## 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.