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Comment by jhou2 | Hacker News Reader

Sigh, smh. The statistical flaws in this "back of the envelope" calculation are something else.

This was a study based on "a Financial Times multiple choice survey of 77 high net worth and affluent mainland Chinese individuals, 'admittedly not a statistically significant sample size,'” According to this survey, 9 individuals out of these 77 Chinese bought property in Vancouver. After some more mathematical shenanigans, this is extrapolated to imply that Chinese mainlanders buy 33% of the Vancouver real estate market. Really?!? And this statistically baseless extrapolation becomes newsworthy?

http://www.vancouversun.com/business/chinese+investors+third...

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Hmmm. Sorry, I don't think I agree with you. Sure, from a frequentist perspective this analysis is "unpublishable," but from a Bayesian perspective is yields some important insights.

First of all, the main point of the study is not to obtain am accurate point estimate of Chinese buyers in Vancouver. The main point is to underline the importance of more studies.

In other words your criticism kind of makes the analyst's point for him.

Second, you would be surprised at the amount of information even small sample sizes can provide when there is great uncertainty about the true data distribution.

Third, this analysis is in agreement with two other

In other words, don't get hung up on the exact %. Nobody really cares about the difference between 33% and 35%. What decision makers need to know is whether it's a lot or a little. This "quick and dirty" analysis supports the contention that it's a "lot", not a "little".

Furthermore, this study was not done in isolation. The NAR study and the urban planner's study both point in the same direction.

Taking all this evidence under consideration suggests that overseas buyers are likely a driving force in the run up in house prices in Vancouver. And that's newsworthy.

> Second, you would be surprised at the amount of information even small sample sizes can provide when there is great uncertainty about the true data distribution.

This isn't about sampling error, this is about inverting conditionals while ignoring base rates. This is like saying 'one third of surveyed Somalis in America report living in Minnesota, therefore, one-third of Minnesota is Somalian'. That conclusion doesn't follow, whether you surveyed 10 Somalis or 1000.

That is, there is no reason to expect P(Vancouver purchase|Chinese) = P(Chinese|Vancouver purchase) = 0.33.

If that number happens to be right, it is by coincidence; it only works if you are lucky enough that the relative sizes of Chinese buyers and Vancouver sales are just right. (Specifically, that the size of the Chinese buyer population is identical to the size of Vancouver sales; if there are a million Chinese buyers worldwide and a million Vancouver sales over that same period, and a third of Chinese buyers say they bought in Vancouver, then yes, a third of Vancouver sales will be to Chinese.)

If you knew two of the three variables of global Chinese size/Vancouver sales size/P(Vancouver purchase|Chinese), even if you just had a vague but defensible prior, you could (weakly) estimate the third. But in isolation, each variable means nothing.

> This isn't about sampling error, this is about inverting conditionals while ignoring base rates. This is like saying 'one third of surveyed Somalis in America report living in Minnesota, therefore, one-third of Minnesota is Somalian'. That conclusion doesn't follow, whether you surveyed 10 Somalis or 1000.

That's not even remotely what was done in the article by my reading. More like: 33% of Somalis * total number of Somalis / total people in Minnesota.

"That's not even remotely what was done in the article by my reading."

That's what it was described as in the grandparent:

"This was a study based on "a Financial Times multiple choice survey of 77 high net worth and affluent mainland Chinese individuals, 'admittedly not a statistically significant sample size,'” According to this survey, 9 individuals out of these 77 Chinese bought property in Vancouver."

'mainland Chinese' are a reference class much larger than 'Chinese buyers of Vancouver properties', as they are buying globally. If this description is wrong, then one should correct it - not introduce irrelevancies like how 'well with Bayesian reasoning this sorta small sample is OK!'

"More like: 33% of Somalis * total number of Somalis / total people in Minnesota."

Which is still wrong, since there are lots of Somalis not in Minnesota.

> 'mainland Chinese' are a reference class much larger than 'Chinese buyers of Vancouver properties', as they are buying globally.

And 9/77 of mainland Chinese are buying properties in Vancouver, so you multiply that by total number of people in mainland China (that are high net worth and affluent) and then multiply that by the average property value bought by them. That gets (a rough approximation of) the property value bought by Chinese mainlanders in Vancouver, now divide that by the total property market in Vancouver to get the percent of Vancouver being bought by Chinese mainlanders.

