Consider the following two sentences:
I don't think you love your father.
I think you don't love your father.
Is the second sentence correct? I was taught it is wrong.
Both sentences are correct and mean the same thing, that is, "I believe that you do not love your father."
The first phrasing is vastly preferred by native English speakers for no real reason, other than perhaps it sounds a bit more polite due to its indirectness and implication of possible uncertainty.
There's a nice discussion of "negative raising (shifted or transferred negation)" at englishcorner that addresses your question fairly precisely.
The page mentioned above provides a reference (pp. 354-355 of Practical English Usage by Michael Swan) for its list of exceptions to negative raising, but unfortunately provides no reference in support of its main assertion, that native speakers "prefer to make the first verb negative instead of the second".
It appears that most native speakers will regard the two sentences as having the same meaning, but in my experience, some regard the form "I don't think x" as equivalent, for purposes of argumentation, to "I don't think." After all, it doesn't say what one thinks, it says what one doesn't think.
Both sentences are grammatically well-formed, and in casual conversation would usually be understood to mean the same thing. However, I suggest one avoid "I don't think x" constructions in formal writing or speaking.
A more-diffuse discussion of negative raising appears at englishpage.com.
I'm not a native speaker but from logical point I think these sentences are not quite the same. I don't think you love your father. By this you just doubt that the person loves his father. You are not sure. I think you don't love your father. This is more strong. You are sure and the stress goes on don't.
Neither sentence is incorrect.
If you say "I don't think you love your father", then you imply that you do not know whether or not I love my father.
If you say, "I think you don't love your father", that means that you think that you know that I don't love my father.
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