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Andrew Steele

Law of small numbers Add to ...

One of the more surprising things about studying statistics is the multitude of names for basic concepts.

For instance, take the technical description for the ridiculous claim Stephen Harper made at the Toronto Reference Library last week.

Under fire for shoveling stimulus money at a significantly higher rate into Conservative-held ridings, particularly those of cabinet ministers, the Prime Minister looked back over his recent travels and declared it simply wasn't true.

"I have been on the road the last week. I've done four major announcements - three were not in Conservative ridings," he said.

Wow. According to the research conducted by the Prime Minister, 75 per cent of projects he announced in the last week were not in Conservative ridings. Clearly, the opposition is just plain wrong. If anything, it's the Conservative ridings that are getting screwed.

Here is where that myriad of names thing comes in.

In logic, this would be called a hasty generalization. Some other fun names I might have written if an undergrad tried to pull this in a paper include the fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, generalization from the particular, leaping to a conclusion, hasty induction, law of small numbers, unrepresentative sample, and - for fans of the Latin - secundum quid.

Hasty generalization is "the fallacy of examining just one or very few examples or studying a single case, and generalizing that to be representative of the whole class of objects or phenomena."

And the Prime Minister didn't just stop there.

Hasty generalization can be unconscious and innocent. When it is done consciously and with the malicious intention of excluding cases to mask the true nature of a phenomena, it is the fallacy of exclusion and can be a particularly nasty form of selection bias.

Unconscious and malicious selection bias has a long - and at times horrid - history in the social sciences. Those wanting to find some of the most offensive examples can consult Stephen Jay Gould's Mismeasure of Man.

If there are sampling or methodological problems in the study Liberal MP Gerard Kennedy undertook that demonstrated the bias against opposition ridings and in favour of Tory ridings, then by all means they should be put forward.

Certainly, Mr. Kennedy only sampled those projects he could identify, and that sample could be skewed by the logic that projects in CPC-held ridings would get more media attention because of increased government motivation to highlight them.

But the Conservative response consists exclusively of three types of falacies:

1. Ad hominem attacks (attacking the man saying the charge, not the charge itself). An example would be Transport Minister John Baird's empty retort that the Liberals are "up to political mischief."

2. Hasty generalizations. The best example is the Conservative response on the day Mr. Kennedy issued his report, in which they countered that the single example of the site where the announcement took place was not scheduled to begin immediately. Partially rebutting a single element of a thousand point charge does not address the charge.

3. Fallacies of exclusion. The Prime Minister's argument this week stands out as the best example of that.

Basically, in his statement, the Prime Minister was knowingly attempting to have the listener draw a false conclusion by presenting a purposely-crafted and biased data set as representative of the entire set.

In doing so, he was taking Canadians for fools.

Considering the recent cheque logo shenanegans and the confirmation from a nominated CPC candidate that stimulus follows party, the Prime Minister needs to address this charge four-square or risk a major scandal that will not only injure his reputation, but risk the recovery by possibly slowing the pace of project funding.

On the policy side, remaining funds should simply be flowed to municipalities to distribute as needed. This is by far the fastest, and most transparent, way to launch infrastructure quickly.

Rhetorically, the Conservatives have a major advantage in rebuttal. They are the government and control the actual list of where contracts went. Simply releasing the full list should address the charge.

Of course, for that to happen, two other things must be true:

1. They must actually have such a list. (Judging from Parliamentary Budget Officer's report into the "uneven," "inconsistent" and "missing" record keeping in the multi-billion dollar stimulus spend, it is actually possible the government does not know where the money went.)

2. They must be spending the money fairly and wisely, distributing it efficiently and relatively evenly across Canada.

Don't hold your breath.

I am beginning to suspect we will only see the full list of projects in the appendix of an Auditor-General's report years from now, if ever.

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