"We already have methodology for measuring the happiness of Facebook users: by considering how many positive words people use in their status updates (see the USA Gross National Happiness Index). This method allows us to see whether a person's Facebook relationship status affects how positive and negative they are." (from post, emphasis mine)

No it doesn't. Correlation vs. Causation.

Counter-example: assume these two men (simplifying to single and non-single categories) are equally happy in real life:

Singles' non-relationship status updates: "Jeff is psyched for his Super Bowl party!" vs. Non-singles' non-relationship status updates: "Tony is psyched for his Super Bowl party!" Comparison by Fb methodology: equal happiness level

Single's relationship status updates: [non-existent] vs. Non-singles' relationship status updates: "Tony loves his super awesome girlfriend Melissa!!! Sweetheart, you're the bestest gf evarrrr!!!1!" Comparison by Fb methodology: Tony seems happier.

Conclusion: obvious nonsense. Somebody tell these guys to take a stat class.