Boslaugh, J.

Fremont Plaza, Inc., and Mary Rodamar have appealed from the order of the district court which dismissed their appeal from the Dodge County Board of Equalization.

Mary Rodamar owns the land underlying the Fremont Mall which is leased to Fremont Plaza, Inc., under a long-term lease. Fremont Plaza owns all of the improvements on the land. As the interests of both parties in this matter are the same, they will be referred to as the taxpayer. This appeal involves six parcels of land, which will be referred to as the mall.

The Dodge County assessor fixed the actual value of the mall for tax purposes at $4,337,285 for the 1983 tax year. The taxpayer filed a timely protest with the Dodge County Board of Equalization (Board) based on unequal assessment. The protest was disallowed, and the taxpayer appealed to the district court. The county cross-appealed, contending the assessed valuation was too low.

The taxpayer’s amended petition alleged that the actual value of the mall as determined by the assessor did represent the fair market value of the property on that date; that the use of the Nebraska Agricultural Land Valuation Manual (Land Manual) to value unimproved farmland resulted in that property’s being assessed at not more than 45 percent of its actual value; and that the assessor used only the procedure described in the Land Manual to determine the value of such property. The taxpayer further alleged the assessor used the Marshall Valuation Service and comparable sales to determine the fair market value of its property and that the assessor did not attempt to correlate the results of the two different methods of appraisal to determine uniform valuation as required by Neb. Const, art. VIII, § 1, and Neb. Rev. Stat. § 77-201 (Reissue 1981). The taxpayer sought to have the assessed value of its property reduced to the same percentage of actual value as agricultural land was assessed.

*305 The matter was heard March 26 and 27, 1985. The district court found that the assessor had correctly applied state-approved criteria in valuing the taxpayer’s property for the 1983 tax year, that the resulting value represented the actual value of the property for that year, and that the taxpayer had failed to produce clear and convincing evidence to sustain its claim of disproportionate assessment. Both the taxpayer’s appeal and the county’s cross-appeal were dismissed. This appeal followed.

The trial court found that the value of the taxpayer’s property as fixed by the Board in the amount of $4,337,285 was the actual value of the property. The taxpayer does not contest this finding, but contends that this value is disproportionate to the values placed on other property in the county. The taxpayer contends the trial court erred because it sustained its burden of proving disproportionate assessment, the assessed valuation of its property should have been reduced to the same percentage of actual value as agricultural land, and its appraiser’s fees should have been taxed as costs.

The county has not appealed from the dismissal of its appeal, but seeks affirmance of the district court’s order in all respects.

At the outset we note that an appeal from a judgment of the district court concerning action by a county board of equalization is heard as in equity and reviewed de novo. Kearney Convention Center v. Board of Equal., 216 Neb. 292, 344 N.W.2d 620 (1984). A taxpayer may question the assessed value (actual value) of the taxpayer’s real estate, the lack of proportionate and uniform valuation of the property, or both issues, in a proceeding before a board of equalization. Gordman Properties Co. v. Board of Equal., ante p. 169, 403 N.W.2d 366 (1987).

In an appeal from action by a county board of equalization the taxpayer has the burden of proving “the contention that the value of the taxpayer’s property has not been fairly and proportionately equalized with all other property, resulting in a discriminatory, unjust, and unfair assessment.” Gordman Properties, supra at 178, 403 N. W.2d at 372. In such a case

“[t]here is a presumption that a board of equalization has faithfully performed its official duties in making an *306 assessment and has acted upon sufficient competent evidence to justify its action, which presumption remains until there is competent evidence to the contrary. Such presumption disappears when there is competent evidence on appeal to the contrary, and from that point on the reasonableness of the valuation fixed by the board of equalization becomes one of fact based upon the evidence, with the burden of showing such valuation to be unreasonable resting upon the appellant on appeal from the action of the board.”

(Emphasis omitted.) Gordman Properties, supra at 178, 403 N.W.2d at 372, citing Hastings Building Co. v. Board of Equalization, 212 Neb. 847, 326 N.W.2d 670 (1982).

As we explained in Gordman Properties at 179, 403 N.W.2d at 373, this presumption is more properly characterized as “a principle of procedure involving the burden of proof, namely, a taxpayer has the burden to prove that action by a board of equalization fixing or determining valuation of real estate for tax purposes is unauthorized by or contrary to constitutional or statutory provisions governing taxation.”

The taxpayer first contends the district court erred in finding the two dissimilar methods of appraisal used by the county to value urban and agricultural real estate did not result in the disproportionate assessment of the two classes of property. The taxpayer contends it presented sufficient evidence to sustain this claim and that its case is virtually identical to Kearney Convention Center v. Board of Equal., supra, in which this court ordered the assessed value of the taxpayer’s property be reduced to the same percentage at which agricultural land was assessed.

