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What does 16% Scotland mean on an ancestry test?

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Full Scottish of any generation before you would mean

1/(2^g)

for the g-th generation:

50% for a parent,
25% for a grandparent,
12.5% for a great-grandparent,
etc.

Remember that these results are based upon samples which might not lead you in the right direction. The specific numbers might be off.

But that's a significant result, just like the comment that your combined Scottish, Irish, Welsh is around 25%, which suggests a grandparent (or the equivalent) from the British Isles.