The ‘Homer Simpson’ of economics

Homer Simpson once said, “Oh, people can come up with statistics to prove anything, Kent. Forty per cent of all people know that.”

While a quote like that might make some economists cringe, it does serve as a segue to an explanation of the statistical phenomenon known as Simpson’s paradox (different Simpson). It relates to how individual groups can have similar trends, but when the groups are combined, the trend gets flipped upside down.

Simpson’s paradox is something we see whenever the percentage change in average price for a number of individual markets moves in the opposite direction compared to the combination of them.

Consider the following hypothetical example. Let’s say Canada is made up of just three local housing markets (A-town, B-town, and C-town) and that average price in each of them is up by 10 per cent compared to the same month last year:

# sales this month last year

# sales this month

Year-over-year % change: sales

Average price this month last year

Average price this month

Year-over-year % change: average price

A-town

100

40

-60

$600,000

$660,000

10

B-town

100

100

0

$400,000

$440,000

10

C-town

100

160

60

$300,000

$330,000

10

Canada

300

300

0

$433,333

$410,667

-5.2

While combined sales are unchanged and the average price in each housing market has climbed by 10 per cent, the average price for combined sales is down by 5.2 per cent. Intuitively, one might think that that average price for combined sales should be up because price rose in each of the three markets. Simpson’s paradox suggests that applying intuition to statistics can result in mistaken conclusions.

Our favourite analogy to explain Simpson’s Paradox involves calculating the average height for a classroom of kids: first, calculate the average height. Now excuse the five tallest kids and recalculate average height. While the average has shrunk, the kids haven’t.

The example serves to illustrate how changes in the mix of sales (or kids) can result in changes in average price (or average height).

The MLS® Home Price Index overcomes the shortcomings of average price measurement, because it is not affected by changes in the mix of sales the way that the average (or median) price is. That’s because the HPI involves “apples-to-apples” comparisons of typical homes at the neighbourhood (i.e. subarea) level.

For example, when I look at the description for a Benchmark two-storey single family home in my neighbourhood, it’s basically an exact description of my house — and I can track the evolution of prices for these properties over time in an area no larger than where I walk my dog every night.

The bottom line is that Simpson’s Paradox suggests that understanding average price changes requires understanding of how it is being affected by changes in the mix of sales, whether at the subarea level or for larger areas. That’s because changes in the mix of sales can result in average price changes that contradict your intuition. I think Homer Simpson says it best: ‘d’oh!’

As our Director and Senior Economist, Housing Data and Market Analysis, Shaun Cathcart provides housing market intelligence to Boards, Associations, members, and real estate industry stakeholders. He spends much of his time analyzing and writing about Canadian housing trends. In his downtime, you can find him on his bike, on the volleyball court, and enjoying time with his family.


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