The county argues the instant case is distinguishable because the evidence presented by this taxpayer is different and less reliable than that presented in Kearney Convention Center.

In Kearney Convention Center the taxpayer presented stipulated and uncontradicted testimony of an appraiser concerning his study of 550 detailed appraisals of urban and rural property to determine the fair market value of agricultural land as compared to its assessed value. The appraiser had concluded the fair market value-actual value for agricultural *307 land in the county was uniformly undervalued for the tax year in question, and, as a result, such land was uniformly assessed at 44 percent of its actual value. The expert based his opinion on a review of comparable sales in the county for 1980 and 1981. There was no evidence presented by the county of any attempt to correlate the different methods.

The record shows the taxpayer in this case presented the following evidence concerning disproportionate assessment.

Robin Hendricksen, the chief appraiser for the Dodge County assessor’s office, testified for the taxpayer. He testified that three methods of appraisal were used by the assessor to determine the value of property in the county. Commercial property was valued by determining reproduction cost in conjunction with comparable sales. Residential real estate was valued by determining reproduction cost and the appropriate depreciation rate, with reproduction cost information obtained from the Residential Cost Handbook. In determining such reproduction cost various factors were considered, including the state of improvements on the property; the presence of built-in appliances and carpeting; the quality of construction; plumbing; the presence of abasement, garage, or fireplace; and the general condition of the property. The depreciation rate was determined by considering the age of the structure and any recent improvements added. Market studies were also used, and the method, in essence, was one using comparable sales.

Nonresidential, commercial, and industrial properties were valued in basically the same manner, except the Marshall Valuation Service, published by Marshall and Swift Publication Company, was used to determine reproduction costs. Market analysis, or comparable sales, was again used to determine the ultimate appraisal figure. When no comparable sales were available, the assessor made an independent appraisal based on the age of the structure and loss of value.

Land underlying residential homes was valued on the basis of market studies of vacant lots. The assessor endeavored to find the actual fair market value of the properties.

Residential improvements on agricultural land were valued in much the same manner as those on residential land. Comparable sales were used as guides where available. *308 Commercial improvements on agricultural land were valued by using an effective age life lapse system, using the Marshall and Swift valuation system to obtain appropriate reproduction costs.' This differed from the valuation of commercial improvements on urban land in that market studies were not used as guides.

The assessor did not consider income to commercial or industrial property in his appraisals. The income approach was used, however, to verify the values obtained from the cost approach. The resulting values were then correlated and adjusted.

The value of unimproved agricultural land was determined solely on the basis of the Land Manual. The assessor first determined the usage of the land and then considered the soil type. Each soil type is classified according to a manual prepared by the Soil Conservation Service. Those classifications were then converted through the use of a chart which adjusts soil conservation designations to Department of Revenue designations. Finally, the value for each designation was multiplied by the number of acres per classification and the results were added together to obtain the total value. Hendricksen testified there was no attempt made to correlate the values computed under the Land Manual process with the fair market value of the property.

Hendricksen then testified that he had done a few informal studies to determine such a correlation and had concluded the ratio was in the “30 to 40 range, some 50. There was a wide variance.” Hendricksen had compared the assessed valuation of agricultural lands to comparable sales of such land, using arm’s-length sales of agricultural land in the studies. The information was obtained from form 521s, real estate transfer statements, filed from 1981 through early 1984, with the majority of sales having occurred in the “ ’83-’84” area.

Hendricksen also testified he had received copies of the results of a similar study undertaken by the state. The state reported the assessment-sale ratio for unimproved farmland in Dodge County was 40.22 percent for the 1983 tax year.

Hendricksen then testified that the value placed on unimproved farmland in the county for the 1983 tax year did *309 not represent the fair market value of such property but that the valuations established for other property in the county for that year did represent the fair market value of such property.

Hendricksen further testified that in appraising agricultural land the assessor did not consider the size of the farm, its proximity to a town or marketplace, location within an adverse weather area, presence of utility service, or any other factor. He conceded these would be relevant factors in determining the fair market value of the property and would be reflected in its sale price.

Hendricksen testified the manuals used to determine reproduction costs for residential and commercial property had been updated, as of January 1, 1984, to values current as of January 1, 1982. The values had not been updated further because, it was his opinion, based on a review of comparable sales, no significant changes in market value had occurred during that time. The agricultural manual had not been updated for the 1983 tax year, and the witness did not know to what year the values set forth in the manual were tied.

