4-3-2-1 Rule
An empirical rule that ascribes 40 percent of the value of a standard lot (see lot,
standard) to the quarter of the lot fronting on the street, 30 percent to the next
quarter, 20 percent to the third quarter, and 10 percent to the rear quarter. Compare
Harper rule; Hoffman rule; one-third, two-thirds rule. Note: Lots with a depth greater
than the standard lot cannot be valued in accordance with this rule as stated above.
The rule is sometimes altered by omitting the word "standard." It thereby becomes
applicable to extra deep lots but produces inconsistent results as applied to lots
of varying depths.
65/35 Rule
Rule states that the value of a triangular lot with its base on the facing street
will be approximately 65 percent of that of a rectangular lot of the same frontage
and depth. The value of the triangular lot with its apex on the facing street will
be 35 percent of that of a rectangular lot of the same base and depth.
Abstraction Method
Method of land valuation in the absence of vacant land sales, whereby improvement
values obtained from the cost model are subtracted from sales prices of improved
parcels to yield residual land value estimates. Also called residual land technique.
Accuracy
Accuracy. The closeness of a measurement, computation, or estimate to the true,
exact, or accepted value. Accuracy also can be expressed as a range about the true
value. See also precision and statistical accuracy.
Adaptive Estimation Procedure (AEP)
A computerized, iterative, self-referential procedure using properties for which
sales prices are known to produce a model that can be used to value properties for
which sales prices are not known. Also called "feedback."
Additive Model
A model in which the dependent variable is estimated by multiplying each independent
variable by its coefficient and adding each product to a constant.
Adjustments
Modifications in the reported value of a variable, such as sale price. For example,
adjustments can be used to estimate market value in the sales comparison approach
by modifications for differences between comparable and subject properties. Note:
Adjustments are applied to the characteristics of the comparable properties in a
particular sequence that depends on the method of adjustment selected.
Age/Life method
A method of estimating accrued depreciation founded on the premise that, in the
aggregate, a neat mathematical function can be used to infer accrued depreciation
from the age of a property and its economic life. Another term is "straight-line
depreciation" (see depreciation, accrued; and depreciation method, straight-line).
Algorithm
A computer-oriented, precisely defined set of steps that, if followed exactly, will
produce a pre-specified result, for example, the solution to a problem.
Allocation by Abstraction
A method of separating a whole property value into land and improvement components.
The appraiser estimates replacement cost new, subtracts an appropriate amount for
depreciation, and subtracts the remainder from the whole property value to estimate
the land value.
Allocation by Ratio
A method of separating a whole property value into land and improvement components,
in which the appraiser develops proportions of land and improvement values for comparable
properties and applies those proportions to the subject's whole property value.
Allocation Method
A method used to value land, in the absence of vacant land sales, by using a typical
ratio of land to improvement value. Also called land ratio method.
Ancillary Data
Subsidiary data used to define the area of interest, for example, topographic, administrative,
or geologic data. Ancillary data may be digitized and merged with the primary image
data to facilitate analysis.
Appraisal Emulation Model
The appraisal emulation model (see Section 3.2.2.1 Comparable Sales Method) follows
the steps that an appraiser might follow in forming a value estimate (although not
with the same insight or flexibility that a qualified appraiser brings to the assignment).
The model selects “comparable sales” using some standard criteria. It then rates
those comparable sales by suitability, based on the physical and sales characteristics
of each comparable sale, by adjusting the varying elements (much as is done on an
appraisal form); the model then calculates an estimate of value.
Appraisal Methods
The three methods of appraisal, that is, the cost approach, income approach, and
sales comparison approach.
Appraisal Principles
The economic concepts underlying appraisal. See under principle of: anticipation,
balance, change, conformity, contribution, and substitution. See also competition;
demand; highest and best use; and variable proportions, law of.
Appraisal Ratio
(1) The ratio of the appraised value to an indicator of market value. (2) By extension,
an estimated fractional relationship between the appraisals and market values of
a group of properties. See also level of appraisal.
Appraisal Ratio Study
A ratio study using independent expert appraisals as indicators of market value.
Appraisal-Sale Price Ratio
The ratio of the appraised value to the sale price (or adjusted sale price) of a
property; a simple indication of appraisal accuracy.
Assessment Progressivity (Regressivity)
An appraisal bias such that high-value properties are appraised higher (or lower)
than low-value properties in relation to market values. See price related differential.
Assessment Ratio
(1) The fractional relationship an assessed value bears to the market value of the
property in question. (2) By extension, the fractional relationship the total of
the assessment roll bears to the total market value of all taxable property in a
jurisdiction. See level of assessment and fractional assessments.
Assessment Ratio Study
An investigation intended to determine the assessment ratio and assessment equity.
Assessment-Appraisal Ratio
The ratio of the assessed value of a property to an independent appraisal.
Assessment-Sale Price Ratio
The ratio of the assessed value to the sale price (or adjusted sale price) of a
property.
Automated Valuation Model
An automated valuation model (AVM) is a mathematically based computer software program
that produces an estimate of market value based on market analysis of location,
market conditions, and real estate characteristics from information that was previously
and separately collected. The distinguishing feature of an AVM is that it is a market
appraisal produced through mathematical modeling. Credibility of an AVM is dependent
on the data used and the skills of the modeler producing the AVM.
Average
The arithmetic mean.
Average Deviation
The arithmetic mean of the absolute deviations of a set of numbers from a measure
of central tendency, such as the median. Taking absolute values is generally understood
without being stated. The average deviation of the numbers 4, 6, and 10 about their
median (6) is (2 + 0 + 4) / 3 = 2. The average deviation is used in computing the
coefficient of dispersion (COD).
Baltimore Rule
Synonymous with Bernard rule.
