I think the simple answer is probably no - people are just good at seeing patterns in data that is actually random. Testing the frequencies of these data against a Poisson distribution I get a p-value of something like 0.7. In other words, this looks exactly like it would if people were posting at random and independently of one another.
And 23-27 January is not Christmas where I come from...
Peter Norvig has some good illustrations of this in this article on recognizing bad experiment design. Scroll down until you get to the pictures of dots on a square; the really random ones look less random than the ones that aren't actually random.
I've voted this post up since it was a reasonable thing to ask and it has given excellent example of 1) how humans are overactive pattern seekers and 2) how cognitive biases can be overcome with statistical tests.
Echoing the others:
If we suppose these are 22 iid samples from a Poisson then the max likelihood estimate for the Poisson parameter is 0.82 (the sample mean). Simulating such draws from such a Poisson and looking at sample correlation between Jan 15-Feb 4 and Jan 16-Feb 5, the p-value is 0.1. And when testing Poisson-ness vs negative binomial clustering (with the same mean), the locally most powerful test uses statistic (x-1.32)^2, and gives a simulated p-value of 0.44.
I'm tempted to mention Poisson distribution (used to explain a lot of clustering phenomena). Not sure what difference it would make whether the difference is perceived or real.
Here's my idea: when the site is inactive for more than a day or two, people who care about the community become a little apprehensive that it may be stagnating, and are a little more likely to post now rather than postpone their planned post to later. If the inactivity continues for another day or two, their apprehension will grow and may hit the threshold for several people on the same day, so you get an over-compensating spike.
Those numbers don't actually look all that clumpy to me in the first place. I mean, "1" is a bigger clump than "0", but other than the negative clump (jan 23-27), nothing particularly clumpy jumps out at me from your data.
EDIT: I have noticed though that it seems as if my own active participation on LW as an individual seems to be "clumpy", but that's a bit of a separate thing, not exactly the same sort of thing as what you're talking about.
There is probably a little clumping because of day-of-the-week effects, but this looks pretty random to me.
Yeah, I've noticed this pattern in lots of contexts. My intuition is similar to yours: for many people, seeing others engaging in an activity encourages the urge to engage in that activity, and not seeing others discourages it. (I'd be surprised if there weren't empirical data on the subject -- it's such an easy thing to test -- but I don't know of any.)
I think the simple answer is probably no - people are just good at seeing patterns in data that is actually random. Testing the frequencies of these data against a Poisson distribution I get a p-value of something like 0.7. In other words, this looks exactly like it would if people were posting at random and independently of one another.
And 23-27 January is not Christmas where I come from...
15 Jan - 0 posts
16 Jan - 1 post
17 Jan - 1 post
18 Jan - 1 post
19 Jan - 0 posts
20 Jan - 2 posts
21 Jan - 0 posts
22 Jan - 1 post
23/24/25/26/27 Jan - 0 posts
28 Jan - 1 post
29 Jan - 1 post
30 Jan - 0 posts
31 Jan - 3 posts
1 Feb - 2 posts
2 Feb - 1 post
3 Feb - 0 posts
4 Feb - 1 post
5 Feb - 3 posts
Maybe 23-27 was Christmas? But I've gotten a general feeling that activity spikes around the same time. Perhaps when the site is populated with posts, people spend more time here, and then think more on related topics, and thus are more likely to post?
Note that this is all posts, not just promoted posts. It also includes rationality meetups and quotes threads - maybe it'd be more interesting analysis without that... I definitely get the feeling that a thought provoking post generates more. Whereas inactivity generates more inactivity. Thoughts?