A previous post examined requested rent and estimated rents
in Venice California.
This post conducts a nonparametric 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

3bedroom + 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 Zscore, and pvalue 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

(wEW)/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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