Base-Home Approach
A method of appraising single-family residential properties whereby each residence
to be appraised is Compared with one having common or typical characteristics and
of known value, called the base home, and differences between the two in terms of
condition, size, number of garages, and the like are weighted by the appraiser in
the determination of the value of the property to be appraised.
Bernard Rule
A term generally applied to an empirical rule of appraising a corner lot by adding
together the value ascribable to it as an inside lot on the main street and the
value ascribable to it as an inside lot on the side street. Sometimes known as the
Lindsay-Bernard or Baltimore rule. Compare Zangerle curve.
Beta
A measure of the volatility of a particular stock Compared to the stock market as
a whole.
Bias
A statistic is said to be biased if the expected value of that statistic is not
equal to the population parameter being estimated. A process is said to be biased
if it produces results that vary systematically with some factor that should be
irrelevant. In assessment administration, assessment progressivity (regressivity)
is one kind of possible bias.
Binary Variable
(1) Binary variables are qualitative data items that have only two possibilities-yes
or no (for example, corner location). (2) A variable for which only two values are
possible, such as results from a yes-or-no question, for example, Does this building
have any fireplaces? Used in some models to separate the influence of categorical
variables. Also called a dichotomous variable or a dummy variable. See also continuous
variable; discrete variable.
Blended Model
A blended model (see Section 8.8: Value Reconciliation) is one where more than one
modeling technique is used in deriving the estimate of value. Typically, the technique
involves running a hedonic model and a repeat sales index. The results are then
compared and evaluated. Based on each result, the blended model reports a final
estimate of value. In addition to the hedonic model and repeat sales index, many
blended models also include the results of a tax-assessed value model.
Bootstrap
A computer-intensive method of statistical inference that is based on a repeated
re-sampling of data to provide more information about the population characteristics.
The bootstrap is a data-driven procedure that is particularly useful for confidence
interval approximation when no traditional formulas are available or the sample
has been drawn from a population that does not conform to the normal distribution.
Build-up Method
The build-up method yields an overall capitalization rate from two components. The
building capitalization rate and the land capitalization rate are weighted by the
percentage of property value each represents and then added together to yield an
overall rate.
Building Residual Technique
A capitalization technique used when land value is known and residual income to
the building or improvement is capitalized to obtain the building or improvement
value.
Calibration
The process of estimating the coefficients in a mass appraisal model.
Categorical Variable
A variable summarizing more complex qualitative judgments by assigning each to a
category or giving each a rating. For example, quality of construction might be
categorized as poor, fair, average, or good, or assigned a rating from 1 to 4. The
categories might then be scaled by assigning a value of 100 percent to the average
category and values of 60 percent and 120 percent to the extremes of poor and good.
Central Tendency
(1) The tendency of most kinds of data to cluster around some typical or central
value, such as the mean, median, or mode. (2) By extension, any or all such statistics.
Some kinds of data, however, such as the weights of cars and trucks, may cluster
about two or more values, and in such circumstances, the meaning of central tendency
becomes unclear. This may happen in ratio studies when two or more classes of property
are combined.
Central Tendency, Measure of
A single point in a range of observations around which the observations tend to
cluster. The three most commonly used measures of central tendency are the mean,
median, and mode.
Check Digit
An extra digit used for the purpose of performing a check. For example, using X
and 0 to indicate even divisibility or non divisibilityby 2 would result in the
sequence of numbers 1, 2, 3, 4 being represented as 10, 2X, 30, 4X. Computer systems
generally have a number of such checks built in to ensure that the machine made
no errors in writing or reading data, the data entry clerk did not transpose digits
or leave out records, and so on.
Chi-Square
A particular statistic, and a particular frequency distribution associated with
it, of interest in inferential statistics. (Chi, a Greek letter, is symbolized by
X).
Chronological Age
The number of years elapsed since an original structure was built. Synonyms are
actual age and historical age. Contrast with effective age.
Coefficient
(1) In a mathematical expression, a number or letter preceding and multiplying another
quantity. For example, in the expression, 5X, 5 is the coefficient of X, and in
the expression aY, a is the coefficient of Y. (2) A dimensionless statistic, useful
as a measure of change or relationship; for example, correlation coefficient. See
also coefficient of dispersion and coefficient of variation.
Coefficient of Concentration
The percentage of observations falling within a specified percentage (say, 15 percent)
of a measure of central tendency.
Coefficient of Determination (R2)
A statistic that characterizes two or more sets of numbers. The coefficient of determination,
when multiplied by 100, gives the percentage strength of the (linear) relationship
between or among the sets of numbers. (See also correlation.) For two variables,
the coefficient of determination and the square of the correlation coefficient are
identical; for three or more variables, the coefficient of determination measures
the strength of the relationship between the dependent variable and all the independent
variables combined.
Coefficient of Dispersion (COD)
The average deviation of a group of numbers from the median expressed as a percentage
of the median. In ratio studies, the average percentage deviation from the median
ratio.
Coefficient of Variation (COV)
A standard statistical measure of the relative dispersion of the sample data about
the mean of the data; the standard deviation expressed as a percentage of the mean.
Coincidence, Line of
Synonymous with the preferred term merge line.
Comparable Match
This concept involves the development of value based on analysis of similar (but
not identical) properties using some measure of utility (such as size or capacity)
as the basis of comparison. For example, when appraising an engine lathe manufactured
by Company A, the appraiser has comparables of other similar engine lathes of the
same size manufactured by Companies B and C. Obviously, Compared to a direct match,
this technique becomes more subjective, which requires additional analysis of the
elements of comparison.
Comparable Sales; Comparables
(1) Recently sold properties that are similar in important respects to a property
being appraised. The sale price and the physical, functional, and locational characteristics
of each of the properties are Compared to those of the property being appraised
in order to arrive at an estimate of value. (2) By extension, the term "comparables"
is sometimes used to refer to properties with rent or income patterns comparable
to those of a property being appraised.
