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I'm trying to understand the correct ways of expressing a null hypothesis. So I've created this case and I'd like to know if I'm on the right track.

Case 1: There is a general understanding that keeping a pot closed with a lid reduces the time taken to cook. This is because more heat is trapped in the pot. I (as a researcher) seem to have a different view that other factors such as the type of pot also matters. So I want to test if this is true and I'm going to test a number of different types of pots both with and without the lids on.

Null Hypothesis (I hope I'm correct here) : There is no difference is cooking time, whether or not the pot is covered

My question in this regard: I'm confused about the null hypothesis being the 'default' situation with 'no change'. So I also tend to think that the null hypothesis is the generally accepted condition that cooking with the lid on reduces cooking time.

So what is my correct null hypothesis?

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  • $\begingroup$ Your description of your case is ambiguous to me. It sounds like you want to determine if the type of pot has an effect of cooking time after having controlled for lid. Is that what you want to know? Or do you think that the lid is irrelevant to the cooking time? Or do you think that it is the type of pot that's relevant instead of the lid, & that other people were confused because they inappropriately looked at the lid in isolation? $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 27, 2016 at 19:07
  • $\begingroup$ Wow! @gung that's amazing, how you interpret that little para... After looking at your comment, I am clearer now. So I actually meant that the lid indeed has an effect, but not only that matters. However, the people have looked at only the lid in isolation. Perhaps as a result of testing the lid only, I may find that the lid really has no effect, and this may lead to further studying the type of pot as well... I hope that makes sense :) $\endgroup$
    – itsols
    Commented Sep 28, 2016 at 1:51

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The null hypothesis depends on that you can find a test for it. In your case of cooking time, you are likely to randomly source some pots, cook with and without the lid and then compute a t-test for dependent observations or a signed rank test to compare the cooking times needed.

These are two tests that you have at hand and they are suited to test the null hypotheses of "no difference in mean" and "no difference in signed rank sum". So as you want to apply a test with null hypothesis "no difference", that is the way to formulate your null hypothesis.

It has nothing to do with, whether something is generally accepted to be one way or the other. It needs to fit the tests you can or want to perform.

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  • $\begingroup$ Thank you Bernhard. Is it possible to express my null hypothesis in Ho notation and if so could you show me how? Thanks! $\endgroup$
    – itsols
    Commented Sep 27, 2016 at 16:13
  • $\begingroup$ What do you mean by $H_0$-notation? $\endgroup$
    – Bernhard
    Commented Sep 28, 2016 at 11:53
  • $\begingroup$ I meant as symbols. $\endgroup$
    – itsols
    Commented Sep 28, 2016 at 12:01
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    $\begingroup$ Do you mean something like $H_0: \overline{with lid} = \overline{without lid}$? That's easy for a t-test but I could not tell you, whether there is a symbol for the signed rank sum in Wilcoxon's test. Or maybe I don't understand the question. $\endgroup$
    – Bernhard
    Commented Sep 28, 2016 at 12:54
  • $\begingroup$ Yes, that's what I meant. Thanks! I wasn't sure how you'll express this. $\endgroup$
    – itsols
    Commented Sep 28, 2016 at 15:12

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