rather shocking situation calling for corrective action.
Respondent has but one assessment roll for all villages, towns and cities. This roll is utilized for all special district purposes as well as for schools (Nassau County Government Law, § 602 [L 1936, ch 879, as amd]; Nassau County Administrative Code, § 6-1.0, subd 4; §§ 6-7.0, 6-17.1 [L 1939, chs 272, 701-709, as amd by L 1940, ch 458, § 2]).
Nassau and Tompkins Counties are the only two counties in the State of New York having a Board of Assessors. Section 504 of the Nassau County Charter, adopted in 1935 (L 1935, ch 938, repealed by L 1939, ch 272, now Nassau County Administrative Code, ch VI) authorized the Board of Assessors to assess all real property subject to taxation within the county for State, county, school and/or special district purposes (Nassau County Government Law, §§ 601, 602). Under section 609 of the same law: "the office of assessor in towns is abolished * * * and its powers and duties are transferred to the County Board of Assessors”.
Under the Administrative Code of respondent there is a tax or assessment district (§ 6-2.0, as provided in Real Property Tax Law, § 102, subd 1) and pursuant to the Nassau County Government Law the Board of Assessors establishes uniform assessment throughout the county. Implicit in the abolition of the office of Town Assessors and the transfer of the assessment power to the County Board of Assessors is the fact that the County Board of Assessors has succeeded to the powers and duties of the former Town Assessors and has standing to represent the towns to seek review of the State equalization rates for the towns in Nassau where assessments are established by its County Board of Assessors.
Annually, the SBEA sitting in Albany holds hearings at which any aggrieved taxing district may protest those equalization rates which the SBEA is mandated to establish for each [529]*529county, city, town and village (Real Property Tax Law, §§ 202, 1214).
At these hearings representatives of all taxing districts are given an opportunity to protest — that is, all but respondent. SBEA interprets article 12 of the Real Property Tax Law to limit protests to taxing districts only and since respondent is not a taxing district, it has no standing. While respondent’s Board of Assessors have been permitted to appear informally and submit protests in writing, they have consistently been denied a hearing. Both the present chairman of the board and former vice-chairman testified they felt "demeaned” when attempting to voice their protests, of the State^ rate. The lasting feud between respondent and SBEA in this respect has resulted in total frustration. With almost mechanical regularity, each year representatives of respondent board seek leave to be heard but are denied.
I find this preclusion by SBEA to be based upon a misinterpretation of article 12 and failure to recognize respondent’s charter. (See Nassau County Government Law, §§ 601, 602, 609.) Article 12 requires SBEA as part of its procedure for establishing State equalization rates to sample the ratio of assessments to market value for each major type of taxable real property in all cities, towns and villages and in the case of a city in a county having a county department of assessment, SBEA shall establish a rate for that portion of the county roll within the city. Article 12 must be read in conjunction with the Nassau County Government Law. From this it is clear that respondent’s Board of Assessors must assess all real property in the county liable to taxation for State, county, town school and/or special district purposes. Respondent’s Board of Assessors represent the taxing district since the Town Assessors have been abolished. To deny them a hearing is violative of due process.
In passing, it is noted that at the hearings conducted by SBEA, the hearing officer who is called upon to make a judgment as to the validity of State rates frequently is a member of SBEA’s staff. This is a highly questionable procedure. In effect it makes SBEA — prosecutor, Judge and jury— all in one.
The State rate once determined is the result of an administrative decision (Real Property Tax. Law, § 202, subd 1, par [b]) not reviewable by the taxpayer but by the taxing district under the limitation of an article 78 proceeding (Real Prop[530]*530erty Tax Law, § 760; Matter of O’Brien v Assessor of Town of Marmaroneck, 20 NY2d 587, 596, 597).
Our State rates are the results of processes which are obscure and complex as testified by the three university professors and a recognized real estate appraiser. In the establishment of the State rates the SBEA avails itself of all information it has in its offices from appraisals and sales (Real Property Tax Law, § 1202, subd 2).
Prior to the amendment of section 720 in 1969, following the O’Brien decision, State equalization rates were not admissible (People ex rel. Yaras v Kinnaw, 303 NY 224, supra; Wolf v Assessors of Town of Hanover, 308 NY 416, supra). These cases stand for the proposition that procedures for the select parcel proceeding outlined in Hagy and approved in Yaras and Wolf (supra), were the proper methods to be used in an inequality trial. In the 1961 amendment to subdivision 3 of section 720 the Legislature had provided that evidence of State equalization rates were admissible in conjunction with a sample parcel proceeding. No change was made in the method by this amendment.