I don't know where you're getting anything else than this. The top level parent only described this as "some more mathematical shenanigans" yet you assume that therefore it has to be this nonesense of swapping P(A|B) with P(B|A). The article makes it clear that that's not the case, so I don't know who you're arguing with.

> Which is still wrong, since there are lots of Somalis not in Minnesota.

Yes, 67% of them in this hypothetical, as accounted for in the first factor. This process isn't inherently wrong, the debate is whether the small sample size makes the uncertainty too large to be useful.

> And 9/77 of mainland Chinese are buying properties in Vancouver, so you multiply that by total number of people in mainland China (that are high net worth and affluent) and then multiply that by the average property value bought by them. That gets (a rough approximation of) the property value bought by Chinese mainlanders in Vancouver, now divide that by the total property market in Vancouver to get the percent of Vancouver being bought by Chinese mainlanders.

And now you've done the correction for the base rates which I discussed in my original: once you know the relevant populations and fractions, then yes, you can get out the right fraction. But it's highly unlikely the correct version will just happen to equal the original fraction in the survey, and no correction was included in the summary. Let me quote again what I am criticizing:

Note there is nothing about 'total number of people in mainland China'. Nothing about 'average property value'. Nothing about 'total property market in Vancouver'. I don't know where you're getting all this. The procedure as described is just plain wrong, nothing to do with sample sizes or Bayesian methods.

> This process isn't inherently wrong, the debate is whether the small sample size makes the uncertainty too large to be useful.

That's what the comment thought they were defending, but they were wrong. They misunderstood the problem entirely. It was interpreting the survey meaning totally incorrectly by inverting the conditional, the problem was not precision/sampling error.

There's nothing the least bit mathematically fallacious about the line you quote: it's just stating the results of a survey. You are critiquing something that has to occur after that point.

The very next line from the source you're quoting:

> After some more mathematical shenanigans, this is extrapolated to imply that Chinese mainlanders buy 33% of the Vancouver real estate market.

I.e. "there's more that I'm not talking about because I already think the first step is so inaccurate that it doesn't matter what's next".

Which seems more likely? (A) that the above snarkily referred to what was done in the article, or (B) that the above referred to a mathematical fallacy that is otherwise entirely absent from anything anyone here is talking about until you showed up.

Even if the top poster were saying what you suggest, how were they supposed to get 33% out of 9/77 = 11%? Your suggested error would give 11% instead.

I find it believable, since 30% of population in Vancouver is Chinese http://worldpopulationreview.com/world-cities/vancouver-popu... This figure is also from 2011 so it's probably higher by now.

Seeing this touted feel like reading: Breaking news, a city with 100% Caucasian population does not see a single Chinese buyer!

To make it a real quality clickbait, here is my take, "A city where Chinese buyers fails to conquer, and here is why"

When they say "Chinese" these discussions about real estate usually mean Chinese citizens, not ethnically Chinese locals. It doesn't seem to be explicitly said here but I'm pretty sure that's what he means, see the other paragraphs talking about government investigation into offshore buyers.

Yeah. Would it still be click bait if the headline were "30% of the people in Vancouver are ethnically Chinese, and people often live in houses"?

-9 out of 77 Chinese were asked if they have Vancouver property -BS extrapolation leads to 33% figure I believe it

Ladies and gentlemen, just remember that economic bubbles aren't only bubbles in assets, finance, and the structure of the economy, but also the psychology of the people.

The number is actually closer to 1-2%.

You are underestimating. In Markham, ON, we recent found out that our offers on these million dollar homes (stretching us near the limits of good financial sense) were getting discarded because we had a condition of 5 days needed to confirm mortgage (the so called financing condition). People are apparently buying homes with "clean" offers. I call BS on this. The average buyer doesn't have a million dollars lying around their checking account. If I was an "upgrade" buyer (improving my existing home), I'd need time to sell my existing home.

Btw ... I am the child of immigrants so have no problems if these homes are being bought up by Chinese Canadians. I do have a very big problem if these homes are being bought by illicit funds or funds that have not been taxed correctly. I pay my share (and it is a big share .. every professional couple in Canada is essentially in the 1% and paying for it despite all the student loans we incurred). We have all these financial controls that apply to us about reporting foreign income and paying taxes, etc. This needs to be applied fairly and across the board.

