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Only thirteen words put N first and I third, and three letters share the second box between them.
A and O take the second box in five words each and E takes three. No other letter appears there, so the page is three small branches and nothing else.
NAILS, NAIVE, NAIAD, NAIFS and NAIRA carry the A branch, and NOISE, NOISY, NOILS, NOILY and NOINT carry the O branch.
NOISE and NAIVE are the two most people would produce, with NAILS close behind. The two branches are the same size and neither is obviously richer, which makes the second box a genuine coin flip.
NEIGH, NEIFS and NEIST make up the E branch. NEIGH is the only one you would reach for and it is the single word on the page ending in H, so guessing it either wins or eliminates a whole branch.
S closes four of the thirteen, thirty one percent, with E, T and Y on two each. L and S tie for the fourth box at three words apiece.
Nothing here repeats a letter, so a visible double rules the pattern out at once.
Both are common and they sit in the two equal branches, so either one splits the page cleanly. NOISE also tests the S ending.
A water nymph, and also the aquatic larval stage of some insects. It sits in the A branch and is the only word here ending in AD.
Yes, it runs N, E, I, G, H. The E in the second box puts it in the smallest branch and the H at the end makes it unique on the page.