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So, I've been filling out online applications lately, and according to a few firms I apparently qualify as disabled: http://imgur.com/G25t7Lc
Not all applications have this, however, and it's nothing I really considered before. Should I be writing a diversity statement when doing apps talking about my problems, or just click the check box and talk about it if asked in an interview?

Were I you, I would approach listing yourself as disabled under some categories very carefully--e.g., major depression, schizophrenia, bipolar disorder. That is, I probably wouldn't disclose those issues.