Query in lecture video: Defining Hypothesis

Course Q&A Math for Machine Learning Probability & Statistics for Machine Learning &...
1

Hey guys,
I have a small query in the aforementioned lecture video. Either it’s a discrepancy or my understanding of the topic is missing something.

At 1:41, Luis states the following:

There’s a lot of evidence that shows that the email is spam. Then the null hypothesis is rejected and the alternative hypothesis that the email is spam is accepted as true. But this doesn’t work the other way around. If the evidence gathered is not enough to show that the email is spam, then you can reject the null hypothesis. However, that does not mean that the email is ham, only that we don’t have enough evidence to show that the email is spam.

According to this, if we have:

Lot of evidence of the email being spam → Reject Null Hypothesis, & Accept Alternative Hypothesis

But even if:

Evidence gathered is not enough for the email being spam → Reject Null Hypothesis

So, when exactly do we accept Null Hypothesis? I believe the above scenario should be as follows:

Evidence gathered is not enough for the email being spam → Reject Alternative Hypothesis + Don’t Accept or Reject Null Hypothesis

Let me know if this is a verbal discrepancy, or I am missing something here.

Cheers,
Elemento

1 Like
2

Hey Guys,
Just a follow up to this query. In the lecture video “p-value”, I saw 2 scenarios being mentioned:

  1. p-value < alpha: Reject H0 & Accept H1 (I believe it is analogous to “lot of evidence of the email being spam”)
  2. p-value > alpha: Don’t Reject H0 (I believe it is analogous to “evidence gathered is not enough for the email being spam”)

This means that the above point is actually a discrepancy in the lecture video, where Luis has stated incorrectly. I believe it should be:

If the evidence gathered is not enough to show that the email is spam, then you can cannot reject the null hypothesis. However, that does not mean that the email is ham, only that we don’t have enough evidence to show that the email is spam.

And then based on this statement, I believe we can say that “Don’t reject H0” doesn’t imply “Accept H0” or “Reject H1”.

Let me know if I am on the correct path. Thanks in advance.

Cheers,
Elemento