# Does being on Twitter make you a worse scientist? Yes… a bit.

Posted on Sep 19, 2014 in Bayes, Science, Social Media

I was intrigued by this claim, found in a Twitter survey of the “Top 50 Science Stars on Twitter” that “most high-performing scientists have not embraced Twitter”. That article is debatable on other grounds, as well, in particular in terms of what defines a “Top Scientist” on Twitter. In fact, on closer inspection, the data on which this strong statement is based are fairly debatable, having been obtained by “sampl[ing] Twitter usage among 50 randomly chosen living scientists from the Scholarometer list” (sigh).

Even so, it is interesting to use some real maths to answer the question: Assuming it is true that top scientists shun Twitter, does being on Twitter make me (statistically) less of a good scientist? In other words, is it more probable for me to be a “mediocre” scientist if I’m a Twitter user?

To answer this question, we need one of the cornerstones of scientific inference, a mathematical result called “Bayes theorem”. In a nutshell, Bayes Theorem is a rule to invert the order of conditioning of propositions. It works by relating the probability of A given that B is true, P(A | B), to the probability of B given that A is true, P(B | A). The relationship is the following:

P(A | B) = P(B | A)P(A)/P(B)

where P(A) is the probability of A being true (independently of B) and P(B) is the probability of B being true (independently of A).

So let’s get Bayes Theorem to bear on our question: What is the probability of being a Top Scientist (TS), as opposed to a Mediocre Scientist (MS), given that one is a Twitter User (TU)? Thanks to Bayes, the answer is:

P(TS | TU) = P(TU | TS)P(TS)/P(TU)

We now need numbers for all the probabilities on the left hand side.

P(TU | TS) is the probability of being a Twitter user, given that one is a Top Scientist.

P(TS) Is the probability of being a Top Scientist.

P(TU) is the probability of being a Twitter User, regardless of whether one is a Top or a Mediocre Scientist. We can rewrite this as

P(TU) = P(TU | MS)P(MS) + P(TU | TS) P(TS)

where

P(MS) is the probability of being a Mediocre Scientist, P(MS) = 1 – P(TS), and

P(TU | MS) is the probably of being a Twitter User if one is a Mediocre Scientist.

We don’t have numbers for all those probabilities, but we can take some informed guesses.

Let’s define “Top Scientist” as “being in the top 10% of all scientists”. Then

P(TS) = 0.1 and P(MS) = 0.9

Next, we need  P(TU | TS). If the “findings” of the above article are to be believed, this number ought to be smallish. We don’t know how small, but I’m going to guess that it is plausible that it lies between 0.01 and 0.1.

For P(TU | MS), it is reasonable to suppose that this number is higher than the probability of being on Twitter if one is a Top Scientist (the implication of the article being that if one is a Mediocre Scientist, they have more time to waste on Twitter). So it is plausible to believe that P(TU | MS) lies between 0.5 (half of the Mediocre Scientists are on Twitter) to 0.9 (almost all Mediocre Scientists are Twitterati).

We now have all the ingredients to compute the probability that a scientist that uses Twitter is a Top Scientist, subject to the various plausible assumptions made above.

Depending on the choice one makes for P(TU | TS) and P(TU | MS), we obtain that the probability of being a Top Scientist, which is 10% before one factors in that the person is a Twitter user, decreases if one is on Twitter, and it lies between 2.1% and 0.12%, depending on what one believes about the relative probabilities of Twitter usage between Top and Mediocre Scientists.

So the answer to the initial question: “does being on Twitter make me a more mediocre scientist?” is “yes, a bit”: anywhere between a factor of 5 and 90 less so.