Archive for the ‘probability’ Category

I came upon this article while doing the Morning Links on my other blog (where it is cross-posted):

Thorp, the founding principal of Gateway High in San Francisco – one of the most highly touted public schools in the state – has accepted that same position at Gashora Girls Academy in landlocked Rwanda. This means he will leave behind his attorney wife, Donna Williamson; his three adult children; his 3-year-old sheepdog, Jake; and his top-floor flat with a roof deck in order to live in a shared house and spend a minimum of three years swatting at mosquitoes.

“Rwanda is not without its challenges,” he says while stroking Jake in a living room that is sunny and easy and will probably seem sunnier and easier with each passing day until his departure. “There is the risk that at some point during this stint I will get malaria.”

I let out a wee guffaw at that last sentence. Yes, there is “the risk” of getting malaria–it’s even higher than the States(!)–but that doesn’t get you far. This region sees more lightening than anywhere else in the world; why not mention that shocking elevated risk instead? Truth is, your chances of getting malaria in Rwanda are small even if you don’t take medication (like most other expats I know and me), and if you are popping pills (as I’m sure Principal Thorp will), then it’s just silly to mention.

But I’m missing the storm for the clouds, aren’t I? The crux of his comment is not about the risk of malaria, it’s about the general hardship he will have to suffer for his cause. One fights the urge to weep looking over what he will be giving up:

  • Attorney wife Donna Williamson
  • Three adult children
  • Jake, the 3-year-old sheepdog
  • Top-floor flat with a roof deck
  • Sunny and easy living room that will seem sunnier and easier with each passing day
  • Sympathetic journalists

Ok, so leaving your family isn’t trivial, but would this be the chosen framing if his departure were for Belgium? As much as I hate to betray my own winsome exoticism, the expatriate life in Rwanda is not often equivalent to a perpetual safari. If you’re in Kigali, as Principal Thorp will be for at least part of his stay, you’ll be in a house, not a hut, and if you cook over a fire it will be because most ranges here are fueled with gas.

Gérard Prunier, an Africa scholar, has described Rwanda as being the “darling of foreigners” because the “blacks were polite and everything was clean.” In the same book, he later described it as “virtuous, Christian, respectable, and boring.” If Rwanda presents challenges for the expat, it more likely has to do with these than malaria or lightening strikes alike.

Read Full Post »

I think it was Jay Leno who had a bit long ago with the observation that while we know we’re more likely to die in a bathroom accident than on a commercial flight, we’re always going to worry about the latter more because no one’s ever opened their medicine cabinet and been sucked out into a slipstream at 30,000 feet. Similarly, I’ve not yet padded into the bathroom for a glass of water and found myself clenched in the jaws of a croc when I turned on the tap:

Deaths by crocodile attacks in Nyagatare district, along the crocodile infested Akagera River have compelled government to rush to the rescue of worried area residents, The New Times has learnt.

This comes after 14 year old Stella Mutesi, the latest victim was killed by a crocodile about a month ago while she was drawing water from the river.

Rosette Rugamba, Rwanda Development Board’s Deputy CEO in Charge of Tourism and Conservation, acknowledged the regrettable incident on Sunday explaining what is being done to prevent other such nasty deaths.

The article gives no indication as to how often this happens, but I’d bet death by croc is extremely rare relative to other life departures in Rwanda. Thankfully it appears this fact is being acknowledged in the government response:

Even though plans are underway to fence off the park so as to check human – wildlife conflicts, Rugamba underlined that in this particular case water scarcity is the challenge, which is going to be hastily addressed, “at the national level.” Safe water sources are said to be scarce in the area, leaving the residents with one alternative, albeit a deadly one – Akagera River.


Rugamba says a research study on where to erect boreholes in the communities has been concluded, by the ministry in charge of lands.

“The study has actually been done and finished, showing various points where the community can get water from without getting near the river. This issue is being addressed at a national level.”

Still, there’s a perversity to the fact that it takes a croc killing, a non-event in probabilistic terms, to draw attention to the bland common killer represented by a lack of access to drinking water.

Read Full Post »

I only have an elementary grasp of statistics, but I know enough to become frustrated when I read some article proclaiming that the results of some test were “statistically significant,” as if that statement was, well, significant. Not only is it often insignificant (as the word is commonly used), but it is also an incomplete statement.

