NCSS 2019, v19.0.2	5/27/2020 1:33:40 PM      1

Appraisal Ratio Study

Dataset	C:\Users\egrossman\Desktop\ICLEF\newdatafile.xlsx
Ratio Formula	Ratio = Assessment / Sale

Ratio Summary Statistics Section ─────────────────────────────────────────────────

Break				Wtd.		
Column	Count	Median	Mean	Mean	IQR	SD	COD	COV	PRD	PRB
[None]	1140	0.9472	0.9685	0.8765	0.1958	0.3303	21.373	34.1020	1.1050	-0.0482

Wtd. Mean: Weighted Mean
IQR: Interquartile Range
COD: Coefficient of Dispersion
COV: Coefficient of Variation
PRD: Price-Related Differential
PRB: Coefficient of Price-Related Bias

Additional Ratio Summary Statistics Section ─────────────────────────────────────────
										5%
Break					15%	Wtd.	Wtd.			Trim.
Column	Count	Min	Max	Range	COC	COD	COV	MADM	MAPDM	Mean
[None]	1140	0.0031	2.3429	2.3398	61.404	19.342	1046.3883	0.0973	10.269	0.9622

15% COC: Coefficient of Concentration (Percentage of Ratios within 15% of the Median)
Wtd. COD: Weighted Coefficient of Dispersion
Wtd. COV: Weighted Coefficient of Variation
MADM: Median Absolute Deviation from the Median
MAPDM: Median Absolute Percent Deviation from the Median
5% Trim. Mean: 5% Trimmed Mean (Mean after the 5% most extreme Ratios of each side are removed)

Appraisal and Sale Price Summary Statistics Section ────────────────────────────────────

Break		Appraisal	Sale Price	Appraisal	Sale Price
Column	Count	Mean	Mean	Median	Median
[None]	1140	156152.3	178162.0	129300.0	143009.5

Confidence Interval Section ─────────────────────────────────────────────────────
						Ratio		
Break		Ratio	Median 95% C.I.	Ratio	Mean 95% C.I.	Wtd.	Wtd. Mean 95% C.I.
Column	Count	Median	Lower	Upper	Mean	Lower	Upper	Mean	Lower	Upper
[None]	1140	0.9472	0.9393	0.9574	0.9685	0.9494	0.9877	0.8765	0.8400	0.9129

NCSS 2019, v19.0.2	5/27/2020 1:33:40 PM      2

Appraisal Ratio Study

Dataset	C:\Users\egrossman\Desktop\ICLEF\newdatafile.xlsx
Ratio Formula	Ratio = Assessment / Sale

Normality Assumption Section ───────────────────────────────────────────────────
Break				    ------------------ P-Values (< 0.1 rejects Normality) --------------------
Column	Count	Skew	Kurt	S-W	A-D	M-I	K-S	D-S	D-K	D-O
[None]	1140	0.5962	3.8769	0.0000	0.0000	< 0.1	< 0.1	0.0000	0.0000	0.0000

Skew: Skewness (Negative values indicate left skewness; positive values indicate right skewness; values close
     to 0 indicate little skewness.)
Kurt: Kurtosis (Negative values indicate fatter tails; positive values indicate a strong peak and lighter tails.)
S-W: Shapiro-Wilk W Test
A-D: Anderson-Darling Test
M-I: Martinez-Iglewicz Test
K-S: Kolmogorov-Smirnov (Lilliefors’ adjusted) Test
D-S: D'Agostino Skewness Test
D-K: D'Agostino Kurtosis Test
D-O: D'Agostino Omnibus (Skewness and Kurtosis) Test

Tests for which the Normality assumption is rejected are highlighted in red.

Comparative (Horizontal Equity) Plots ──────────────────────────────────────────────

NCSS 2019, v19.0.2	5/27/2020 1:33:40 PM      3

Appraisal Ratio Study

Dataset	C:\Users\egrossman\Desktop\ICLEF\newdatafile.xlsx
Ratio Formula	Ratio = Assessment / Sale

Horizontal Equity Test Assumption: Normality ────────────────────────────────────────

                    	 Test		Reject Normality?
Normality Attributes	Value	P-Value	(α = 0.1)
Skewness Test	7.6726	0.0000	Yes
Kurtosis Test	10.3602	0.0000	Yes
Skewness and Kurtosis (Omnibus)	166.2022	0.0000	Yes

Horizontal Equity Test Assumption: Equal Variance ─────────────────────────────────────

Unable to test equal variance assumption since there is no horizontal grouping.

Tests of Horizontal Equity -  ─────────────────────────────────────────────────────

Unable to test horizontal equity since there is no horizontal grouping.

Price-Related Bias (PRB) Scatter Plots ─────────────────────────────────────────────

NCSS 2019, v19.0.2	5/27/2020 1:33:40 PM      4

Appraisal Ratio Study

Dataset	C:\Users\egrossman\Desktop\ICLEF\newdatafile.xlsx
Ratio Formula	Ratio = Assessment / Sale

Price-Related Bias (PRB) Details ─────────────────────────────────────────────────
Y = (Ratio - Median Ratio) / Median Ratio
X = Ln(0.5 * (Sale Price + Appraisal / Median Ratio)) / Ln(2)
						PRB	Reject	          95% C.I. of	
						(Slope)	Vertical	         PRB (Slope)	
Break		Pearson	PRB	Std		Test	Equity?	     -----------------------	
Column	Count	Correlation	(Slope)	Error	T Value	P-Value	(α = 0.05)	Lower	Upper
[None]	1140	-0.1563	-0.0482	0.0090	-5.3377	0.0000	Yes	-0.0659	-0.0305	

Pearson Correlation: the common measure of the linear relationship of two variables.
PRB (Slope): Coefficient of Price-Related Bias. This is the slope of the regression line (for example, a PRB
     of 0.032 indicates a 3.2% increase in assessment ratio for every 100% increase in value).
Std Error: The standard error of the estimate of PRB.
T Value: The test statistic for testing whether PRB is statistically different from 0.
PRB (Slope) Test P-Value: This P-Value indicates the likelihood that the slope is flat (PRB = 0) given the sale
     price and appraisal values in question.
Lower and Upper: Lower and upper confidence limits for the value of PRB.

