But average class size isn't the most relevant metric for *students*.
Classes are like families in Portugal. Most of them are small, but because they are small, a minority of individuals are in them. Most students are in the comparably few huge classes.
@TimScharks@UW It's surprisingly hard to get data on class sizes, but Marquette University provides binned data. If we use bin averages, we get the table below. Average class size is 26. Average *experienced* class size, the average size experienced by a student, is very nearly twice that, 51.
@TimScharks@UW This leads to some cool results. If you stood on campus and asked passers-by "How big is your next class", the professors' answers would average 26 (there's one prof per class) but the students' would average 51 (bigger classes have more students in them).
Now that the family and class sizes examples are clear, we can turn to a classic result in this area, the Friendship Paradox.
The weak form of the friendship paradox says that with high probability your average (mean) friend has more friends than you do.
It's not just IRL friends; the same holds for facebook friends, twitter followers, instagram followers, twitch followers, houseparty friends, or whatever it is that you kids do these days.
We just followed @rihanna. She's got 100M twitter followers. We follow 2849 other people as well.
Even if NONE of them had a single follower, the mean number of followers that people we follow have would be 100M/2849=35100 followers!
When you look it at that way, it's not so surprising. Mean values are driven by large outliers. If you follow a few highly-followed people, the weak friendship paradox will apply to you.
One recent study showed that the weak friendship paradox holds for 93% of facebook users.
The strong friendship paradox is a lot more surprising. It says that for most people, their median friend will have more friends than they do.
Now following @rihanna isn't going to do the trick, and in fact the strong form of the paradox doesn't hold for @callin_bull.
But it does hold for 84% of facebook users. This seems surprising. Wouldn't you think that half of people would have more friends than their median friend?
They don't, for the same reason that we encountered with family composition and class sizes.
Think about it this way.
Suppose most of us have 10-50 friends (back to IRL).
An introvert with five friends makes five people feel good about themselves; a socialite with a hundred friends makes a people feel unpopular.
That's the strong friendship paradox.
At least until tomorrow, we'll leave with a cheery thought. The same principle applies to intimate relationships as well.
Chances are, the majority of your partners have slept with more people than you have.
Sweet dreams.
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One of our key pieces of advice is to be careful of confirmation bias.
There's a thread going around about how the crop below is what happens when Twitter's use of eye-tracking technology to crop images is fed with data from a misogynistic society. I almost retweeted it. But…
…that story fits my pre-existing commitments about how machine learning picks up on the worst of societal biases. So I thought it was worth checking out.
While it would be fish in a barrel to drag this paper as a contribution to the pseudoscience of homeopathy, we'll largely pass on that here. More interestingly, this single paper illustrates quite a few of the points that we make in our forthcoming book.
The first of them pertains to the role of peer review as guarantor of scientific accuracy.
In our book we suggest that one never assume malice when incompetence is a sufficient explanation, and one never assume incompetence when an understandable mistake could be the cause.
Can we apply that here?
I bet we can.
A lot of cartographic software will choose bins automatically based on ranges. For example, these might be the 0-20%, 20-40%, 40-60%, 60-80%, and 80-100% bins.
As the upper bound changes over time, the scale slides much as we see here.
We've written several times about what we describe as Phrenology 2.0 — the attempt to rehabilitate long-discredited pseudoscientific ideas linking physiognomy to moral character — using the trappings of machine learning and artificial intelligence.
For example,, we've put together case studies on a paper about criminal detection from facial photographs...
From the book: "Mathiness refers to formulas and expressions that may look and feel like math—even as they disregard the logical coherence and formal rigor of actual mathematics."
(Admittedly the shock-and-awe factor is minimal here in this sum of two quantities)
"When an equation exists only for the sake of mathiness, dimensional analysis often makes no sense."
If Boris claimed the threat level was a *function* of these two quantities, fine. But to say it is a *sum* makes zero sense.
1. I recently tweeted about a particularly poor piece of science reporting in the science/tech news site @BigThink. In that article, they describe a new study as showing that spending two hours a week in nature is essential for happiness. bigthink.com/surprising-sci…
2. In our course, we encourage our students to question as strongly those claims that support their beliefs as those that challenge them.
I believe myself that time in nature improves well-being, so in the spirit of following my own advice, let’s look closely at this story.
3. The @BigThink story oversells the study. First of all, this is an observational study that establishes association, not causation. It could be that time in nature causes a sense of well-being. Or it could be that a sense of well-being causes people to spend time in nature.