So I downloaded the raw housing data from each quarter from 1970 to 2011 from http://www.jparsons.net/housingbubble/ and performed some very simplistic analysis using Matlab.

I calculated the change in inflation-adjusted housing prices from each quarter, resulting in 167 values.

Here is a histogram of the change in housing prices from 1970 to 2007 with 15 bins (15 unique x-axis values):

Here is a histogram of the change in housing prices from 1970 to 2011 with 15 bins (15 unique x-axis values):

You can clearly see that from 2007 to 2011, the distribution looks more skewed.

I then performed a Chi-squared goodness of fit test. The output of the test "p" tells you the probability that the distribution is a normal distribution. But be careful here. You can only confidently say that the distribution is not normal when p < 0.05. Otherwise you can't really say much.

Here are the results, depending on the number of bins:

__10 bins:__p (1970 to 2007):

**0.2097**

p (1970 to 2011):

**0.0766**

__15 bins:__p (1970 to 2007):

**0.5536**

p (1970 to 2011):

**0.0021**

__20 bins:__p (1970 to 2007):

**0.2895**

p (1970 to 2011):

**0.1234**

__25 bins:__p (1970 to 2007):

**0.6482**

p (1970 to 2011):

**0.2923**

So it wasn't unreasonable to assume a normal distribution of housing price changes. Ideally the results should be more granular, and it's a very limited dataset (only 167 values).

The code used to do this was:

[~, p] = chi2gof( quarterly_change(1:150), 'nbins', nbins )

[~, p] = chi2gof( quarterly_change(1:167), 'nbins', nbins )

The lowest value was Q1 of 2008 in which housing prices dropped 7.8% in one quarter. If a normal distribution was used from 1970-2007, then dropping 7.8% in one quarter was 5.4 standard deviations from the mean. Put another way, if we assumed a normal distribution, the chance of getting a drop in prices of 7.8% or greater was .00000002.

normcdf( -.0784, mean(quarterly_change(1:150)), std( quarterly_change(1:150) ) )Put another way, the chance of it dropping between 0% and 7.8% and was 39.8%.

ans = 1.9682e-008

normcdf( 0, mean(quarterly_change(1:150)), std( quarterly_change(1:150) ) ) ...

- normcdf( -.0784, mean(quarterly_change(1:150)), std( quarterly_change(1:150) ) )

ans = 0.39804

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