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).

  • 1
    $\begingroup$ Does this answer your question? stats.stackexchange.com/questions/352326/… $\endgroup$
    – bogovicj
    May 27, 2021 at 20:09
  • $\begingroup$ Thank you. Very close but not. I see a contradiction in these two confusion matrices (CM). The FN and FP are swapped. I see two variations of CM, one for classification and another for hypothesis testing. Rejecting something which is true, called FN. From wiki: en.wikipedia.org/wiki/False_positives_and_false_negatives "FN is a test result which wrongly indicates that a condition does not hold" condition = H0 And therefore, Rejecting true H0 should be called FN, type II error. $\endgroup$
    – belz
    May 28, 2021 at 21:25

1 Answer 1


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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