Comparative Unit Method
(1) A method of appraising land parcels in which an average or typical value is
estimated for each stratum of land. (2) A method of estimating replacement cost
in which all the direct and indirect costs of a structure (except perhaps architect's
fees) are aggregated and specified with reference to a unit of comparison such as
square feet of ground area or floor area, or cubic content. Separate factors are
commonly specified for different intervals of the unit of comparison and for different
story heights, and separate schedules are commonly used for different building types
and quality classes.
Comparison Factor
A comparison factor is a difference between two properties that influences market
value and can be measured. The number of bedrooms in a single-family residence is
a comparison factor.
Comparison Unit
Comparison units express an overall value attributable to a property in terms of
the value per unit of measure. The sale price of a vacant lot, for example, can
be expressed as a cost per square foot or cost per front foot. The income produced
by a property can also be expressed in comparison units, such as rent per square
foot.
Confidence Interval
A range of values, calculated from the sample observations, that are believed, with
a particular probability, to contain the true population parameter (mean, median,
COD). The confidence interval is not a measure of precision for the sample statistic
or point estimate, but a measure of the precision of the sampling process (see reliability).
Confidence Level
The required degree of confidence in a statistical test or confidence interval;
commonly 90, 95, or 99 percent. A 95 percent confidence interval would mean, for
example, that one can be 95 percent confident that the population measure (such
as the median or mean appraisal ratio) falls in the indicated range.
Contingent Valuation Method (CV)
In economics, a method of valuing public goods. The CV method uses survey questions
to elicit people's preferences for public goods by finding out what they would be
willing to pay for specified improvements in them. The method is thus aimed at eliciting
people's willingness to pay, expressed in dollar amounts.
Continuous Data
Data that can take any value in a given range. They are often based on measurements
(for example, lot size). Quantitative and continuous data can be thought of as synonymous.
Continuous Variable
A variable for which it is conceivable that, given any two observed values, a value
lying between them may occur. For example, temperature and finished living area
are continuous variables; quality class and number of fireplaces are not. See also
binary variable and discrete variable.
Correlation Coefficient (r)
A statistic that characterizes two or more sets of numbers and, when squared and
multiplied by 100, gives the percentage strength of the (linear) relationship between
the two sets of numbers. For example, if the coefficient of correlation between
measures of the height and weight of a group of people were 0.9, then one would
deduce that knowing the height of someone (loosely speaking) would explain (or account
for) 81 percent of the weight.
Correlation Matrix
The table of numbers used to display the correlation coefficients for each pair
of variables when three or more variables are thought to be correlated.
Data
Information expressed in any of a number of ways. " Data" is the general term for
masses of numbers, codes, and symbols generally, and "information" is the term for
meaningful data. "Data" is the plural of datum, one element of data.
Data Edit
The process of examining recorded data to ensure that each element of data is reasonable
and is consistent with others recorded for the same object, such as a parcel of
real estate. Data editing, which may be done by human beings or by computer, is
essentially a mechanical process, distinct from verifying the correctness of the
recorded information by calling or writing property owners.
Data Management
The human (and sometimes computer) procedures employed to ensure that no information
is lost through negligent handling of records from a file, that all information
is properly supplemented and up-to-date, and that all information is easily accessible.
Dependent Variable
A variable, such as sale price, the value of which is predicted by the values of
other variables, such as location and finished living area. Such a variable may
be said to depend on the other (independent) variables.
Degrees of Freedom (d.f.)
The number of values, in a set of observations, that could be assigned arbitrarily
within the specification of a system. For example, in stratifying a sample of n
objects into k strata, there are k 1 degrees of freedom, because, if k 1 frequencies
are specified, the remaining frequency is determined by the total size n. The term
is used in statistics in several slightly different senses but is important primarily
only in connection with a certain aspect of inferential statistics, where it becomes
a means of relating the value of a statistic that has been calculated from a sample
to a table of critical values for such statistics that have been calculated for
a wide range of potential sample sizes and amounts of information defined by the
particular statistic of interest.
Demographics
Characteristics of human populations, for example, size, density, and distribution.
Depth Curve
A graph of depth factors showing the estimated percentage relationships between
the front-foot values of a given lot and the front-foot value of a lot of standard
depth as the depth of the given lot varies. Note: Usually the depth of the given
lot is plotted on the x-axis, and the percentage relationship between the front-foot
value of the given lot and that of a lot of standard depth on the y-axis.
Descriptive Statistics
(1) The branch of the science of statistics that is concerned only with characterizing
or describing a set of data (numbers). (2) By extension, the measures used to characterize
a particular set of data. Compare inferential statistics.
Direct Market Method/Analysis
One of two formats of the sales comparison approach to value (the other being the
Comparable Sales Method). In the direct market method, the market analyst specifies
and calibrates a single model used to estimate market value directly using multiple
regression analysis or another statistical algorithm.
Direct Match
Establishes value on the basis of a direct match to an identical asset, for example,
estimating the value (either retail or wholesale) of automobiles using a blue book.
If the manufacturer, the model number, the age, and the accessories are known, it
is simple to find the value of the subject in the various automobile blue books.
Adjustments are limited to mileage and, more importantly, condition.
Dissimilarity Function
An algorithm used to assign an index of dissimilarity (or similarity) to properties
as Compared to a subject.
Distribution-free Statistics
A set of robust nonparametric methods whose interpretation or reliability does not
depend on stringent assumptions about the distribution of the underlying population
from which the sample has been drawn. See also parametric statistics.
Effective Age
The typical age of a structure equivalent to the one in question with respect to
its utility and condition, as of the appraisal date. Knowing the effective age of
an old, rehabilitated structure or a building with substantial deferred maintenance
is generally more important in establishing value than knowing the chronological
age.
Economic Life
The period during which a given tangible asset, building, or other improvement to
property is expected to contribute (positively) to the value of the total property.