The taxpayer then presented testimony by William C. Fisher, a real estate appraiser. Fisher testified he had been an appraiser since 1965, had once held a position with the Department of Roads, then associated with a realty firm in Grand Island as an appraiser, and subsequently left that firm to start his own firm in 1972. He testified he had had extensive training in appraisal work, was a member of the Appraisal Institute, and had been active in various real estate groups. He had conducted appraisals in Nebraska as well as several surrounding states and had appraised all types of commercial, industrial, and farm property.

Fisher testified that he had attempted to determine the value of farmland in the county for use in comparing those values with the value of the taxpayer’s property. Fisher testified he utilized the following methodology to determine the value of farmland as of January 1,1984. He first hired an abstracter to obtain all of the sales of farmland in 1983 and 1984. The sales were then reviewed by the witness, and sales which were obviously not arm’s-length transactions were discarded. The remaining sales were verified to ensure they were arm’s-length *310 transactions by reviewing the transfer statements in the assessor’s office and through private sources. After verification was completed, there were 30 usable sales.

Fisher then prepared a chart which illustrated the sales data of each transaction and the assessed valuation. Another chart was prepared which illustrated the soil and land classifications involved in each sale. Each sale involved tracts consisting of more than 20 acres.

Fisher defined an arm’s-length transaction as one in which a willing buyer agreed to pay a certain amount to a willing seller for a specific parcel of property, each knowing all the uses for which it was suited and neither under any duress to buy or sell. He also testified that, in his opinion, arm’s-length sale prices are the best determinant of fair market value.

The taxpayer then presented testimony by Dr. Gary M. Hoeltke, a research psychologist and senior vice president of Selection Research Incorporated (SRI). Hoeltke testified his responsibilities at SRI included designing and analyzing different research studies for clients of the company. Hoeltke had received a doctoral degree in educational psychology and measurement, with a specialty in statistics and research, in 1966.

Hoeltke was employed by the taxpayer to make a comparison between sales values and assessed values of farmland in the county using the 30 sales identified by Fisher. Hoeltke testified he employed the following methodology. He first determined the 30 sales were representative of land in the county. To do so he made a comparison of the percentages of the various classifications of land in the sales to the percentages of such classifications in the county, using the classifications from the Land Manual. He also compared the distribution of sale land with the distribution of land in the county.

Hoeltke then testified he compared the sales values to the assessed values of the properties, using the following methodology. To obtain the first sample group, he deleted the effect of improvements from two of the sales using the same ratio used by the county for assessment purposes. He then figured the average sale price and the average assessed value and compared them using two different methods. He next redid *311 the analysis deleting all 12 sales which included improvements, thereby forming a second sample group.

In making the comparison Hoeltke testified he used the chi-square technique, which permitted the comparison of several different classifications simultaneously. He testified that essentially the same results were obtained using either set of data. The resulting ratio of assessed value to sale value was 40 percent. Hoeltke testified these results indicated the difference between assessed value and sale value was a greater difference than could be ascribed to chance. He also testified it was his opinion that a purely random sample would be a practical impossibility in this case due to the size of such a sample and the difficulty of obtaining accurate data.

The county then presented testimony by Frank W. Frost, who testified that he operated an appraisal and consulting firm and had been an appraiser for 29 years. He also testified he was a member of the American Institute of Real Estate Appraisers and various similar organizations.

Like the taxpayer’s expert witness, Frost made an independent review of farmland sales in the county for the 1983 tax year. He testified that, in his opinion, the sales sample was not representative of the value of farmland in the county because the largest sale involved 160 acres, while the typical size of a farm in the county was 320 acres.

The county then presented testimony by James R Scott, an associate professor of decision science and chairman of the department of management and information systems of Creighton University. Scott’s doctoral work was primarily in applied statistics. He reviewed the statistical analysis performed by Hoeltke and concluded the study was flawed because it was based on sales data which he believed were not representative of property in the county which had not been sold. It was his opinion the only way to achieve an accurate statistical study of the comparison of actual value to assessment value would be through a random sample taken from the entire county.

The county then presented testimony by Bruce B. Johnson, a professor of agricultural economics at the University of Nebraska. Johnson testified the average size of farms in the county was 318 acres, while the average sale of farmland *312 consisted of 109 acres during the period of 1977 through 1982. He also testified that, given the market for farmland in the state, it would be difficult to find enough specific sales to provide a statistically sound representation of the total land base. In addition, he testified that he had participated in the development of the Land Manual and believed it was based on the value of the dollar sometime in the early 1970s.

