I saw on The Generation Project where a man took a DNA test that showed he was some percentage Native American or was the chance that he as Native American.
Can a DNA test prove that I have Native American ancestry?
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There are several tests that can show if you have Native American ancestry. I just posted a summary of the 3 core types of genealogical DNA tests in answer to another question, so please read here for general information on DNA testing:
Specifically, for Native American ancestry:
Y-DNA: If you have Native American ancestry on your direct paternal line (your father's father's father etc), then you will have a Y-DNA haplogroup that has been found to be specific to Native Americans -- C3b, Q1a3a1, Q1a3a4
mtDNA: If you have Native American ancestry on your direct maternal line (your mother's mother's mother etc), then you will have an mtDNA haplogroup that has been found to be specific to Native Americans -- certain subgroups of A, B, C, D and X.
Autosomal: Provides biogeographical percentages of your overall ancestry, not limited to direct maternal or direct paternal line. However, this test is limited in how many generations back it can detect a Native American ancestor. Typically, if you had a full-blooded Native American great-great-grandparent or closer ancestor, you should have inherited enough of the NA ancestor's autosomal DNA for it to be detected by this test. However, if the full-blooded NA ancestor was further back than great-great-grandparent, then you may or may not have inherited enough DNA from that ancestor to be detected by this test.