The O’Brien case (supra, p 595) which followed in 1967 held that the State rate standing alone was insufficient "to sustain the finding of inequality in a particular assessment”. The majority in O’Brien noted that the amendment of section 720 continued a requirement for the selection of parcels to prove inequality. Following the decision in O’Brien the Legislature further amended subdivision 3 of section 720 in 1969. Here again, the selected parcel procedure was retained unchanged, but this amendment provided that irrespective of whether or not parcels are selected: "evidence may be given by either party as to * * * the state equalization rate established for the roll containing the assessment under review.”
This amendment applied to all proceedings commenced to review the 1970 roll (tax status date May 1, 1969 and subsequent proceedings only). Those proceedings permitted petitioner to prove ratio by introducing into evidence the State rate (Guth Realty v Gingold, 34 NY2d 440). For the years prior to 1969, which are part of this proceeding, the State equalization rates may only be introduced in conjunction with the selected sample parcels.
The Guth decision now allows use of the State equalization rate as the sole basis for ratio for the year 1970 and, of course, for the years subsequent thereto. However, a word of caution: [531]*531it must be noted, the decision in Guth did not hold that the State rate was absolute. Instead, the court ruled (p 450) that "the party who seeks to use the rate will be put to his proof that such use is justifíed in that case. ”
Mindful of the enormity and almost prohibitive expense to a petitioner in protesting an assessment by use of selected parcels and actual sales methods as prescribed by the statute, Guth seeks to eliminate this expense to the taxpayer that he may have his day in court without undue financial burden. Moreover, this was the intent of the Legislature with the 1969 amendment to subdivision 3 of section 720 of the Real Property Tax Law. (See Legis Memorandum, L 1969, ch 302, § 2.)
Guth advocated the use of the State equalization rate whenever and wherever possible. A further reason for use of the State rate, it will eliminate a biased selection, for it is well known that in every selected sample parcel proceeding including this one, each side chooses parcels at the extreme "ends of the spectrum” (Guth, at p 449). Much ingenuity has been expended by the SBEA in attempting to devise methods to establish a rate by which the various taxing districts of the State receive distribution. It is well settled that the board’s methodologies may be determined only by ascertaining what that method really is. If the method is a sham or "hocus pocus”, as respondent likes to describe it, a mere facade concealing many errors and weaknesses, it must be disregarded and legal rights and benefits determined according to the real facts, but if it is ascertained that the methods employed were legally operative and fairly representative, the methodology must be approved. The first issue is the respondent’s contention that the board’s method resulted in a downward bias.
METHODOLOGY — DOWNWARD BIAS
The random sampling method used by SBEA or "equal probability sampling” is one which is drawn in such a way that each property has an equal probability of being selected; hence, the sample has statistical reliability, and from this one may compute the standard error. Respondent contends, however, since SBEA has adopted an 80% exclusionary rule; since the sampling is weighted with residential properties; since there is only a minimal number of commercial, industrial, public utility, railroad and vacant properties sampled; and since in at least one town (Town of Oyster Bay) (1970) there was no sampling of industrial, public utility or railroad prop[532]*532erty, this results in a downward bias or lower State rate and an underestimate of aggregate ratio. The method used (80% rule) precludes 20% of the total population from any possibility of ever being selected. SBEA’s rules and procedures, eliminating sales data to improve its "coefficient of variation”, appears to be based upon a prior judgment made by SBEA as to the proper extent of variability to appear in the sample. Deductions drawn from this method lack statistical precision.
Moreover, SBEA’s "two-thirds rule” which requires sampling of parcels previously appraised in prior surveys interrupts the statistical accuracy of the random sampling procedures and precludes admission of new properties from the sampling procedure which tend to have a higher ratio. Any planned elimination of property from a sampling constitutes judgmental interference with the sampling and reduces the objectivity of the procedure. To the same effect is SBEA’s procedure of comparison of market value of an appraised sample with its own estimate of what the new value is. The rule seems to be — if there is a substantial difference, more appraisals are made. Does this not force a preconceived estimate of increase in market value? The evidence shows in 1961 SBEA’s survey was based on sales which were 100% residential; 1965 the sales used by SBEA were 99.4% residential; 1968 the sales used by SBEA were 99% residential and for 1970, 98.3% residential, most all of which were in the $35,000 range while the average market value of appraised properties in the 1970 survey was $82,855. The use of this sales material in the survey procedure shows:
Aggregate Ratio of Aggregate Ratio of
Survey Year Appraised Parcels Sales Parcels
1961 44.98% 29.67%
1963 43.36 29.88
1965 36.39 27.52
1968 35.19 24.49
1970 28.48 20.36
But then, is not the downward bias compensated, at least to some degree, by SBEA’s use of increasing market values two to three years prior to formulation of the State rate? (For a more detailed discussion, see "Analysis of Methodology”, filed with this decision.)
