A previous post of mine generated an interesting series of email exchanges between myself and reader Greg. Part statistics, part epistomology, and part real estate, I thought the discussion — a tribute to liberal arts education — worth posting on its own. The end state, alas, was inconclusive.

Readers who cringe at memories of college stats classes are excused from reading this entry.

Greg:

Kevin, I am dying to know how the Palo Alto medians you report compare to sales volume during that period. While the median is decent summary statistic, I think it would be even more interesting and helpful to look and the distribution and number of sales on the graph directly. Could you plot all Palo Alto sales on a day by day basis, so we could see what the cloud of points actually looks like? (BTW, you may need to toss a couple of outliers out so they don’t compress the scale on the other points).

Kevin:

I want to make sure I understand what cut of the data you’re intrigued by. Is it something like the attached [following] PA scatter diagram? If so, I’m happy to post it, along with any insightful comments that either you or I come up with. At first glance, this data doesn’t tell me a compelling story one way or the other; I’m assuming by your comments that one would expect a declining volume of sales during the time that prices were declining, and an increasing volume of sales during the time that prices were increasing?

Greg:

Thanks for the attachment. I’ve attached it [following] back with one new sheet which shows trailing 2-week sales volume. What I’m trying to get at is this: what distribution of sales prices are responsible for each of your median calculations?

My line of thought is this: there is a real population of home prices/values out there, but we’re limited to looking at a small sample, i.e. the prices of homes that transacted. As the number of sales goes down, the confidence interval we have around our population mean estimate should go up. I am trying to figure out how to calculate this confidence interval, and interpret what it means for home buyers.

I’m over in China right now on a project, so I don’t know if I’ll be able to figure this out to my satisfaction in the immediate short term.. but I do look forward to thinking about it more and hearing your thoughts on it as well.

Kevin:

First, your diagram: I’m not sure that I’m pulling any real insights from it, apart from it partially reflecting the natural cycle of real estate sales, which tend to peak in the spring.

Secondly, I’m not sure I agree with your paragraph on the “real population of home prices.” This may be more of an epistomological argument than a real estate one, but the way I look at it is that value is conferred only through an arms-length transaction between two willing parties. Homes that haven’t sold obviously also have a value, but it’s an unknowable value (though estimatable) until they go on the market and sell as well. Thus the universe of homes that have sold is not, in fact, a sample set from which we can figure out a confidence interval about the “real population”; instead, the universe of homes that have sold is, for all practical purposes, the real population.

Tags: For buyers, For sellers, Palo Alto, Real estate, Real estate data
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