>>770
敢えて強いニュアンスを出したのだからI think it is not〜で俺の場合はいいのだよ。
君はこれが読めるかい？

I'd say "I think it's not true" would be used when you are sure that it's false. And "I don't think it's true" would be more if you just kind of think that it might not be true.
In other words I'd use "I think it's not true" if I'm more confident that it's not true.