Probabilities and statistics, these are the right glasses to see the world. They protect us from our cognitive biases. But we should be careful. Although numbers don’t lie, people do; and often to themselves.
1. Graphs upside-down
Few weeks back, an important research institute in Brazil published a study claiming that 65% of Brazilians think that women in revealing clothes deserved to be raped.
It was a national shock. For the next couple of weeks, nobody could understand how such liberal people could turn out to be so chauvinist.
Social scientists came to the news to announce that end was near, psychologists denounced the macho soul hidden in the Brazilian subconscious, protests were called upon in Facebook, and even the country president twitted about it to show her indignation.
To me (and anyone used to numbers), it was clear that the only smelly thing about that result was the number itself. If a survey reports that 65% of people are cobalt blue, but you never saw any cobalt-blue person in your whole life, you don’t shout against the pigment, you question the statistics.
Well, in fact, the institute published an erratum last week: “Oops! Sorry, it wasn’t 65%, but 26%…, my bad.” Apparently, someone read a graph upside-down, or something like this.
Funny enough, I didn’t see any analyst coming to public this week to explain why the end of the world is just not behind the door anymore, or any psychologist to admit that we are macho, mas não muito. Protesters discretely changed topics and the president, who has a degree in economics and should have been able to smell a fishy number, didn’t twit again.
2. It’s a gut feeling
I like probabilities and statistics a lot. But I also know that sometimes they may be wrong due to different reasons. Honest mistakes, technical incompetence, intentional manipulation.
Nevertheless, probabilities and statistics are still the right glasses to see the world. They protect us from ourselves, as we have brains that are awfully biased towards wrong answers.
Most people think they are better drivers or more intelligent than the average. And they come back from a week trip to Paris telling how French are snob based on a few little-representative experiences.
I know people who are afraid of flying, but even so, they face their fear every winter to visit ski resorts. That’s it: they are afraid of a transport with virtually zero risk, but they go practicing a sport with very sizeable risks.
People (including myself) feel silly buying a lottery ticket with combinations like 01-02-03-04-05-06, and they feel they have better chances if the ticket reads something like 03-12-19-31-42-48. It’s not rational, it’s really a gut feeling, as everyone with high-school education knows that the chances are exactly the same for both combinations.
Some of these people who buy lottery tickets don’t believe that it would be worth going to a shrine like Lourdes to try a miraculous healing. But assuming that the 67 miraculous healings attributed to that shrine really took place among the 60 million sick pilgrims who visited it in the last 150 years, chances of getting cured in Lourdes are 0.0001%. Ridiculously small, but still 10 times bigger than of wining a 49-numbers lottery with either combinations above.
3. Then, you project didn’t get funded
And speaking of lottery, let’s talk about one of my favorite topics: distribution of resources.
Suppose you are applying for a grant or for a new job. If you are short-listed, it means that you should be among the top-10 candidates. Of course, your chances are still 1/10 of being successful in the first call.
Question: how many calls should you be short-listed in to have really good chances of being successful?
Simple, if p is the probability of success in one call (1/10) and n is the number of calls, the probability of success is P = 1-(1-p)n. Then, P = 19% in 2 calls (just Google “1-(1-1/10)^2”); 41% in 5 calls; 65% in 10 calls. You need to be short-listed 22 times to have success chances over 90%!
You can take home two lessons from this exercise:
- First, if your project wasn’t funded or if you didn’t get the job, don’t give up. Keep trying. Just 21 more runs to go…
- Second, you may count on luck, but it is better to work to improve your p. If you move to top 5, you need only 11 calls to go over 90%. What can you do to improve p? Easy: publish more papers; do more networking; kill a couple of competitors.
Anyway, just to finish, the chances that this will be the most successful week of the year for someone is roughly 1/52. Much Bigger Outside has about 100 visitors per week (Thank you all!), which means that there are 86% chances that one of these visitors will just going to have the most successful week of the year. I hope that it is you!
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- Do you want to known how to use statistics to find a partner for life? I did the math for you, check here.