Missing not at random data makes some Facebook users feel sad

This article, published last week, explained how “some younger users of Facebook say that using the site often leaves them feeling sad, lonely and inadequate”. Being a statistician gives you an advantage here because we know that naive estimates from missing not at random (MNAR) data can be very biased. The posts you see on Facebook are not a random sample from your friends’ lives. We see pictures of their vacations, abnormally flattering pictures of themselves, reports on their major achievements, etc… but no view of the mundane typical daily occurrences. Here is a simple cartoon explanation of how MNAR data can give you a biased view of whats really going on. Suppose your life occurrences are rated from 1 (worst) to 5 (best), this table compares what you see to what is really going on after 15 occurrences:

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