This period is typically shorter than the period during which the improvement could
be left on the property, that is, its physical life.
Elasticity
(1) The responsiveness of supply and demand to changes in price. Supply or demand
that changes rapidly in response to price changes is "elastic." Supply or demand
that changes slowly in response to price changes is "inelastic." (2) A measure of
the responsiveness of tax yields to changes in economic conditions. The yield of
an elastic tax increases rapidly in a growing economy. The yield of an inelastic
tax increases slowly. Often measured by the formula: percent change in tax percent
change in personal income
Error
The difference between the actual value of a variable and the expected value of
the variable exclusive of sampling problems. Errors may be positive or negative,
although in common speech taking the absolute value of the errors is sometimes implied.
In multiple regression analysis, the term "error" is often used loosely to mean
residual.
Exploratory Data Analysis
That part of statistical practice concerned with reviewing the data set to isolate
structures, uncover patterns, or reveal features that may improve the confirmatory
analysis
Exponent
A symbol usually written to the right and above an expression to indicate particular
mathematical operations. For example, 62 means 6 + 6, or six squared. Fractional
exponents indicate inverse operations; for example, an exponent of + signifies a
square root. Exponents are also called powers. Valuation models make use of the
following properties of exponents: A number raised to the exponent 0 is always 1.00;
zero raised to any power is zero; any number raised to the power 1 is itself. Negative
numbers cannot have exponents less than 1.
Factor
(1) An underlying characteristic of something (such as a house) that may contribute
to the value of a variable (such as its sale price), but is observable only indirectly.
For example, construction quality is a factor defined by workmanship, spacing of
joists, and materials used. Factor definition and measurement may be done subjectively
or by a computer-assisted statistical algorithm known as factor analysis. (2) Loosely,
any characteristic used in adjusting the sales prices of comparables. (3) The reciprocal
of a rate. Assessments may be equalized by multiplying them by a factor equal to
the reciprocal of the assessment ratio, and value can be estimated using the income
approach by .
Feedback
See adaptive estimation procedure.
Frequency Distribution
A table showing the number or percentage of observations falling in the boundaries
of a given set of classes. Used in ratio studies to summarize the distribution of
the individual ratios. See also class; histogram; and mode.
Geographic Information System (GIS)
(1) A database management system used to store, retrieve, manipulate, analyze, and
display spatial information. (2) One type of computerized mapping system capable
of integrating spatial data (land information) and attribute data among different
layers on a base map.
Goodness-of-Fit Statistics
Statistics used in multiple regression analysis and other kinds of statistical modeling
to express the amount, and hence the importance, of the errors or residuals for
all the predicted and actual values of a variable.
Harmonic Mean Ratio
The reciprocal of the arithmetic mean of the reciprocals of each value in the data
set. The harmonic mean ratio is less affected by extreme values in the data set
than the arithmetic
Hedonic Model
Hedonic pricing attempts to take observations of the overall goods or services and
obtain implicit prices for the goods and services. Prices are measured in terms
of quantity and quality. When valuing real property, the spatial attributes and
property-specific attributes are valued in a single model. Calibration of the attribute
components is performed statistically by regressing the overall price onto the characteristics.
Heterogeneous
Unlike; without interrelation. The opposite of homogeneous.
Heteroscedasticity
The quality of a dependent variable having inconstant variance for all values of
the independent variables. The opposite of homoscedasticity.
Hoffman Rule
An empirical rule that ascribes two-thirds of the value of a lot to the front half.
Compare Harper rule; Hoffman-Neill rule; 4-3-2-1 rule; one-third, two-thirds rule.
Hoffman-Neill Rule
An extension of the Hoffman Rule to cover lots of depths other than half that of
the standard lot.
Homogeneous
Possessing the quality of being alike in nature and therefore comparable with respect
to the parts or elements; said of data if two or more sets of data seem to be drawn
from the same population; also said of data if the data are of the same type (that
is, if counts, ranks, and measures are not all mixed in together).
Homoscedasticity
The quality of a dependent variable having constant variance for all values of the
independent variables. For example, if regression residuals were plotted against
living area, a band of uniform width would indicate homoscedasticity; a trapezoid
would indicate heteroscedasticity.
Horizontal Inequity
Differences based on criteria other than value range in the levels of assessment
of groups of properties. For example, properties in one neighborhood may have a
higher level of assessment than similar properties in another neighborhood. See
vertical inequity.
Hybrid Model
A model that incorporates both additive and multiplicative components. See also
additive model and multiplicative model.
Income Approach
One of the three approaches to value, based on the concept that current value is
the present worth of future benefits to be derived through income production by
an asset over the remainder of its economic life. The income approach uses capitalization
to convert the anticipated benefits of the ownership of property into an estimate
of present value.
Inferential Statistics
The branch of statistical studies concerned with making predictions about the values
of a large number of observations of a variable on the basis of a small number of
observations of that variable and related facts. (2) By extension, the statistics
calculated in such predictions.
Interquartile Range(IQR)
The result obtained by subtracting the first quartile from the third quartile. By
definition 50 percent of the observations fall within the IQR.
Inwood Coefficient
A factor used to obtain the present worth of a level stream of income; also known
as the present worth of 1 per period factor.
Iowa
Type Curve
A classification of survivor curves by their basic mathematical shape into three
families of, respectively, 6, 7, and 5 curves; hence the alternate designation of
"Iowa
18 type curves." Type survivor curves are used to smooth original survivor curves,
to help determine the probable life of single units, and as a means of checking
the adequacy of the depreciation reserve balance or of estimating an adjustment
factor in the appraisal procedure.
Iteration
One repetition or repeated cycle in a process of estimating values as close as possible
to actual values by repeated approximations. The results of each approximation are
used in the next one.
