Connecting Myers Briggs and the Hogwarts Houses

Here is a link to someone's idea of the connection between Myers Briggs and the Hogwarts Houses:
http://aroomofrequirement.wordpress.com/2012/12/03/the-sorting-hat-of-harry-potter-and-myers-briggs-personality-typology/

I like this approach quite a lot, actually, but I don't think this table isn't exactly accurate. While I like how they use the functions instead of the temperaments (which doesn't work at all, I've tried it) I think that it would be more accurate with different houses representing the functions. The way they organized it, each house is represented by two functions, however the placement of the houses is uneven. In my opinion, to make it truly accurate, each house must be represented by both an N or S function and a T or F function.

Here is the original from the link shown above with my thoughts added.
Extraverted Intuition (Ne): Imaginative and innovative, they search for new ideas, people, and possibilities. Gryffindor. (I agree.)
Introverted Intuition (Ni): They examine patterns, symbols, and meanings to solve complex puzzles. Ravenclaw. (I agree with this one too.)
Extraverted Sensing (Se): They spontaneously seize the moment, following anything that draws their interest. Gryffindor. (Maybe... Or Hufflepuff. Or maybe even Slytherin.)
Introverted Sensing (Si): They rely on a strong memory, drawing information from past experiences and traditions. Slytherin. (Definitely)
Extraverted Thinking (Te): They sort, organize, and make decisions.  They speak their mind. Slytherin. (Or Ravenclaw.)
Introverted Thinking (Ti): They operate from pure logic, sorting theories and solving problems. Ravenclaw. (Or Slytherin)
Extraverted Feeling (Fe): They nurture relationships, promote collaboration, and validate others. Hufflepuff. (Or maybe Gryffindor.)
Introverted Feeling (Fi): They rely on their values and empathy to create inner and outer harmony. Hufflepuff.  (Still could be Gryffindor.)

So, I would say that in my opinion
Hufflepuff: Se and Fi
Gryffindor: Ne and Fe
Slytherin: Si and Ti
Ravenclaw: Ni and Te

Here it is. My take on the connections between Myers Briggs and The Hogwarts Houses: (You'll notice that each personality type has two houses to represent it, except for ENTJ and INTJ which are purely Ravenclaw and ESFP and ISFP which are purely Hufflepuff.

Personality Type	Primary Function	Supportive Function	Primary House	Secondary House
ENTP	Ne	Ti	Gryffindor	Slytherin
INTP	Ti	Ne	Slytherin	Gryffindor
ENTJ	Te	Ni	Ravenclaw	Ravenclaw
INTJ	Ni	Te	Ravenclaw	Ravenclaw
INFP	Fi	Ne	Hufflepuff	Gryffindor
INFJ	Ni	Fe	Ravenclaw	Gryffindor
ENFJ	Fe	Ni	Gryffindor	Ravenclaw
ENFP	Ne	Fi	Gryffindor	Hufflepuff
ISTP	Ti	Se	Slytherin	Hufflepuff
ESTP	Se	Ti	Hufflepuff	Slytherin
ESFP	Se	Fi	Hufflepuff	Hufflepuff
ISFP	Fi	Se	Hufflepuff	Hufflepuff
ESTJ	Te	Si	Ravenclaw	Slytherin
ISTJ	Si	Te	Slytherin	Ravenclaw
ESFJ	Fe	Si	Gryffindor	Slytherin
ISFJ	Si	Fe	Slytherin	Gryffindor

According to this chart, I am a Ravenclaw, which is true. My brother (who is an ISTP) is a Slytherin or a Hufflepuff. I'm not sure yet whether this fits or not. My parents are either Hufflepuffs or Gryfindors, which makes sense.
Now, I don't claim that this chart is entirely accurate. In fact, I'm actually quite sure it isn't. In my opinion, Myers Briggs and Hogwarts Houses are two completely different typing systems and it is impossible to truly connect them.