What kind of empirical foundation are you looking for in a personality type indicator? What is the problem with the orientation of the lead function matching that of one's overall introversion/extraversion preference?
The real question is: how do you even know it's true? How do you know, without some kind of empirical foundation - meaning, without some verification
in reality, and not just some possibly fictitious but definitely made up idea in someone's head (Myers and Briggs)? Because that's the only basis for the conclusion that the dominant function follows I/E and J/P: back around 1940 AD, someone just pulled the whole idea out of a hat. Does that mean it's false? Not necessarily. But it doesn't mean it's true either; and until the idea can be verified in reality by testing it against other hypotheses, it stands as arbitrary hypothesis.
And there are other possible hypotheses. The test you just took shows one of them. It reveals your dominant function without using any arbitrary MBTI formula. And in your case, the Ti also matches for your type. But my result did not precisely match up with INTP.
That quiz didn't even give a type, just a ranking of functions.... this quiz could also use a lot of work, particularly with the Ni scoring.
The standard MBTI test itself could use a lot of work. Yet it stands, not only the test of time, but the test of public faith. And it gives uncomplicated, predictable results which most people like. Maybe it's not true, but it is generally pleasing, like a sugar-pill placebo.
Extroverted Intuition (Ne) ||||||||||||||||||||||| 10.92
Introverted Thinking (Ti) |||||||||||||||||||||| 10.38
Introverted Intuition (Ni) ||||||||||||||||| 7.95
Introverted Feeling (Fi) |||||||||||| 5.39
Extroverted Thinking (Te) ||||||||||| 4.93
Extroverted Feeling (Fe) ||||||||| 3.98
Extroverted Sensation (Se) ||||||||| 3.71
Introverted Sensation (Si) |||||||| 3
In my case there is more of a clear type pattern, but just because these tests give you results that don't match up to a MBTI type, that doesn't mean that MBTI needs to be thrown away entirely. It means that the online quizzes are not too great anyway and you can figure out your type through other means. But if you have already read Psychological Types I think you already understand this... so I'm not quite sure which direction you are going with this.
The direction - away from infectious dogma that causes some people to fret for years over their type, an issue that otherwise is of very little consequence. What has real consequence? Perhaps some actual introspection, starting with knowing what
I feel and why
I feel it, instead of hiding behind a general label/description that also covers 375,000,000 other people.
If I were to say that my type is an introvert, what is that a type of? Is it a type of behavior, a type of cognition, or a type of attitude? And if N is my dominant function, what is it a function of? With a little searching, you will find that the answers to these questions reduce to dead ends.
Psychological Types was a chore to read at times, a bit dated, and the type descriptions were fascinating but sometimes vague. They depended upon how well Jung himself understood the types, particularly some of the more mysterious ones which he described as feeling-states that Jung may never have experienced directly. And he says nothing whatsoever about dominant functions being determined by I/E and J/P (closure/non-closure). That is a Myers-Briggs fiction, not a Jungian one.
Anyway, I found out what an over-concern with typology in general was over 20 years ago: a distraction from doing my personal growth work. Being overly concerned with determining one's type can lead to an endless empty black hole.