Kruskal-Wallis Test
A test in inferential statistics, valid for all types of numerical data, that seeks
to determine whether the observations in a sample came from one population as opposed
to three or more distinct, homogeneous subpopulations. This test is used in assessment
to analyze assessment ratios from three or more classes of property to determine
whether significant assessment biases are present among the classes of property.
When only two classes are being Compared, the appropriate test is the Mann-Whitney
test.
Land Ratio
The ratio of land area to building area. The land ratio can be an important factor
in grouping properties for income approach appraisal by means of direct sales comparisons.
Land Ratio Method
A technique used to estimate the value of property from a knowledge of normal net
income, the discount rate, the remaining economic life of a property, the value
of the building, the income path attributable to the building, and the income path
attributable to the land. The technique estimates total value by discounting the
income stream attributable to the land and adding the result to an independent estimate
of the value of the building. See also allocation method.
Land Residual Technique
See abstraction method.
Land-to-Building Ratio (Land-to-Improvement Ratio)
The proportion of land area to gross building (improvement) area. For a given use,
the most frequently occurring ratio will be that of a functioning economic unit.
Linear Regression
A kind of statistical analysis used to investigate whether a dependent variable
and a set of one or more independent variables share a linear correlation and, if
they do, to predict the value of the dependent variable on the basis of the values
of the other variables. Regression analysis of one dependent variable and only one
independent variable is called simple linear regression, but it is the word simple
(not linear) that distinguishes it from multiple regression analysis with its multiple
independent variables.
Location Value Response Surface Analysis
A mass appraisal technique that involves creating value influence centers, computing
variables to represent distances (or transformations thereof) from such points and
using the variables in a multiple regression or other model to capture location
influences. Implementation of the technique is enhanced by the use of a geographic
information system. Some geographic information systems permit the value influence
centers to be displayed and measured as a three dimensional grid surface, the results
of which can be likewise used in calibration techniques to arrive at the contribution
of location based on the model specification.
Log-Linear Relationship
A correlation between two variables such that if the value of one variable changes
by a certain percentage, the value of the other changes by a certain amount. (Recall
that logarithms permit multiplication to be done by means of adding logs.) For example,
there is a log-linear relationship between x and y in the following sequence: x
5 6 7 8 y 20 30 45 67.5
Logarithm; Log
The number that, when used as an exponent for another number (called the base),
results in a third number of some practical interest (called the antilogarithm).
There are two bases that are used with any frequency; the base 10 produces what
are called common logarithms, and the base 2.71828 (e) produces what are called
natural logarithms. For example, log10100 = 2; 102 = 100. Logarithms were originally
used to simplify complex calculations involving multiplications inasmuch as two
numbers can be multiplied by adding their logarithms and taking the antilog of the
result.
Mann-Whitney Test
A test in inferential statistics, similar to the Kruskal-Wallis test, that seeks
to determine whether the differences in values between two sets of observations
from any population are statistically significant.
Market Adjustment Factors
Market adjustment factors, reflecting supply and demand preferences, are often required
to adjust values obtained from the cost approach to the market. These adjustments
should be applied by type of property and area and are based on sales ratio studies
or other market analysis. Accurate cost schedules, condition ratings, and depreciation
schedules will minimize the need for market adjustment factors.
Market Analysis
A study of real estate market conditions for a specific type of property.
Market Value
Market value is the major focus of most real property appraisal assignments. Both
economic and legal definitions of market value have been developed and refined.
A current economic definition agreed upon by agencies that regulate federal financial
institutions in the United States is: The most probable price (in terms of money)
which a property should bring in a competitive and open market under all conditions
requisite to a fair sale, the buyer and seller each acting prudently and knowledgeably,
and assuming the price is not affected by undue stimulus. Implicit in this definition
is the consummation of a sale as of a specified date and the passing of title from
seller to buyer under conditions whereby: The buyer and seller are typically motivated;
Both parties are well informed or well advised, and acting in what they consider
their best interests; A reasonable time is allowed for exposure in the open market;
Payment is made in terms of cash in United States dollars or in terms of financial
arrangements comparable thereto; The price represents the normal consideration for
the property sold unaffected by special or creative financing or sales concessions
granted by anyone associated with the sale.
Market-Related Adjustment
Accounts for changes in market conditions between the time a comparable sold and
the effective date of the appraisal. See market adjustment factors.
Mass Appraisal
The process of valuing a group of properties as of a given date, using standard
methods, employing common data, and allowing for statistical testing.
Mass Appraisal Model
A mathematical expression of how supply and demand factors interact in a market.
Mean
A measure of central tendency. The result of adding all the values of a variable
and dividing by the number of values. For example, the mean of 3, 5, and 10 is 18
divided by 3, or 6. Also called arithmetic mean.
Median
A measure of central tendency. The value of the middle item in an uneven number
of items arranged or arrayed according to size; the arithmetic average of the two
central items in an even number of items similarly arranged; a positional average
that is not affected by the size of extreme values.
Median Absolute Deviation
The median of the absolute deviations from the median. In a symmetrical distribution,
the measure approximates one-half the interquartile range.
Median Percent Deviation
The median of the absolute percent deviations from the median; calculated by dividing
the median absolute deviation by one-hundredth of the median.
Merge Line
An imaginary line dividing a through lot or parcel into two parts, along which,
corner and alley influence being ignored, the value of the land is at its minimum
and is the same whether the depth be calculated from one street or the other. Note:
It is customary to locate the merge line of a rectangular through lot at a point
at which the ratio of its distances from the two streets is equal to the ratio of
the respective unit-foot values of the two streets. This formula, however, does
not produce results consistent with the above definition when used in conjunction
with any of the standard depth tables.
Minkowski Metric
Any of a family of possible ways of measuring distance. Euclidean distance, a member
of this family, computes straight-line distances (as the crow flies) by squaring
differences in like coordinates, summing them, and taking the square root of the
sum. In mass appraisal model building, Minkowski metric usually refers to the sum
of absolute differences (not squared) in each dimension, and resembles a "taxicab"
or city block pattern. Other alternatives are possible, including the distance as
calculated only for the dimension of greatest difference, but the city block distance
is most common.
