Why is T test reweighting on a word X word co-occurrence matrix so effective? I am going through Stanford NLP class: http://web.stanford.edu/class/cs224u/

A task in the homework is to implement T-test reweighting on a word X word co-occurrence matrix: 
https://nbviewer.jupyter.org/github/cgpotts/cs224u/blob/2019-spring/hw1_wordsim.ipynb#t-test-reweighting-[2-points]

$$\textbf{ttest}(X, i, j) = 
\frac{
    P(X, i, j) - \big(P(X, i, *)P(X, *, j)\big)
}{
\sqrt{(P(X, i, *)P(X, *, j))}
}$$

I have 2 questions:


What is the intuition behind this formula? It looks a little like PMI but I can't understand what it's doing. The T-test explanation out there seems to be unrelated to this task.
It works amazingly well (when evaluated by this test): raw matrix yield a correlation score of 0.014, PMIed matrix 0.123 and t scored matrix: 0.408979. This number seems almost too good to be true for such a simple model. Can anyone bring some intuition/experience about why that is?
IT is very similiar to PMI, here you just expand it to the whole dictionary matrix (matrix representation of the whole vocabulary), normalize it by subtracting quantitive representation of the sum of words found in row i column j and than standardize. (Like when using sklearn Standardize(), similiar atleast)
Intuition? Well why is tf-idf working (generally as text quantification technique), you are focusing on essential n-grams and minimising away the rest, with this re-weighting you are getting close to tf-idf representation in a sence.