From our review of the record we find the taxpayer sustained its burden of proving the claim of disproportionate assessment. There is clear testimony by the chief appraiser of Dodge County that his independent studies showed the value of farmland as determined by the soil classification method varied as compared to the market value of the farm from 30 to 40 percent of market value. There was also clear testimony by this witness that a similar study by the state revealed the assessment-sale ratio for Dodge County farmland was 40.22 percent for 1983. The witness further testified that the assessed value of other property in the county did represent the fair market value of that property.

The county presented evidence to rebut the independent studies undertaken by the taxpayer’s experts, but did not satisfactorily refute the appraiser’s testimony. The county attacked the statistical reliability of the taxpayer’s study; yet, the results of those studies were consistent with the results obtained in the appraiser’s independent studies and the state’s study.

The county also argues the use of the assessment-sale ratio is improper because it does not accurately reflect the actual value of all agricultural property in the county for 1983, because the sales of farmland are insufficient to show the actual value of the land. In support of this position the county relies on Box Butte County v. State Board of Equalization & Assessment, 206 Neb. 696, 295 N.W.2d 670 (1980), where we held that sales were a poor indicator of the actual value of farmland in the county at that time because the sales were made to adjoining owners anxious to utilize rare opportunities to add contiguous tracts to their farms. We find this argument unpersuasive.

In County of Loup v. State Board of Equalization & Assessment, 180 Neb. 478, 480, 143 N.W.2d 890, 892 (1966), we *313 stated:

Ordinarily, the objection to using sale price as the standard or evidence of value is the fact that the sale may not have been in the ordinary course of trade. The character and circumstances of the sale are important in determining to what extent the sale price may be used to fix the value of the property. The same difficulty is involved in the use of sales-assessment ratios. It is important that the computation include only representative sales with the consideration of each sale accurately determined.

The evidence in this case is that the transactions used in the studies were arm’s length. Similarly, there is no evidence that the sales were made to farmers anxious to add adjoining land.

We find the taxpayer established that the two dissimilar methods used by the county resulted in a disparity between the assessment of urban and agricultural property in the county.

This holding answers another issue raised by the taxpayer, namely, whether the district court erred in requiring a showing of “deliberate and intentional discrimination systematically applied throughout the county.” While several cases have utilized such language, the correct standard is that articulated in several more recent cases. In Gordman Properties Co. v. Board of Equal., ante p. 169, 178, 403 N.W.2d 366, 372 (1987), we stated the taxpayer has the burden of proving the contention of disproportionate assessment by showing the property had not been “fairly and proportionately equalized with all other property, resulting in a discriminatory, unjust, and unfair assessment.” A similar standard was set forth in Kearney Convention Center v. Board of Equal., 216 Neb. 292, 344 N.W.2d 620 (1984). The key requirement is that the evidence establish an actual disparity in assessment which indicates the principle of uniformity has been violated, and not a mere difference of opinion as to valuation. LaGord Assoc. v. County of Cass, 209 Neb. 99, 306 N.W.2d 578 (1981); Hastings Building Co. v. Board of Equalization, 190 Neb. 63, 206 N.W.2d 338 (1973).

The taxpayer next contends the district court erred in failing to reduce the assessment of the taxpayer’s property to the same *314 percentage of actual value as applied to agricultural land.

As we stated in Kearney Convention Center,

“ [T]he right of the taxpayer whose property alone is taxed at 100 per cent, of its true value is to have his assessment reduced to the percentage of that value at which others are taxed even though this is a departure from the requirement of statute. The conclusion is based on the principle that where it is impossible to secure both the standards of the true value, and the uniformity and equality required by law, the latter requirement is to be preferred as the just and ultimate purpose of the law.”

Id. at 304, 344 N.W.2d at 626, quoting Konicek v. Board of Equalization, 212 Neb. 648, 324 N.W.2d 815 (1982).

Applying that principle to this case, we find the assessment of the taxpayer’s property should be reduced to 40 percent of its actual value for the 1983 tax year.

The taxpayer’s final contention is that the district court erred in failing to tax the costs of the taxpayer’s appraiser’s fees to the county. The county argues against such action, contending an appraiser would have been required to prove the taxpayer’s case even without the county’s cross-appeal.

Neb. Rev. Stat. § 77-1513 (Reissue 1986) provides:

Whenever any person shall appeal to the district court from the assessment of his property as fixed by the county board of equalization, and the appeal shall be sustained in whole or in part, the cost of such appeal, including costs of witnesses, if any, shall be paid by the county wherein such property is situated____

The statute applies whenever a taxpayer successfully challenges the county and provides for compensation for any witness called to testify on behalf of the taxpayer. Accordingly, the taxpayer in this case is entitled to an order taxing the costs of its witnesses and the appeal to the district court to the county.

The judgment is reversed and the cause remanded with directions to enter a judgment in conformity with this opinion.

Reversed and remanded with directions.