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Lumifer comments on Should you write longer comments? (Statistical analysis of the relationship between comment length and ratings) - Less Wrong Discussion
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Since I critiqued the graphs in the OP and offered to make them better, cleonid was gracious enough to provide me with the dataset for Eliezer (EY) and Yvain (Scott Alexander) (SA) posts and invite me to play with it. For convenience, I'll split my comment into two parts -- the preliminaries and the analysis itself.
First, two caveats.
I'm looking at data for posts by EY and SA. They, being superstars, are not representative of LW members. This analysis will not tell you, gentlereader, whether you would get more karma by making your posts longer or shorter (unless, of course, you are EY or SA :-D).
Next, the data that I have lacks timestamps. Therefore I'm forced to make the assumption (almost certainly false) that nothing changed with time and treat the data as a blended uniform mass. The temporal dimension is, sadly, lacking.
A brief description of the data: we have two tables (EY and SA) which list the number of characters in a post, as well as the number of upvotes and downvotes that the post received. There are about 3100 data points for EY and about 1400 for SA.
The distribution of post lengths for EY and for SA is rather different: EY posts tend to be much shorter. This is visible in the following graph which plots the empirical distributon of post lengths (cut off at 2000 chars, but there is a long thin tail beyond it).
In numbers, the median length of an EY post is only about 200 characters -- half of his posts are less than that. In fact, a quarter of his posts are less than 87 characters. On the other side, 10% of his posts are longer than 950 characters, 5% are longer than about 1500 characters. The mode of the distribution -- the most frequent length of the post -- is around 70 characters.
SA writes more: his median post length is 450 characters, more than double that of EY's. The shortest quarter of the posts is below 165 characters, the longest 10% are over 1900 characters and the longest 5% -- over 2700 characters. The mode for SA's posts is 180 characters, two and a half times as much as EY's mode.
Continued in post 2.