The second issue is whether petitioners’ failure to appraise all selected sample parcels as provided in subdivision 3 of section 720 of the Real Property Tax Law is a fatal defect?
[533]*533In this joint trial petitioners did not appraise all the parcels selected during the period between May 1, 1965 and May 1, 1968. However, during the trial they were permitted and did cross-examine on practically all parcels, relying upon their cross-examination for proof of value which in effect became rebuttal evidence.
Respondent has now renewed its motion at the conclusion of this phase of the case to dismiss the petitions covering the period May 1, 1965 to and including May 1, 1968 on the ground that the petitioners have failed to comply with the provisions of the statute and the case law with respect to inequality trials relating to that period prior to the 1969 amendment to the statute.
In support of its motion respondent contends the law clearly mandates the appraisal valuation of each of the sample parcels and computation of the assessment and the comparison of their average rate of assessment with that of the subject property. Since petitioners failed to comply with this requirement and the case law as respondent finds it to be, there is a failure of proof by the petitioners who admittedly have the burden of proof.
At the trial respondent indicated the mere fact that petitioners in selecting its parcels relied on the sale of those parcels so selected, that, in itself, was not a reliable indication of value but in fact tended to create distortions of value. The evidence does not support respondent’s contention. An arm’s length sale in the open market between a knowledgeable willing buyer and a knowledgeable willing seller is still the best evidence of real property value.
To reiterate, petitioners, with all the years commencing May 1, 1969 relied solely on the State equalization rates as evidence of the inequality of assessments and did not participate in the sample parcel selection or appraise the sample parcels submitted by respondent for these last years. As to this, respondent has also moved for dismissal for petitioners’ failure to engage in parcel selection for these later years.
In Guth, the petitioners not only submitted evidence of State equalization rates but also sales and sample parcels. Respondent argues that petitioners’ failure to select sales and sample parcels herein, is violative of the statute and not in compliance with the holding in Guth.
Here again, petitioners relied upon their cross-examination [534]*534of respondent’s witnesses to determine value for those years. At issue, then, is whether or not one of the parties in an inequality trial may unilaterally refuse to select sample parcels and/or offer sales following the 1969 amendment to subdivision 3 of section 720 and whether or not the parcels selected by one party must necessarily be appraised by his adversary who in turn must file a tabulation of values for the court as provided in subdivision 2 of section 720 and to give evidence of the other categories of proof prescribed in the statute. Respondent’s motion to dismiss petitions for failure to file appraisals for all the years must be denied.
The statute (Real Property Tax Law, § 720, subd 3) prescribes a method whereby parties in an inequality proceeding may seek a judicial determination. Litigants may use the State rates or sample parcels or both. Admittedly, the sample parcel method has many deficiencies (Koeppel, Real Property Tax Review, 19 Buffalo L Rev 565) chief of which is that the bias method of selection (Tilsac Corp. v Assessor of Town of Huntington, 41 AD2d 604, mot for lv to app den 32 NY2d 611) is costly and time consuming. Consequently, the sampling procedure is beyond the financial resources of the average petitioner which prompted the Legislature to enact the 1969 amendment (L 1969, ch 302) to subdivision 3 of section 720 of the Real Property Tax Law permitting evidence of State rates. Either party may call witnesses and produce such proof as it deems best. Appraisal of each and every selected sample is within the sound discretion of the parties and the trial court. One may, if he chooses, offer State rates after 1969, and risk reliance on those alone (Matter of 860 Executive Towers v Board of Assessors of County of Nassau, 79 Misc 2d 821, 826) or upon cross-examination or rebuttal testimony. Petitioner’s failure to appraise all sample parcels is not fatal. In addition, the petitioners choose the method of proof and respondent may not dictate such choice (Matter of Merrick Holding Corp. v Board of Assessors of County of Nassau, 76 Misc 2d 754).
Petitioners also moved to strike the respondent’s selected parcels for the post-1969 years on the ground that these were not sales, not evidence of the State rate or even selected parcels pursuant to subdivision 3 of section 720. Petitioners maintain these were only respondent’s parcels not selected pursuant to statute because all 33 were not appraised after 1969. As held herein, neither side may dictate to the other the method of proof. It is within the discretion of the trial court to [535]*535determine adequacy. Accordingly, petitioners’ motion directed to striking the respondent’s parcel for the last five years under review is denied.
