No, earned income credit is not the same thing as Head of Household . Earned income credit is a refundable credit you get if you worked but had a low income and otherwise qualify.
Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household
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