Thursday, December 18, 2014

Wilcoxon Rent Example



A previous post examined requested rent and estimated rents in Venice California.  




This post conducts a non-parametric statistical test with the rent data.

Question:   Use the requested rent and Zillow rent estimate data repeated below to conduct a Wilcoxon test on the difference in median requested rent and Zillow rent estimates.


Requested
Rent
Zillow
Rent Estimate
1
3798
4000
2
4550
5100
3
4600
4700
4
4895
4600
5
5395
5300
6
5900
4600
7
6500
5100
8
6800
5000
9
6500
6500
10
6500
7100
11
6995
7900
12
7750
6000
13
7950
6900
14
7950
4600
15
8000
4800
16
8000
5200
17
8500
6400
18
8500
8500
19
11500
6900
20
12500
12000
21
12500
6600
22
15000
7600
3-bedroom + Houses in Venice CA on the market on 12/18/14


Answer:   The spreadsheet used in the Wilcoxon statistic calculation is presented below.



Wilcoxon Calculation for difference in requested and Zillow estimated rents
c1
c2
c3
c4
c5
c6
c7
Requested Rent
Zrent
D
ABS(D)
DUM if ! Is positive
Rank ABS(D)
DUM*Rank
3798
4000
-202
202
0
5
0
4550
5100
-550
550
0
8
0
4600
4700
-100
100
0
4
0
4895
4600
295
295
1
6
6
5395
5300
95
95
1
3
3
5900
4600
1300
1300
1
12
12
6500
5100
1400
1400
1
13
13
6800
5000
1800
1800
1
15
15
6500
6500
0
0
0
1
0
6500
7100
-600
600
0
9
0
6995
7900
-905
905
0
10
0
7750
6000
1750
1750
1
14
14
7950
6900
1050
1050
1
11
11
7950
4600
3350
3350
1
19
19
8000
4800
3200
3200
1
18
18
8000
5200
2800
2800
1
17
17
8500
6400
2100
2100
1
16
16
8500
8500
0
0
0
1
0
11500
6900
4600
4600
1
20
20
12500
12000
500
500
1
7
7
12500
6600
5900
5900
1
21
21
15000
7600
7400
7400
1
22
22


The calculation of the Wilcoxon statistic, its standard error and the Z-score, and p-value are presented and explained below.



Calculation for Wilcoxon Test
W
214
Sum of Dum*Rank (ABS(D))
EW
126.5
n*(n+1)/4
STDW
0.684
(n*(n+1)*(2n+1)/24)^0.5
z
127.8
(w-EW)/STDW
p
0
Norm.dist(Z,0,1,0)
n
22
sample size


Discussion of result:  

The overwhelming majority of houses in this sample have a requested rent larger than the Zillow rent estimate.    The median requested rent is significantly larger than the Zillow estimate.

This sample involves relatively large homes in an affluent town.  The results only pertain to this community and set of houses.   It may be the case that Zillow rent estimates are more in synch with requested rents for samples of smaller homes and apartments.    This could occur because most people who live in larger homes own their home and the market for rentals of smaller homes and apartments is more competitive.   Also, Zillow estimate may be closer to requested rents in less affluent areas.


Another article on Wilcoxon Tests:  A previous post used the Wilcoxon test to compare quarterbacks drafted in the first round to quarterbacks drafted in the second round.    Readers of this post might like also like the Wilcoxon quarterback draft post.






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