In Guth, the court did not reject the use of the sample parcel method. It held (34 NY2d, at pp 450-451): "Utilization of the equalization rate which is objectively arrived at * * * would tend to greatly simplify and narrow the scope of these proceedings * * * there is no discernible reason why [the State rates] also may not be used in individual inequality cases.” Nor did Guth hold that State rates alone were absolute except as to the facts in the Guth case itself. Rather, it established that (p 450): "the party who seeks to use the rate will be put to his proof that such use is justified in that case”. Consequently, it rests with the parties and the trial court to determine the quantum of proof necessary. Guth did not abandon selected parcels in all inequality cases. (See Assessment for Real Property Tax Purposes, Kramer, Adelphi Univ Press, p 38.)
It has long been recognized that where the sample parcel method is chosen, there should be "the fair selection of sample parcels, their evaluation, the consequent computation of their rate of assessment, and the comparison * * * with that of the subject property”. This selection, wrote Judge Fuld, should be a fair "cross-section of the situation that exists throughout a tax district.” (Matter of Wolf v Assessors of Town of Hanover, 308 NY 416, 423, supra.)
There need not longer be exhaustive testing of the SBEA’s methodology nor proof of the details of SBEA’s procedures, the same having been amply discussed in Guth and in the instant case. Unless it can be shown the rates applicable to a given tax district are completely biased or have been improperly obtained, the State rates are presumptively correct.
Subdivision 3 of section 720 in no way abridges the functions of the local Board of Assessors whereby the 1969 amendment is unconstitutional. The local Board of Assessors is respondent’s board. The purpose of SBEA rates is to fairly allocate the benefit of tax dollars among the numerous agencies of government within a tax district and throughout the State. Respondent’s Board of Assessors has the duty to assess. This is not taken from them. SBEA’s function is to determine a fair rate for distribution of benefits, and if the local boards are in disagreement, their recourse lies in an article 78 [536]*536proceeding or to protest at the annual hearings , of the SBEA or both.
Since the State rates are presumptively correct (§ 720, subd 3), there is no requirement petitioners must prove the State - rates have been validly established nor that these are expertly and objectively arrived at (see Guth), or that these pertain specifically to the tax unit involved.
Moreover, SBEA does in fact give notice of its tentative rate and the final rate to the towns, villages and cities as well as the Chief Clerk of the County Board of Supervisors and Chairman of the County Board of Assessors, which complies with the statute (Real Property Tax Law, § 1202, subd 1; § 102, subd 19; § 202, subd 1, par [b]). The respondent always. has recourse to the courts to review the State rate in an article 78 proceeding to determine whether the rate fixed was sustained by substantial evidence (Real Property Tax Law, § 760; Matter of O’Brien v Assessor of Town of Marmaroneck, 20 NY2d 587, supra).
From the evidence in this case it is clear that SBEA’s methodology as it applies to respondent county has many deficiencies. (See "Analysis of Methodology” filed herewith.) The State equalization rate as it applies to respondent county is perhaps more subjective than objective. It is a complicated procedure known to many, understood by few. However, our highest court in Guth has given it sanction. The facts in Guth established the State rate was expertly and objectively arrived at.
Ironically, the rate found in the first phase of this trial from the selected sample parcels (annexed hereto, made a part hereof and referred to as "Tabulation of Assessed and Market Values” and comprising nine pages) very closely approximates the State rate for all the years except the last five. For these it will be recalled petitioners offered no appraisal but relied on cross-examination and the State rates. However, even as to these, respondent’s contention as to what the rates should be is untenable.
While SBEA’s methodology is not perfect and has many deficiencies with respect to respondent county, "We cannot say that such a process is inadequate for practical attainment of the rough equality which is all that has heretofore been possible under any system of taxation.” (Loughran, J., People ex rel. Hagy v Lewis, 280 NY 184, 188, supra.)
The methodology of SBEA, like Lewis Carroll’s storybook Alice, all seems to disappear into Wonderland until unraveled by the university professors. While Carroll’s mirror magic is [537]*537strictly fantasy, the mirror is more of a reflection than just the surface portrait. What Alice saw was a reflection of her innermost thoughts. In this respect the complicated methods used by SBEA tend to promote a bizarre conception referred to by respondent as "hocus-pocus”, not without some justification.
It is to be noted the Court of Appeals when it ruled in Guth (34 NY2d, at p 450): "utilization of the equalization rate which is objectively arrived at, and which today is expertly arrived at, would tend to greatly simplify and narrow the scope of these proceedings” that it did not go so far as to say it was scientifically arrived at!
With respect to respondent, it is clear that the lack of representative sample parcels in each of the classes and SBEA’s predetermination of the number to be sampled has magnified the criticism of the present method used by SBEA. However, we find the method is an honest effort to meet the heeds of a taxing district.
