I thought the MBTI gave an X if you were actually at the middle?
So you'd get an I at less than 45%, an E at more than 55%, and an X if you were on the border.
Further, you said they were normally distributed, but didnt talk about the variance. It's possible that people who are just a little from the middle by % of population are meaningfully different than the average -- a quarter standard deviation could be a meaningful amount of change in the real world.
So your argument doesn't actually support your claim: with the inclusion of an X band, it's possible the gap between E and I is meaningful in real world situations. We can't know merely by knowing it's normally distributed, we need to analyze the standard deviation size versus the minimal meangingful difference in the real world.
Several instances I've seen of MBTI didn't offer X, but that's definitely an improvement. The one I got for high school career services actually crashed if you 'tied', because that hadn't been accounted for at all.
Without the X band, "normal distribution" is enough to say things are broken. It means that you're consistently dividing similar people while grouping dissimilar people, which isn't what I like in a cluster.
With the X band, SD becomes important and a wide distribution might provide good results. Anecdotally, this could match the high attention given to E/I versus F/T - high SD axes would be relevant to more people.
Having said that, I'm still skeptical of much of the MBTI literature. It definitely deals in bimodal distributions, asserting that these clusterings are features of the territory rather than the map. If the peak frequency is a value the test can't inform about, I think that still invalidates much of the literature even if the test has some predictive power.
> Several instances I've seen of MBTI didn't offer X, but that's definitely an improvement. The one I got for high school career services actually crashed if you 'tied', because that hadn't been accounted for at all.
While I get the criticism of those tests as poorly implemented pop-psych, it only seems fair to attack the MBTI itself as a concept if you criticize the actual written, send-in-and-evaluate official version. The version I took of that (which came with a ton of propaganda from the testing company) featured both an X band and numeric strength scores for each category. It also featured a lot more questions than the typical online free ones, and had redundant questions the way that standard psych evals do. So at least some of the "professional" MBTI people are providing that kind of test, even if their analysis is all about bimodals and nonsense.
> With the X band, SD becomes important and a wide distribution might provide good results. Anecdotally, this could match the high attention given to E/I versus F/T - high SD axes would be relevant to more people.
My main point was that the joint distribution increases the spread away from XXXX to things like XXFX or XNXX, where even if you're still near the exact middle, there's less people exactly at average, and so the test is more likely to relay at least one fact in one category about the test taker than any particular category is to say something useful.
So even though the test can't say anything about the hyperbox in the middle of the range, it is relatively small because getting a little way away from the exact center likely says something about at least one category, even if the majority still can't have anything useful said about them.
Think of it this way: assume that the test can't say anything about the middle 20% of people for a given trait, and that the traits are independent (ie, how you score on one has nothing to do with the others). The odds that you're XXXX is (0.2)^4 = 0.0016. So only ~1 in 500 people would get nothing out the MBTI, even though ~1 in 5 has at least one category with an X.
And that's assuming a relatively large X band. Drop the X band to 5%, and it's only ~1 in 200,000 that would get XXXX.
> Having said that, I'm still skeptical of much of the MBTI literature.
I threw out the marketing booklet mostly unread after the statistical nonsense of the first few pages was too much when I paid to take the professional version of the test in school.
The test is alright, but not great and modern data analysis can probably do a much better PCA than the MBTI is, but the company is outright moronic in what they say. And others can be much worse.
So you'd get an I at less than 45%, an E at more than 55%, and an X if you were on the border.
Further, you said they were normally distributed, but didnt talk about the variance. It's possible that people who are just a little from the middle by % of population are meaningfully different than the average -- a quarter standard deviation could be a meaningful amount of change in the real world.
So your argument doesn't actually support your claim: with the inclusion of an X band, it's possible the gap between E and I is meaningful in real world situations. We can't know merely by knowing it's normally distributed, we need to analyze the standard deviation size versus the minimal meangingful difference in the real world.