Why rejection of a true null hypothesis is called type I error?

I’m comparing two confusion matrices:

The 2nd is rotated, the Decision is on Y-axis. But I assume both reflect the same concept.

I have two options to render the word “Reject”.

(1) When we look at Null hypothesis matrix, the Reject of a “True Null hypothesis” means a decision which doesn’t reflect reality (convicting an innocent), and this is indeed FP (type I).

(2) Following Confusion_matrix wiki, I interpret Reject as False. Therefore, making a False decision (H0 is false) over Actual True (H0 is true) brings me to claim this is FN (type II).

Topic hypothesis-testing confusion-matrix

Category Data Science

1
answered at

In order to co-exist these two confusion matrices above we need to understand what statisticians call True/False and Positive/Negative. Let’s apply a linear transformation on wiki matrix and replace “Null Hypothesis is True” by “Alternative is False”.

(H0 is False)
Alternative is True		 (H0 is True)
Alternative is False
Reject H0 = Accept Alternative (Positive) TP FP (Type I error)
Don’t Reject H0 = Reject Alternative (Negative) FN (Type II error) TN

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