In this case the experts in reviewing the methods used by the State board with respect to respondent’s taxing district elaborated upon Mr. Stein’s review of procedure to which he testified in Guth. Petitioners seeking to use the State rate for Nassau County have met their burden of proof through the detailed testimony of their experts, Professors Elby, Glasser and Mr. Powers, all of whom reviewed the methods establishing rates generally and two of whom testified to those rates as applied to Nassau County. Elby reviewed the rolls; for example, of the Town of Oyster Bay, one of the three towns in Nassau County, how each roll was prepared and processed through the computer; these rolls for the county were segregated into the 2 cities, 62 villages and 3 towns outside of villages. He testified how each parcel of property is classified, i.e., residential, commercial, industrial, utility, railroad and/or vacant land; that during the years in issue there were five major classifications; that the survey is a random sampling of rolls for selection of parcels to be appraised; thát this "equal probability sample” has been selected in such a manner "that each item in the population has an equal probability of being selected”; that this method is statistically reliable; that the results obtained from this sample may be used to compute a standard error.
He distinguished random and nonrandom sampling, noting that in the nonrandom method, no matter what measurements are found, there is no statistical basis in which to relate [538]*538the selected sample to the population. With random sampling, after measurements are ascertained, these may be related to a known degree of accuracy, as if the entire population were sampled,.
He also reviewed the State’s 80% rule which in effect constitutes an exclusion from the survey of sample parcels of various property classes. There are 76 survey units established by the SBEA for respondent. He conceded that in some years with reference to one of the towns (Oyster Bay), the board did not sample any industrial, public utility or railroad property and of the 19 units established for this town by SBEA comprising the 18 villages and the area of the town contiguous to the villages, the SBEA sampled commercial property in only 2 units despite the fact there are commercial properties in all 19. Hence, it is clear 20% of the classifications have no probability of being selected. While this method precludes each classification from having an equal opportunity of being selected, and while there are other deficiencies, in the main, the method is about as sound as we have been able to establish.
Respondent’s criticisms are not wholly without merit. To refuse to recognize Nassau County as an assessing unit is indeed a denial of the equal protection of the law to its citizens and taxpayers.
The equalizing methods of SBEA while unnecessarily complicated, confusing and more subjective than objective insofar as the evidence in this case is concerned are still perhaps the best method to attempt to fairly distribute and equalize the tax burden which all must share. The late Loughran, J., in writing for the majority in People ex rel. Hagy v Lewis (280 NY 184, 187-188, supra) summarized the problem: "The equalizing method used by the courts below may perchance give effect to lopsidedness * * * But this possibility seems to us to be so remote as to be negligible in the ordinary case.”
Accordingly, respondent’s motions to dismiss these proceedings and to strike the testimony of Professor Elby and the State equalization rates as the same apply to respondent county, are denied. The rates as found by SBEA will be considered along with the other evidence.
Petitioners in this inequality trial have the burden of proof to establish that the assessments upon their respective properties were unequal. Procedures to be followed are found in subdivision 3 of section 720 as amended by chapter 942 of the Laws of 1961, and chapter 302 of the Laws of 1969.
[539]*539Near the conclusion of an extensive cross-examination of Professor Elby, he testified:
"A You are looking for a ratio of estimate. The State Board has developed a complex, rather elaborate system to attempt to achieve an objective, unbiased, hopefully valid system of ratio. It is not perfect but it is still the best that they can do with the charter that they have and with the resources available to them. Whether the results are valid or not starts to depend on how precisely you want the State rate determined. If you are saying, 'Is it valid to the second decimal point?’, the answer is, 'Of course not’.
"If you are saying, 'Is it valid to the actual percentage point that they come up with?’ 'Probably not.’ 'Is it valid to within a point or two of that?’ that is another question and that gets into a long analysis of non-sampling errors as well as sampling errors. I think the non-sampling errors are much more significant here. The State Board itself makes no particular claim that when it says that the State rate for Glen Cove in 1968 is 32, that they are guaranteeing that it is between 31 and 33.” This pretty well summarizes the entire problem.
The court has heard the evidence with respect to the selected sample parcels and attached hereto and made a part of this decision is an addendum containing separate decisions on each of the 34 selected parcels setting forth the court’s findings with respect to market value or its reasons for disregarding any of the parcels for failure of adequate and proper proof. The court’s nine-page tabulation of these results is also attached and entitled "Tabulation of Assessed and Market Values”. [Said separate decisions and tabulation are omitted from publication.] Attached as well is the court’s "Analysis of Methodology”, previously referred to and made a part of this decision.
Accordingly, the court finds and decides the ratios for each of the years under review to be as follows:
Tax Status Date Ratio
5/1/65 30%
5/1/66 30
5/1/67 30
5/1/68 29
5/1/69 28
5/1/70 25
5/1/71 24
5/1/72 22
5/1/73 20
[540]*540These, then, are the rates to be used in the third phase of this ratio trial, which shall commence immediately.
