How representative is Facebook?

If your friends are like mine, your Facebook feed last week turned red, as people changed their profile pictures to some version of the Human Rights Campaign's equality sticker. (For a slideshow of the variety, click here.) It seemed as if everyone had changed their profile picture. But did they?

On Friday, Facebook reported an analysis by Eytan Bakshy of the changes. There was an uptick of profile photo changes last Tuesday, March 26, "around the time when HRC began urging their Facebook followers to change their profile pictures at 1 pm EST." The uptick was pretty large, with 2.7 million (120 percent) more profile photo changers than usual. Here's Facebook's graph:

Notice that there are no scales on the Y axis, and only the bottom graph has scales on the X axis. Both graphs display time series model; in the bottom, Facebook's number crunchers have smoothed out the data, presumably by lengthening the scale. But, without scales on both axes, we can't know for sure. (Without a scale, we also can't tell where the growth begins - remember, you need to know where the beginning point - 0 - is.) So what, exactly, is this graph telling us? That there was an uptick at some time between March 25 and March 27.

Did all 2.7 million users change their profile photos to some variation of the HRC meme? We have no way of knowing that. I would guess that some did, and others changed their profile pictures to something different. Also, how many people wanted to change their profile pictures but didn't want to take the time to figure out how do it? That's relevant to the next point Facebook's data team makes: that users closest in age

to 30 years showed the greatest increase in updating. This suggests that, on average, 3.5% of 30-year-old Facebook users updated their profiles in response to the events surrounding the HRC campaign. We also found a small, but significant difference expression between genders. On average, 2.3% more self-reported female users updated their profile photo, compared to 2.1% more self-reported males.

Isn't age also self-reported on Facebook, as one of the commenters on Bakshy's post points out? And while we're about it, how many of the profile changers were people as opposed to other organizations? Maybe Facebook has this information. If so, I'd like to see it included in its post.

Oh, and one more point: Facebook has more than 163,000,000 users in the United States, according to socialbakers.com. So that 2.7 million figure is less than 2% of all Facebook users.

I found this column because of a blog post by Rebecca Rosen of TheAtlantic.com titled "Facebook: 2.7 Million People Showed Their Support for Marriage Equality by Changing Their Profile Pictures." Remember, when you're reading these things: it's important to think critically about the statistics and graphs in front of you.