One other datapoint: the listing agents in the area have websites in Chinese and with prices in Yuan. Any delusion I had that the money is coming from incomes earned in Canada is firmly gone.

People have talked about ideas such as taxing second homes and requiring residency or citizenship to buy a home. Both seem good ideas that will never be implemented. How about mortgage income tax relief for Canadians (like the US or even more aggressive than that)? Allow full borrowing against RRSPs and prevent buyers from discriminating against offers based on financing conditions. The freaking MLS data is regulated anyways so might as well.

They aren't holding cash. What they are doing is accepting the risk of not being able to finance the property. They're risking the 1% earnest money, but feel it's low risk because they have a good relationship with a bank or know they have good credit.

As for people selling and moving into a new house? Again, they're accepting the risk that they will be able to get bridge financing and sell their existing house.

Conditions have monetary value to both the purchaser and the seller. If you are losing out to people with clean offers, bump your offer by 5% and you'll find that sellers will wait another 2-4 weeks for their money. That's what I had to do to get a house in San Jose (just moved in!).

It's the same as the "discount for debit cards and cash" you can get in electronics stores.

Get a good real-estate agent that _knows_ the area, and listen to what they say the house will sell for. Ours was spot-on 100% of the time.

Next, you need to realize at what points in the sale the power in the relationship changes. Up to offer acceptance? The seller has the power, so offer more money to keep contingencies on the sale. After acceptance power starts to shift to the buyer. Here in California building reports are attached to the house, so a bad foundation is information everyone gets. This means the seller is likely to negotiate the price down or fix things if a bad report comes in. Of course, you have to spend $$ to find that out, and your mortgage application fees are then throw-away, so...

Finally, be honest about what you can afford. If you're not at the tippy-top of your price range, you will be able to stretch just a little bit to get that really sweet house you want.

Thanks for you thoughts. The challenge we're facing is whether the Mrs will do stay-at-home while the baby is young or not. If it is just my income, I know we'll have to stretch for a house we want. If we have both incomes, net of childcare, we should be okay. Canada has 5 year mortgage terms. That is distressing me to no end. If interest rates go to 5% in 5 years, we might have huge isues. If I had a 3.75%, 25 year US mortgage, I'd take it in a heart beat. I don't think a US lender will be willing to lend against Canadian property due to exchange rate risks (among other reasons).

It sort of depends on how long you intend to live in a house. For mortgages that are on 5yr terms, look at longer term averages.

For example, New Zealand (another market I'm familiar with) is currently running at 4%/yr for a 2yr mortgage and 5.5% for a 5yr. However, for budgeting purposes, most people will budget at 8%/yr, since that's the long-term average.

Just to completely freak you out, during the GFC, I hit 12% annual interest. My parents hit 20% during the Canadian inflation crisis of '81. :)

Go for the high end, don't be afraid of a smaller house, build up the equity and then move. However, be aware that closing costs are significant, so it's best to amortize them over several years - that's why housing calculators ask how long you will live in a house.

Frankly? If you're afraid of 5%, you probably don't want to own a house, or at least, you don't want to own _that_ house.

Mortgage income tax relief strongly punishes renters - my commercial landlord doesn't get any tax breaks, while you do. It also increases property prices, by reducing the cost of borrowing money.

Well, everyone has been blaming the prices on rich Chinese buying up everything, but this is the first actual evidence that I've seen no matter how flimsy it is.

EDIT: I should have been clearer that I never doubted that Chinese money was coming in, but I've previously seen nothing to convince me that it was significant or indicate how significant it was. Even if this estimate is of by a factor of two, it is still fairly significant.

meta question:

are there any meta-journalism news site offering analysis like yours?

Channel 4 (uk) Fact Check site? http://blogs.channel4.com/factcheck/

..but I'm not sure who checks the fact check site!

The NHS runs a good one for health scare stories [1]. If there is some health story, wait a day or two and they are likely to have explored the facts.

1. http://www.nhs.uk/news/Pages/NewsIndex.aspx

It's good to hear that Stats Canada is going to put some solid numbers to all the speculation.

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