The analysis appended for the most part is a summarization of the testimony of Dr. Stuart, respondent’s expert. Improvement in some of the techniques used by SBEA may be sought; perfection is a practical impossibility.
From the totality of the evidence, I find the State rates statistically adequate, legally operative and fairly representative when weighed against any other known method. A most redeeming feature of their use is that these permit a petitioner to seek relief in the courts without prohibitive expense.
ANALYSIS OF METHODOLOGY
The basis for determining equalization rates is a survey made by the SBEA once every two or three years. This survey is a review and sampling of an assessment roll in order to determine the market values of sampled properties to find their relationship to actual assessed values. Over the past several years, surveys have been made as follows: 1957, 1959, 1961, 1963, 1965, 1968, 1970 and 1973.
In order to prepare a survey, the SBEA receives from each town, city or village assessor, a copy of its roll for the year which will be surveyed. While Nassau County no longer has Town Assessors, the entire roll does find its way to Albany and is used by the SBEA. The roll is segregated into the three towns and two cities with the town further segregated into villages and unincorporated areas. The result of this is to divide Nassau County into 76 separate units.
The information contained on the roll, parcel identification, assessed value and type of property is placed in data processable form. All properties are classified as to type, the main classifications being residential other than apartment houses, commercial, industrial, farm and vacant land, public utilities and railroads. All sampling procedures and determination of ratios are now done by the SBEA, not for the entire assessment roll but within each of the 76 units comprising Nassau County. Each unit is set up with properties comprising that unit, arranged by class with the class having the greatest percentage of the roll at the top and followed with the other [541]*541classes in descending order. The SBEA now chooses the classes which will be sampled in each unit by selecting the classifications up to 80% of the total assessed values for that unit. If, for example, residential properties comprise more than 80% of the total assessed value of the roll for the unit being reviewed, only the. residential class will be sampled. By various other rules, large unit properties, depending upon their size and the percentage which their assessed value bears to the total assessed value of the roll, will also be brought into the sample and appraised by the field appraisal staff of the SBEA.
The SBEA predetermines the number of parcels to be selected for appraisal in each class to be sampled. Based upon the total number of appraisals to be made in each class, the class will be stratified into value intervals, each interval containing the same total actual assessed valuation as any other so that at least two appraisals will be made per interval. Once this process has been completed for each class to be sampled, the properties to be sampled and appraised are randomly selected. The SBEA also provides for backup parcels to be selected should the first selections prove incapable of being appraised. According to the SBEA’s own rules, of the parcels appraised, not more than two thirds can be parcels appraised for a previous survey. The evidence demonstrates clearly that this rule is violated with regularity, and the same parcels are selected and appraised over and over again in survey after survey. For the 1968 survey for the Town of Oyster Bay, in 11 of the 19 units, 100% of the appraisals were of parcels previously appraised in the prior survey.
Within the framework and context of the rules and procedures of the State board, once the property classifications to be sampled have been determined and once the number of appraisals to be made for each property class has been determined, each property class is stratified into value intervals so that there will be at least two samples for each interval in each property class. In each value interval there are at least two samples (appraisals) according to the board’s rules. It is into each of these value intervals that actual sales may be inserted. Once the sampling has been made and the appraisals have been completed, the State board begins work in each value interval for each class. In each interval the State board determines the mean assessed value and the mean market value of the samples. This is done by adding the actual assessed values of the samples in the interval and dividing the [542]*542total by the number of samples for both assessed value and market value determined from the appraisals. The State board then multiplies the actual number of properties in the value interval by the mean assessed value and similarly multiplies the actual number of properties in the interval by the mean market value. This results in a total estimated assessed value and a total estimated market value for the interval being reviewed. The State board uses this same method for each interval for each class. The board now determines a ratio for the sampled class as follows:
They add the estimated assessed values of each interval and the total estimated market values of each interval. This results in a total estimated assessed value for a given class and a total estimated market value for that class. They divide the total estimated assessed value by the total estimated market value and arrive at a ratio for the sampled class. This method is used for each sampled class.
In order to determine the final ratio for the unit being reviewed (the village), the State board proceeds as follows: Starting with the ratio determined for each class, that ratio is applied to the actual assessed value of that class as follows:
The actual assessed value of a class is divided by the ratio determined for that class which will produce a market value figure. The same procedure is done for each of the sampled classes. The market values so determined for each of the sampled classes are totaled to give a total market value figure. This figure is divided into the actual assessed values of all the properties on the roll within those classifications sampled. The result of this division gives the ratio for the entire village. This process is repeated for each village and each city and in the case of the towns in Nassau County, each area of the town outside of the villages. For Nassau County the State board now has 76 ratios, one for each of the units in the county as follows:
One unit for each village; one unit for each section of a town outside the villages; and one unit for each of the two cities. These must be combined in order to provide ratios for each of the three towns, and ultimately combined to produce a ratio for the county.