Say we have a woman, Ms. T, who claims to have a palette so precise as to be able to discern whether her tea was made by pouring hot water over the tea bag or whether the tea bag was added to the hot water. If we wanted to test her claim, basic statistical methodology would be (roughly):

  1. Form a hypothesis, such as “Ms. T cannot tell the difference in how her tea is prepared.” This hypothesis, called the null hypothesis, is formed for the express purpose of being disproved.
  2. Form an alternative hypothesis, such as “Ms. T can tell difference in how her tea is prepared,” in the event the null hypothesis is rejected.
  3. Set up an experiment, such as one where Ms. T is blindfolded, given fifty cups of tea prepared either by adding the tea bag or the hot water first, and asking her to identify which method was used for each cup.
  4. Decide what the chances are that Ms. T would randomly be able to guess correctly. These are called the significance levels, which are probabilities that, given our null hypothesis (she can’t tell the difference), the results could have happened merely by chance (Standard values are 5%, 1% and 0.1%, though there’s no particular reason for this.). If our results have a probability lower than these values, we reject the null hypothesis and assume support for the alternative hypothesis because we believe our results are so improbable that the results are not just coincidence. If the probability is higher than our significance levels, we assume support for the null hypothesis.
  5. Compare Ms. T’s results with the results of a group of “normal” people. Let’s say that we find that Ms. T was correct in so many of the test tastes (49 out of 50) that, compared to a normal population, the chances of her randomly guessing correctly that many times was only 3%.

What happens now? Well, remember, our significance levels were 5%, 1% and 0.1%. Since the actual probability was determined to be 3%, our results are “statistically significant” at the 5% level, but are not significant at the 1% and .1% levels. “Significant” in statistics does not mean “important” or considerable”, but rather “indicative” or “expressive.” In plain English, all our results have shown is that if we assume the chances are 5% that Ms. T would be able to guess 49 out of 50 times correctly randomly, a result of 3% is indicative that our results did not happen by chance, and thus the null hypothesis should be rejected.

But remember, the 5% significance level we selected is purely arbitrary–some others might think that .1% is more accurate for significance, that we should only reject our null hypothesis if there is less than one chance in a thousand Ms. T’s results could have happened by coincidence. Furthermore, some researchers have been found to determine the significance levels after they’ve conducted the experiment; that way, they can choose a level ex post that makes their results “significant.”

At best, most journalists’ claims about statistical significance are incomplete because they fail to include the benchmark that determines significance, and at worst, they grossly misinterpret “statistically significant” as meaning “statistically important.”

I find the philosophy behind this type of statistical method to be interesting. I might write a future post on how we subscribe to the same philosophy when determining the burden of proof necessary to convict a criminal. If nothing else, I trust this post has convinced readers that journalists have the third type of lie down pat, whether they realize it or not.

Read Full Post »

Sticking It To The Man

This morning while riding the U-bahn to class no one died–or appeared to be dead–but I did have my ticket checked by one of the subway personnel. This morning only marks the second time I’ve had my ticket checked, meaning that if past experience can be trusted I will only get checked once a month on average. My immediate thought was that if the probability of my ticket being checked is so low, why on earth would I ever purchase a ticket? (As a bit of background for those unaware readers, Germany has an “honor system” for its public city transport; there are no turnstiles, but if passengers are discovered on public transport without a ticket they will be fined.)

For the strictly rational members of Homo economicus, a simple expected value calculation is all that is needed to decide the appropriate course of action. If the expected value of the fine is less than what I would pay for the ticket, then I’d be financially better off by not purchasing a ticket and playing the odds.

To find the expected value of the fine, one merely multiplies the probability of being caught with the value of the fine (≈50 €). In my case, the equation is thus:

( 1/30) * -50€ = -1.67 €

In other words, the expected fine I would expect to receive on any given day is less than 2 €. But what is that compared to the daily cost of a ticket?

Well, because the monthly ticket costs about 50 € it actually has the same daily cost as the fine–in fact, in my case, the ticket is the fine. In other words, if I were caught without a ticket, they would force me to buy the ticket I should have bought anyways. One really needn’t do a probability calculation to see that a purely rational actor would never buy a ticket under these conditions. He or she has nothing to lose and a small chance to be better off by being a literal free-rider.

Of course, my probability distribution is a function of the train I ride on to town–many other trains are checked far more frequently than mine. Nonetheless the lesson is clear: unless the amount of the fine is raised or the chances of getting caught increases, gaming the system would be a rational choice under my circumstances.

Good thing my ticket is already paid for, I suppose.

Read Full Post »