Model Calibration
The development of adjustments, or coefficients based on market analysis, that identifies
specific factors with an actual effect on market value.
Model Specification
The formal development of a model in a statement or equation, based on data analysis
and appraisal theory.
Multicollinearity
Correlation among two or more variables. In regression analysis, high multicollinearity
among the independent variables complicates modeling and will compromise the reliability
of the resulting coefficients. If the multicollinearity is perfect, the multiple
regression algorithms simply will not work and either an error message may result
or the software may purge one or more of the problem variables.
Multicollinearity
The phenomenon of two or more variables being correlated. If the two correlated
variables are both independent variables (note that if they are correlated they
are not truly independent in the relationship sense) used to predict the value of
some other, dependent, variable, then modeling problems will arise. If the multicollinearity
is perfect, the multiple regression algorithms simply will not work; if the multicollinearity
is serious but imperfect, the coefficients generated by the algorithm will be individually
meaningless (although the model as a whole may still be useful).
Multiple Regression, Multiple Regression Analysis (MRA)
A particular statistical technique, similar to correlation, used to analyze data
in order to predict the value of one variable (the dependent variable), such as
market value, from the known values of other variables (called "independent variables"),
such as lot size, number of rooms, and so on. If only one independent variable is
used, the procedure is called simple regression analysis and differs from correlation
analysis only in that correlation measures the strength of relationship, whereas
regression predicts the value of one variable from the value of the other. When
two or more variables are used, the procedure is called multiple regression analysis.
See linear regression.
Multiplicative Model
A mathematical model in which the coefficients of independent variables serve as
powers (exponents) to which the independent variables are raised or in which independent
variables themselves serve as exponents; the results are then multiplied to estimate
the value of the dependent variable.
Multiplicative Transformation
A transformation of a set of variables accomplished by multiplying a variable by
one or more other variables. For example, room area is a multiplicative transformation
of length and width.
Multivariate Statistical Technique
Any of a number of statistical analysis in which data (such as the information on
a single property record card) containing a number of variables (such as lot size,
number of rooms, and construction type) are analyzed to predict the value of some
other variable. See also multiple regression analysis.
Neighborhood
(1) The environment of a subject property that has a direct and immediate effect
on value. (2) A geographic area (in which there are typically fewer than several
thousand properties) defined for some useful purpose, such as to ensure for later
multiple regression modeling that the properties are homogeneous and share important
locational characteristics.
Neighborhood Analysis
A study of the relevant forces that influence property values within the boundaries
of a homogeneous area.
Neighborhood Binary Variable
A binary variable used in a valuation model to separate the effects on value of
distinct neighborhoods.
Normal Distribution
A theoretical distribution often approximated in real-world situations. It is symmetrical
and bell-shaped; 68 percent of the observations occur within one standard deviation
of the mean, and 95 percent within two standard deviations.
Observed Condition Breakdown Method
This divides depreciation into all its various components-curable physical deterioration,
incurable short-lived-item physical deterioration, incurable basic structure (long-lived
items) physical deterioration, curable functional obsolescence, incurable functional
obsolescence, and economic (external) obsolescence-often for each major building
component.
One-Third, Two-Thirds Rule
An empirical rule that ascribes half of the value of a lot to the front third and
the other half to the rear two-thirds. Compare 4-3-2-1 rule; Harper rule; Hoffman
rule.
Parametric Statistic
A statistic whose interpretation or reliability depends on the distribution of the
underlying data.
Percentile
The values that divide a set of data into specified percentages when the data are
arrayed in ascending order. The tenth percentile includes the lowest 10 percent
of the values, the twentieth percentile includes the lowest 20 percent of the values,
and so forth.
Pooled Regression
Combining two or more strata to form one regression model.
Precision
The level of detail in which a quantity or value is expressed or represented. It
can be characterized as the number of digits used to record a measurement. A high
level of represented precision may be used to imply a greater level of accuracy;
however, this relationship may not be true. Precision also relates to the quality
of an operation or degree of refinement by which results are obtained. A method
of measurement is considered precise if repeated measurements yield the same or
nearly the same numeric value. See also accuracy and statistical precision.
Principle of Anticipation
The appraisal principle that value depends on the expectation of benefits to be
derived in the future.
Principle of Balance
The principle of balance as used in appraising is that the greatest value in property
will occur when the type and size of improvements and uses are proportional to each
other as well as to the land.
Principle of Change
The principle of change asserts that all markets are in a continual state of change.
According to this principle, properties generally go through the three stages of
integration (development), equilibrium (stasis), and disintegration (decline).
Principle of Conformity
The principle of conformity states that the value of a group of properties will
rise to its highest possible level in an area where architectural styles are reasonably
homogeneous and surrounding land uses are compatible with the use of the specified
properties.
Principle of Contribution
The principle of contribution requires an appraiser to measure the value of any
improvement to a property by the amount it contributes to market value, not by its
cost.
Principle of Progression
The principle of progression holds that the worth of an inferior property is increased
by its proximity to better properties of the same use class.
Progressivity
See assessment progressivity (regressivity).
Principle of Substitution
The principle of substitution states that no buyer will pay more for a good than
he or she would have to pay to acquire an acceptable substitute of equal utility
in an equivalent amount of time.
Property Residual Technique
A technique used to estimate the value of a property from a knowledge of its net
operating income, discount rate, remaining economic life, the amount of the reversion,
and the income path attributable to the property over the holding period (generally
the remaining economic life of the property). The technique estimates total value
by discounting anticipated income and adding the result to the present worth of
the reversion.
Qualitative Data
Pertaining to the subjective nature of some variable of interest. For example, view,
fire protection, quality, or site/location.
