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I'm new to this area and I'm a little confused with the wordings (although I've done a few calculations including T-Score tests...)

I just need to understand if the wording being used is correct.

Consider this: There are only a few lecturers who actually deliver practical knowledge to their students.

My question: Is it correct to state that the following are null hypotheses?

  1. There are not many lecturers who deliver practical knowledge to their students.
  2. The are only a few lecturers who deliver practical knowledge to their students.

To me, both convey the same meaning. But someone told me that the second statement is incorrect and that I must always include 'not' when forming a statement for null hypotheses.

Please advise. Thanks!

itsols
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    These seem like extremely poorly defined statements (what is "not many" or "a few")? Whether some more precise version of these make sense as null hypotheses depends on what question you wish to investigate. I do not think there is a need to state null hypotheses as a negation - in fact very often they are stated in a totally different manner (e.g. null hypothesis: parameter $\mu=0$, alternative hypothesis $\mu\neq 0$). Perhaps you misunderstood the statement or are not fully conveying the context, in which it was made? – Björn Sep 25 '16 at 14:15
  • @Björn I just made up the case. Let's say, we want to show that graduates lack practical sills and we need to test if this is true. So based on that, do my statements 1 and 2 above make sense for a null hypothesis? BTW, you're correct about me not being too clear about the subject. I would really like to understand if we are allowed to phrase a null hypothesis like I have done above. Thanks! – itsols Sep 25 '16 at 14:38
  • For a start, a null hypothesis needs to be clear. An imprecise statement like the above seems ill-suited for any question. If your re-phrasing, you just swapped "lecturers deleviring practical knowledge" to "graduates lacking practical skills", which does not really make this any clearer. In any case, I think you can phrase a null hypothesis with and without a negation, just not as imprecisely (as well as in a way that seems unsuitable for any kind of measurement) as you have done. – Björn Sep 25 '16 at 14:43
  • The answers to [this question](http://stats.stackexchange.com/questions/31/what-is-the-meaning-of-p-values-and-t-values-in-statistical-tests) might help you to clarify the meaning of null hypothesis. – T.E.G. Sep 25 '16 at 14:45
  • @Björn Thank you for that clarification. So I understand that you can indicate a null hypothesis with and without negation. I rarely see this and when I was pointed out as incorrect by someone else, I was concerned. I'm somewhat clear on this. Maybe a more learning should help. Thanks! – itsols Sep 25 '16 at 14:58
  • @Tahir Thank you for your input. Honestly that is a huge page. I tried but couldn't digest it in full... Maybe slowly :) – itsols Sep 25 '16 at 14:59
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    Null hypotheses are precise statements about some characteristic of one or more populations (precise enough for it to be at least notionally possible to compute the distribution of the test statistic under the null). They are not vague statements and are not about samples. – Glen_b Sep 26 '16 at 00:44

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Null hypothesis states that there is no relationship between response(Y) and predictors (say X).

You can refer to page 67 of this awesome book - Introduction to Statistical Learning for detailed application on null hypothesis. The pdf version is made available by the authors at the official website.

http://www-bcf.usc.edu/~gareth/ISL/

Jasmine Goel
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  • Thanks Jasmine Goel for your your answer and the superb pdf. It is way beyond me but I do understand something :) – itsols Sep 26 '16 at 06:21
  • Just for clarity, can I know this? Let's say, there's a general notion that writing business programs in COBOL is far better than using Pascal or C. Now, if I want to prove (by testing), that it's not the case, can I say *H0 = Writing business programs in COBOL is NOT faster than Pascal or C* ? – itsols Sep 26 '16 at 06:24
  • I think you are confused between response and features (predictors). Response is the dependent variable, which you might want to predict using predictors(which are dependent variables) assuming if there is a relationship between response and predictor. In your example, writing business programs in COBOL is not dependent on PASCAL or C. It is a comparison between the languages. If you say, writing fast business programs is independent of language chosen, then it is a null hypothesis. – Jasmine Goel Sep 26 '16 at 16:46
  • Did you mean predictors are *dependent* variables or was it a typo? – itsols Sep 27 '16 at 03:05
  • When I wrote that *writing programs in COBOL is faster* I meant that *the time taken to build using COBOL is lesser* compared to not using it. And that's the generally accepted idea. I'm sorry for the confusion. – itsols Sep 27 '16 at 03:09
  • Thank you Jasmine Goel. As for this case I've understood the point. And once again, that was a great book! – itsols Sep 27 '16 at 14:51
  • Predictors are independent variables (that was a typo, will edit it). – Jasmine Goel Sep 27 '16 at 15:50