.

We often come across YouTube videos, posts, blogs, and private courses wherein they say "We accept the Null Hypothesis" instead of saying “We fail to reject the Null hypothesis”.

If you correct them, they would say what s the big difference? “The opposite of ‘Rejecting the Null’ is ‘Accepting’ isn’t it ?".

Well, it is not so simple as it is construed. We need to rise above antonyms and understand one crucial concept. That crucial concept is ‘opperian falsification.

This concept or philosophy also holds key to why we use the language “Fail to reject the Null”.

Basically, the Popperian falsification implies that ‘Science is never settled'. It keeps changing or evolving. Theories held sacrosanct today could be refuted tomorrow.

The Popperian falsification implies that ‘Science is never settled’. It keeps changing or evolving. Theories held sacrosanct today could be refuted tomorrow.

So under this principle, scientists never proclaim “X theory is true”. Instead what they try to prove that “the theory X is wrong”. This is called the principle of falsification.

Now having tried your best and you still could not prove the theory X is wrong, what would you say? You would say “I failed to prove theory X is wrong”. Ah.. now can you see the parallels between “I failed to prove theory X is wrong” and “We fail to reject the Null ”.

Now let's come to why you can’t say “we accept the Null hypothesis”.

We could not prove theory X is wrong. But does that really mean theory X is correct? No, somebody smarter in the future could prove theory x is wrong. There always exists that possibility. Remember above that we said, “science is never settled”.

A more classic example is that of the ‘Black Swan’. “Suppose a theory proposes that all swans are white. The obvious way to prove the theory is to check that every swan really is white — but there’s a problem. No matter how many white swans you find, you can never be sure there isn’t a black swan lurking somewhere. So, you can never prove the theory is true. In contrast, finding one solitary black swan guarantees that the theory is false.”

Note: The post is merely to drive home the point of how the language “we fail to reject" came about. It is not a post favoring inductive reasoning over deductive reasoning or vice versa. Neither it is an effort to prove or disprove Karl Popper’s falsification principle.

Reference (Black swan example): https://www.newscientist.com/people/karl-popper/#ixzz70d4aPeIj

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