Procedure Input Settings ──────────────────────────────────────────────────────

Autosaved Template File
C:\Users\egrossman\Documents\NCSS 2019\Procedure Templates\Autosave\Appraisal Ratio Studies -
Autosaved 2020_5_27-13_33_41.t370

Columns Tab
-- Ratio Values Specification ------------------------------------------------------------------------------------------------------------
Ratio Specification:	Appraisal Column, Sale Price Column
Appraisal Column:	Assessment
Sale Price Column*:	Sale
	
·· Horizontal Grouping ····················································································································
Break Column(s):	<Empty>
	
·· Removing Extreme Ratios ············································································································
Remove Ratios less than	Unchecked
Remove Ratios greater than	Unchecked
Remove Outliers using IQR Method	Checked
  IQR Multiplier:	  5.0
	
-- Filtering ------------------------------------------------------------------------------------------------------------------------------------
Include Column:	<Empty>
Included Values:	<Empty>

Summary Reports Tab
-- Sale Price Adjustment by Date ------------------------------------------------------------------------------------------------------
Sale Price Adjustment by Date Summary	Unchecked
	
-- Removed Ratios -------------------------------------------------------------------------------------------------------------------------
Removed Ratios Report	Unchecked

NCSS 2019, v19.0.2	5/27/2020 1:33:40 PM      5

Appraisal Ratio Study

Dataset	C:\Users\egrossman\Desktop\ICLEF\newdatafile.xlsx
Ratio Formula	Ratio = Assessment / Sale

Procedure Input Settings (Continued)

Summary Reports Tab (Continued)
-- Summary Statistics ---------------------------------------------------------------------------------------------------------------------
Ratio Summary Statistics	Checked
Additional Summary Statistics	Checked
  COC %:	  15
  Trim %:	  5
Appraisal and Sale Price Summary	Checked
Confidence Intervals	Checked
  Confidence Level:	  95
	
-- Normality Assumptions for each Horizontal Group -----------------------------------------------------------------------------
Normality Assumptions	Checked
  Normality Test Alpha:	  0.10
Histogram	Checked
Normal Probability Plot	Checked

Horizontal Equity Tab
-- Plots of Horizontal Equity -------------------------------------------------------------------------------------------------------------
Box Plot	Checked
Dot Plot	Checked
Percentile Plot	Unchecked
Error-Bar Chart	Unchecked
Histograms	Unchecked
Density Plot	Unchecked
Combo Plot	Unchecked
	
-- Tests of Horizontal Equity -------------------------------------------------------------------------------------------------------------
Horizontal Equity Test Assumptions - Normality	Checked
  Alpha:	  0.10
Horizontal Equity Test Assumptions - Equal	Checked
Variance	
  Alpha:	  0.10
Tests of Horizontal Equity	Checked
  Alpha:	  0.05

Vertical Equity Tab
-- Vertical Equity - Price Related Bias (PRB) ---------------------------------------------------------------------------------------
PRB Scatter Plots	Checked
Price-Related Bias Details	Checked
  Alpha:	  0.05
  Confidence Level:	  95
  Include Spearman Rank Details	  Unchecked
	
-- Vertical Equity - Ratio vs. Sale Price -----------------------------------------------------------------------------------------------
R vs. S Scatter Plots	Unchecked
R vs. S Tests of Vertical Equity	Unchecked
	
-- Vertical Equity - Ratio vs. Appraisal ------------------------------------------------------------------------------------------------
R vs. A Scatter Plots	Unchecked
R vs. A Tests of Vertical Equity	Unchecked

NCSS 2019, v19.0.2	5/27/2020 1:33:40 PM      6

Appraisal Ratio Study

Dataset	C:\Users\egrossman\Desktop\ICLEF\newdatafile.xlsx
Ratio Formula	Ratio = Assessment / Sale

Procedure Input Settings (Continued)

Vertical Equity Tab (Continued)
-- Vertical Equity - Ratio vs. 0.5(Sale Price + Appraisal / Median) ------------------------------------------------------------
R vs. 0.5(S + A') Scatter Plots	Unchecked
R vs. 0.5(S + A') Tests of Vertical Equity	Unchecked

Report Options Tab
-- Report Options ---------------------------------------------------------------------------------------------------------------------------
Ratio Reporting Scale:	Ratio (1)
Show Definitions	Checked
Column Names:	Names
Value Labels:	Data Values
	
-- Decimal Places --------------------------------------------------------------------------------------------------------------------------
Ratio Statistics:	4
Ratio Statistics (100 Scale):	2
Percent Statistics:	3
P-Values:	4
Test Statistics:	4
PRB:	4
PRD:	4
Correlation:	4
Prices and Appraisals:	1
α in Titles:	Auto (Up to 7)

Sale Date Tab
-- Sale Date Specification ----------------------------------------------------------------------------------------------------------------
Sale Date Column:	<Empty>
	
·· Removing Ratios by Date ·············································································································
Remove Ratios with Date before	Unchecked
Remove Ratios with Date after	Unchecked
	
·· Price Adjustment ························································································································
Adjust Prices To This Date:	Unchecked

Storage Tab
-- Storage Columns ------------------------------------------------------------------------------------------------------------------------
Store Ratios in Column:	<Empty>
Store Time-Adjusted Sale Price in Column:	<Empty>