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Why saying “We accept the Null Hypothesis” is wrong. – An Intuitive Explanation


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

If you correct them, they would say what s the big difference? €œThe 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 €œFail 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 €œX theory is true€. Instead what they try to prove that €œthe 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 €œI failed to prove theory X is wrong€. Ah.. now can you see the parallels between €œI failed to prove theory X is wrong€ and €œWe fail to reject the Null €.

Now let’s come to why you can€™t say €œwe 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, €œscience is never settled€.

A more classic example is that of the €˜Black Swan€™. €œSuppose 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 €œwe 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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