By the above methods the State board has determined a ratio for each unit as described. In order to arrive at a ratio for a town, for example, Oyster Bay, the method is as follows:
The Town of Oyster Bay comprises 19 units, 18 villages and [543]*543that portion of the town outside the villages. Since the board has already determined the ratios for each of these 19 units, prior to 1972, they divided the actual assessed value of the sampled classes in each unit by the ratio for that unit to determine a market value figure for that unit. These market value figures are totaled which results in a total market value for Oyster Bay. The board then divides this total market figure by the actual assessed value of all properties in the sampled classes on the roll for Oyster Bay. The result is an unadjusted ratio for Oyster Bay. From 1972 onward, the method changed slightly in that the total actual assessed value for all properties is used and not just those properties in the sampled classes. This results in higher estimated market values.
The SBEA estimates the market value for all of the unsampled property classes by dividing into the actual assessed values of such properties the ratio they have determined for the sampled classes. The resultant total becomes an estimated market value which is added to the estimated market value of the sampled classes in the town. The total actual assessed value of all properties in the town is divided by the estimated market value of all properties in the town to produce an unadjusted ratio for the town. This method of finding the estimated market value of unsampled classes by using the ratio developed for the sampled classes assumes that the ratio is identical. The evidence shows that the unsampled classes, especially railroad and utility properties, are considerably greater than the ratios for residential or commercial properties. This method, therefore, creates an underestimate by overstating the market values of the unsampled classes. Table 1 then contains the various adjustments to the ratio, which will be discussed later.
Once having found ratios for each of the three towns and the two cities, the board then combines the adjusted ratios to determine a ratio for the county. The board divides the total assessed value of each town and city by the ratio determined for that town and city to give a total indicated market value. These total indicated market values for each town and city are added to produce a total market value indication.
The actual assessed values of all property on the Nassau roll is then totaled and divided by the total market value indication to produce a ratio for the county.
After computing the ratio attributable to a town by combin[544]*544mg the village and unincorporated area ratios or, after computing the ratio for the county by combining the ratios of the three towns and two cities, the SBEA makes several adjustments to arrive at a final ratio figure. In this regard they apply an adjustment for properties subject to veterans, clergy and aged exemptions and for changes in the level of assessment.
With respect to the adjustment for exemptions, the actual assessed values of all properties with such exemptions are subtracted from the total assessed value column. From the estimated market value column, the same ñgure is subtracted. The new assessed value total is divided by the new market value total to produce a ratio. Aside from the fact that it is irrelevant in estimating aggregate ratio to subtract out properties which have tax exemptions, the properties subtracted are considered to be assessed at 100% of true value, which the SBEA knows is not true. The effect of this adjustment is to reduce the final ratio by at least one percentage point. This constitutes an absolute mathematical certainty tending to reduce the ratio, a totally unfounded and untenable procedure. .
The level of assessment adjustment is made to update the SBEA ratio from a base year when a ratio is being developed for the roll of a later year. The most interesting aspect of this adjustment is that it is zero in every year in issue herein. Petitioner’s expert testified that only certain changes in assessments on the roll are used by the SBEA in computing this adjustment, but the testimony of Mr. Stein in the Guth case (34 NY2d 440) was that all changes in assessments enter into this adjustment. If such is the case, it is difficult to comprehend how the adjustment is always zero.
In this regard too, it is interesting to note how the SBEA combines the ratios from two survey years to get a ratio for a current tax roll. For example, in arriving at the ratio for the Town of Oyster Bay for the 1970 tax roll, the SBEA used both the 1965 and 1968 surveys. The ratio from each of these surveys was given equal weight to arrive at the 1970 Town of Oyster Bay ratio, yet the 1970 ratio is not the mean between the two earlier ratios. Analysis of this method shows that the SBEA is not using the actual assessed values of the current roll to arrive at a ratio for that roll. They are in effect using the ratios from the two earlier surveys and somehow combining them to come up with a rate which is guaranteed to fall [545]*545between the two. The evidence shows that any figures may be substituted for the assessed values, and the results will always be the same.
Critical analysis of the SBEA methods and procedures may be divided into three major categories: selection procedures, sampling errors and nonsampling errors. The selection methods of the SBEA do not conform to orthodox statistical procedures for random sampling. It is almost a judgment procedure with a downward bias. This results from the application of the 80% rule by which up to 20% of the population to be sampled is completely excluded and never permitted to enter the sampling frame. For the 1968 survey made in Nassau County, residential properties existed in 75 of the 76 survey units and were sampled in all 75 units. Commercial properties existed in 75 of the 76 units but were sampled in only 30. Industrial properties existed in 48 of the 76 units and were sampled in only 5. Public utility and railroad properties existed in 72 of the 76 units and were sampled in only 5. Vacant land existed in all 76 units and was sampled in only 9 units.
