One of the basic rules in textual criticism is to choose the “more difficult” reading. Another way to say this is to ask what reading would most likely give rise to the other reading, and to prefer the former.
In John 7:8, Jesus’ brothers are taunting him, telling him he should go to Jerusalem for the festival of Tabernacles. Jesus responds, “You go up to the festival yourselves; I am not going up to this festival (ἐγὼ οὐκ ἀναβαίνω εἰς τὴν ἑορτὴν ταύτην), for my time has not yet fully come.”
The problem of course is that he does go to Jerusalem (v 10). So was Jesus being honest?
This is certainly what gave rise to the alternate reading, “I am not yet (οὔπω replacing οὐκ) going up.” The external evidence for οὔπω is actually quite strong (P66, 75, Vaticanus, but not Sinaiticus), but internally it is inconceivable that a scribe would have changed οὔπω to οὐκ and introduce the issue of Jesus’ honesty. οὐκ is preferred in all major translations (except the KJV following the MT).
Notice also that the explicitly continuous translation “I am not going up” (ἀναβαίνω) favored by most translations at least paves the way for the reader to hear “not yet.”
The more complete answer is supplied by the condition, “my time has not yet fully come.” As Carson argues, Jesus’ “itinerary is regulated by the Father” and hence the time is not yet right. But he would go when instructed to do so by his Father.