Qualitative Variable
Something that can be appreciated but not objectively reduced to an unambiguous
scale. For example, view is a qualitative variable.
Quantitative Variable
Pertaining to the objective nature of some variable of interest, that is, something
that can be measured or counted with little ambiguity. For example, number of bathrooms
is a quantitative variable.
Quantity Survey Method
A method of estimating reproduction cost in which a complete itemization is made
of all labor and material costs by component and subcomponent and all indirect costs;
these are added to obtain an estimate of the cost of a structure or a reasonable
bid for a contractor to submit on a proposed project.
Quotient Transformation
A transformation of two or more variables accomplished by dividing one by the other.
For example, the length of a room is a quotient transformation of its area and its
width. Like the multiplicative transformation, many useful quotient transformations
are less intuitively obvious than the one in the example given.
Ratio Study
A study of the relationship between appraised or assessed values and market values.
Indicators of market values may be either sales (sales ratio study) or independent
"expert" appraisals (appraisal ratio study). Of common interest in ratio studies
are the level and uniformity of the appraisals or assessments. See also level of
appraisal and level of assessment.
Regression Coefficient
The coefficient calculated by the regression algorithm for the data supplied that,
when multiplied by the value of the variable with which it is associated, will predict
(for simple regression) or help to predict (for multiple regression) the value of
the dependent variable. For example, in the equation, Value = $10,000 + $5,000 +
number of rooms, $5,000 is a regression coefficient.
Regression Line
The line on a graph that represents the relationship defined by the regression coefficients.
For example, the line from the relationship given in the definition of regression
coefficient would cross the y-axis at the value $10,000 and would go up $5,000 for
each movement of 1 to the right. This example illustrates one of the subtleties
required in understanding regression analysis: in fact, there is no line, because
the independent variable is not a continuous variable, but it is easier to talk
about the relationship by pretending that the variable is continuous and represent
the relationship by a line rather than the more nearly correct series of vertical
bars on a bar chart.
Regressivity
See assessment progressivity (regressivity).
Repeat Sales Analysis Model
Repeat sales analysis (see Section 4.4: Time Series Analysis) aggregates changes
in value and statistical means for properties sold more than once during a specified
period of time in a given geographic area. For example, in a zip or postal code
area, estimate market-level housing price changes. If an individual property has
not been substantially changed since its last sale, this analysis matches each pair
of sales transactions (thus the name “repeat sales”). The amount of appreciation
(or depreciation) is calculated from the time of the first sale to the second and
so on, providing an estimate of the overall appreciation of that local housing market
during that time period. The larger the number of available sales pairs, the more
statistically reliable the estimate of overall housing price trends will be. Because
this analysis is based on identifying properties where more than one sale has occurred,
the challenge is to identify enough observations to provide a meaningful index of
housing values, while keeping to as small a geographic area as possible. A repeat
sales index may also overestimate market appreciation if the data contains pairs
of sales in which the second sales price reflects substantial improvements (or other
alterations) made to the property after the first sale. On the other hand, repeat
sales indices can and do provide very useful valuation estimates in jurisdictions
where the data is insufficient to support hedonic models. In addition, they may
prove to be more accurate in tracking housing values for the houses that a hedonic
model may struggle with (especially those subject to extreme positive or negative
influences) when a prior sale is known on the property.
Residual
The difference between an observed value and a predicted value for a dependent variable.
Residual Technique
A method of arriving at the unknown value of a property component by subtracting
the known values of other components from a known overall value.
Residual Value
The value of the property after cleanup of environmental contamination. This may
be more or less than the original value depending on counterbalancing effects of
stigma and improvements to plant efficiency.
Residual Value of Improvements
A value ascribed to improvements on a parcel of land by deducting from the total
value of land and improvements (as determined by composite appraisal) the value
of the land alone (as determined by comparison with other parcels). Contrast residual
value of land. Note: A residual value of improvements is usually estimated only
when the land is obviously not improved to its highest and best use.
Residual Value of Land
A value ascribed to land alone by deducting from the total value of land and improvements
(as determined by composite appraisal) the value of the improvements (as determined
by the depreciated reproduction cost method). Contrast residual value of improvements.
Root Mean Square (RMS)
The square root of the average value of the sum of the squares of the differences
between values in a set and the corresponding values that have been accepted as
correct or standard. Used to measure map accuracy.
Russell-NCREIF Index
A performance measure for institutional real estate, maintained by the National
Council of Real Estate Investment Fiduciaries Research Institute.
Sales Chasing
Sales chasing is the practice of using the sale of a property to trigger a reappraisal
of that property at or near the selling price. If sales with such appraisal adjustments
are used in a ratio study, the practice causes invalid uniformity results and causes
invalid appraisal level results, unless similar unsold parcels are reappraised by
a method that produces an appraisal level for unsold properties equal to the appraisal
level of sold properties. (2) By extension, any practice that causes the analyzed
sample to misrepresent the assessment performance for the entire population as a
result of acts by the assessor’s office. A subtle, possibly inadvertent, variety
of sales chasing occurs when the recorded property characteristics of sold properties
are differentially changed relative to unsold properties. Then the application of
a uniform valuation model to all properties results in the recently sold properties
being more accurately appraised than the unsold ones.
Sales Ratio Study
A ratio study that uses sales prices as proxies for market values.
Sales Ratio/Assessment Ratio
The ratio of an appraised (or assessed) value to the sale price or adjusted sale
price of a property. See also assessment-sale price ratio.
Spatial
Refers to the location of, proximity to, or orientation of objects with respect
to one another in N-dimensional space. Generally refers to phenomena that can be
mapped in two or three dimensions on or near the earth's surface.
Standard Deviation
The statistic calculated from a set of numbers by subtracting the mean from each
value and squaring the remainders, adding together all the squares, dividing by
the size of the sample less one, and taking the square root of the result. When
the data are normally distributed, one can calculate the percentage of observations
within any number of standard deviations of the mean from normal probability tables.