The review parcel procedure by which at least two thirds of the samples have been used in prior surveys guarantees a complete exclusion of parcels whose assessed values have been changed. This procedure also prevents new parcels from ever entering the sampling frame because the evidence demonstrates that in many survéy units, only review parcels are used, thus violating even the SBEA’s own two-thirds rule. The effect of this is to prevent higher ratio properties (newer properties) from ever entering the sample.
In addition, the method by which weight is taken away from the industrial, public utility and railroad properties, which may have entered the sample, guarantees that these high ratio properties (at least railroad and public utility) are excluded and can have no effect on the ultimate aggregate ratios determined. The method by which changes are made in the sample after selection, the market value trend, appears to force the results. In this method, the SBEA compares the market value of an appraised selected sample with their own independent estimate of what the market value is. If the results differ, the sample may be eliminated and additional properties may be selected to be appraised. The petitioner’s witness admitted that the SBEA starts off with a predetermined trend for an area. If the survey is significantly different, the sample is augmented with more appraisals. (See Elby [546]*546testimony May 28, 1975.) This is a judgmental interference with a random sample.
The use of nonrepresentative sales overweighs the appraisal results. The sales are almost exclusively small residential parcels which show substantially lower ratios than those of the appraisal parcels. No sales of properties in the unsampled classes are ever permitted to become part of a survey. The court has already commented on this almost total use of residential sales in the main text of the decision herein. The survey is overloaded by the use of sales which bear little relationship to their true proportion to all properties on the Nassau County roll. For example, in Sea Cliff for the 1968 survey, only 8 appraisals were made, yet 47 sales were also used.
With respect to sampling error, that is, the difference one can expect between a sample result and the result obtained from the true population figure if a sample taken from 100% of the population is used, mathematical formulae exist to predict and to control it. Respondent’s statistical expert stated that the SBEA has never measured the sampling error. This expert attempted to compute the error and found it to be large. For the 1970 survey for the Town of Oyster Bay outside of the villages, he found the margin of error for residential properties to run between a possible low ratio of 15% to a high of 24%. In the Village of East Hills only one appraisal was made in each of the seven value intervals for the residential class making it impossible to compute a sampling error.
The SBEA methods provide fertile ground for the proliferation of nonsampling errors, or those errors and mistakes caused by improper appraisal techniques, misrecording of figures and errors in data processing. These are uncontrollable and impossible to predict. In order to keep these to a minimum, controls and checks would be required. The appraisals themselves could be improper or typographical errors could exist, and even incorrect transcription from appraisals to computer could occur. The possibility of computer programming errors also exists. Despite these errors which are inherent in any system, the one area of SBEA methodology, sales information, appears to provide a high degree of nonsampling error. Respondent’s expert checked 364 sales in the 1970 survey for the Town of Oyster Bay and found 107 errors in the recording of sales price information on the computer printouts. It appears that $120 is automatically and arbitrar[547]*547ily subtracted by the SBEA from the sales price of all confirmed sales.
The confirmation of sales is accomplished by requiring buyers to return an unsigned card to the SBEA. Of the cards sent to buyers the response rate is only 55%, and there is no testimony in the record concerning whether cards are sent to all buyers in Nassau County.
It has been stated that the SBEA methods are superior to the selected parcel method because of the greater number of properties sampled by the SBEA in an allegedly objective fashion. Analysis proves that this is not completely true. While it is true that the SBEA sampled 1,215 properties for the 1970 survey for Nassau County, the 1963 survey was based on only 318 samples. In reality, these numbers are not large. For the 1968 survey for the Town of Oyster Bay, the average number of samples was 10 per village. For the 1970 survey, the per village average number of appraisal samples was 11 for Hempstead, 14 for North Hempstead and 11 for the Town of Oyster Bay. A sample size of 10 or 11 or even 14 to determine a ratio for a village could be too small a sample and statistically unreliable. A sampling of 66 parcels for Hempstead outside of the village areas, 63 for North Hemp-stead outside of the villages and 80 for the Town of Oyster Bay outside of the villages in the 1970 survey is likewise too small a sampling. Even the addition of sales under 1,000 in the 1961 and 1963 surveys, and approximately 6,000 in the 1968 and 1970 surveys, while appearing to be large in number is in reality only about 25 to 30 sales per village.
Nevertheless, despite all of the failings and shortcomings of the methods and procedures of the SBEA, it is still far superior to the old-fashioned selected parcel sample method.