When the data are not normally distributed, the standard deviation is less meaningful,
and one should proceed cautiously.
Standard Error
A measure of the precision of a measure of central tendency; the smaller the standard
error, the more reliable the measure of central tendency. Standard errors are used
in calculating a confidence interval about the arithmetic mean and the weighted
mean.
Standard Error of the Estimate (SEE)
An expression for the standard deviation of the observed values about the regression
line; thus it provides an estimate of the variation likely to be encountered in
making predictions from the regression equation.
Statistical Accuracy
The closeness between the statistical estimate and the true (but unknown) population
parameter value it was designed to measure. It is usually characterized in terms
of error or the potential significance of error and can be decomposed into sampling
error and non sampling error components. Accuracy can be specified by the level of
confidence selected for a statistical test. See also accuracy.
Statistical Precision
A reference to how closely the survey results from a sample can reproduce the results
that would be obtained from the entire population (a complete census). The amount
by which a sample statistic can vary from the true population parameter is due to
error. Even if all the sample data are perfectly accurate, random (sampling) error
affects statistical precision (measured by the standard error or standard deviation).
The dispersion of ratios in the population and the sample size have a controlling
influence over the precision of any statistical estimate. When the reliability of
a statistical measure is being evaluated, narrower confidence intervals have greater
precision. See also precision.
Statistics
(1) Numerical descriptions calculated from a sample, for example, the median, mean,
or coefficient of dispersion. Statistics are used to estimate corresponding measures,
termed parameters, for the population. (2) The science of studying numerical data
systematically and of presenting the results usefully. Two main branches exist:
descriptive statistics and inferential statistics.
Stepwise Regression Analysis
A kind of multiple regression analysis in which the independent variables enter
the model, and leave it if appropriate, one by one according to their ability to
improve the equation's power to predict the value of the dependent variable.
Stratification
The division of a sample of observations into two or more subsets according to some
criterion or set of criteria. Such a division may be made to analyze disparate property
types, locations, or characteristics, for example.
Stratify
To divide, for purposes of analysis, a sample of observations into two or more subsets
according to some criterion or set of criteria.
Substitution
The appraisal principle that states that a potential owner will pay no more for
a property than the amount for which a property of like utility may be purchased;
that a property's value tends to be set by the cost of acquiring an equally desirable
substitute.
Sum of Squared Errors
The sum of the squared deviations from the predicted values (rather than the mean
value).
Sum of Squares
The result obtained by adding all the squares of the individual deviations from
some given value. Usually it is the sum of the squares of the deviations of the
individual values of a variable from the mean value.
t-Statistic
A particular statistic important in inferential statistics for certain kinds of
hypothesis testing of certain kinds of data.
t-Test
A particular parametric statistical test useful, among other things, in testing
the level of assessment.
Three Approaches to Value
A convenient way to group the various methods of appraising a property. The cost
approach encompasses several methods for estimating replacement cost new of an improvement
less depreciation plus land value. The sales comparison approach estimates values
by comparison with similar properties for which sales prices are known. The methods
included in the income approach are based on the assumption that value equals the
present worth of the rights to future income.
Time Series Analysis
A family of techniques that can be used to measure the cyclical movements, random
variations, seasonal variations, and secular trends observed over a period of time.
Time-Adjusted
Sale Price
The price at which a property sold, adjusted for the effects of price changes reflected
in the market between the date of sale and the date of analysis.
Trending
Adjusting the values of a variable for the effects of time. Usually used to refer
to adjustments of assessments intended to reflect the effects of inflation and deflation
and sometimes also, but not necessarily, the effects of changes in the demand for
microlocational goods and services.
Trending Factor
A figure representing the increase in cost or selling price over a period of time.
Trending accounts for the relative difference in the value of a dollar between two
periods.
Turnover Ratio
A valuation guideline based on sales activity, the number of times per period (usually
a year) a business sells the average sale value of its inventory during the same
period.
Two-tailed Test
A test in which the alternative hypothesis does not specify the direction of the
relationship, as opposed to a one-tailed test, in which the direction of relationship
is specified. For example, the alternative hypothesis that "a does not equal b"
implies a two-tailed test, whereas "a is greater than b" implies a one-tailed test.
See also null hypothesis.
Type Survivor Curves
See survivor curve;
Iowa
type curve.
U-Test
See Mann-Whitney test.
Weighted Average Method
In personal property appraisal, a method of inventory cost accounting whereby inventory
is valued according to the unit price of all units owned throughout the year, calculated
by dividing total acquisition cost of all inventory by the number of units owned.
Weighted Coefficient of Dispersion
The coefficient of dispersion when the absolute differences between individual assessment
ratios and the measure of central tendency (for example, median ratio) are weighted
on the basis of sale price.
Weighted Coefficient of Variation
The coefficient of variation when the squared differences between individual assessment
ratios and the arithmetic mean ratio are weighted on the basis of sale price.
Weighted Mean Ratio
Sum of the appraised values divided by the sum of the sales prices (or independent
estimates of market value), which weights each ratio in proportion to the sale price
(or independent estimate of market value).
Weighted Mean; Weighted Average
An average in which each value is adjusted by a factor reflecting its relative importance
in the whole before the values are summed and divided by their number.
z-Statistic
The number calculated in a z-test, whose significance is evaluated by reference
to a z-table.
z-Table
A table of critical values associated with the z-test.
z-Test
A test of any of a number of hypotheses in inferential statistics that has validity
if sample size is sufficiently large and the underlying data are normally distributed.
Zangerle Curve
A corner influence graph devised by John A. Zangerle, showing, for any given main
street frontage, the percentage of the side street value to be added as corner influence
to the value of the lot computed as an inside lot fronting on the main street. Compare
Bernard rule.
