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I have been working on my Master's Thesis which included a survey and its results have been put through various tests. The unusual thing about my Thesis is that I have no hypotheses at all, making it a descriptive statistical analysis. However, I have set up hypotheses just for the purpose of calculating p-values for measuring the significance threshold (at 1%, 5% and 10%). In the meantime, my Mentor reminded me of the lack of hypotheses emphasizing the fact that I should not have any.

My question is, can I use the information without using the hypotheses as they are, meaning does the information of the significance threshold have any value without the hypotheses and could I rephrase them so that they look like "claims" rather than hypotheses? I would hate for all this work and information to go to waste but if it's impossible to use it I cannot do much about it.

kjetil b halvorsen
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Mel
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    Maybe relevant: https://stats.stackexchange.com/questions/149917/do-descriptive-statistics-have-p-values, also https://www.tandfonline.com/doi/full/10.1080/00031305.2018.1543137 – kjetil b halvorsen Dec 06 '23 at 13:48
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    None of your work went to waste. All the other output can be used: Parameter estimates, standard errors, etc. are all still usable. – Peter Flom Dec 06 '23 at 13:50
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    You can turn the p-value calculations into a confidence interval.https://en.wikipedia.org/wiki/Confidence_interval – seanv507 Dec 06 '23 at 14:14
  • This confidence interval seems intriguing, might check that out! Thanks all! – Mel Dec 06 '23 at 14:35
  • But why oughtn't you to have any hypotheses? If, for example, as is hinted at by your use of 'descriptive', inference on population parameters is being ruled out for some reason, you oughtn't to have any point or interval estimates either. – Scortchi - Reinstate Monica Dec 07 '23 at 02:23
  • I used to have them at first, but at my University you have to write an application of sorts, which is basically a rough skeleton of what your topic is about, that has to get a green light from a panel/board of Professors, who insisted I deleted my hypotheses in order for this draft to get accepted. – Mel Dec 07 '23 at 08:58
  • you oughtn't to have any point or interval estimates either. - very much true, but I'm trying to sneak in some hahah – Mel Dec 07 '23 at 09:02
  • In every framework, p-values are defined as a probability conditional on a hypothesis being true (that's common across Neyman-Pearson, Fisher and NHST). So the answer has to be no. – Firebug Dec 07 '23 at 15:38
  • I wasn't asking about the history of the proscription, but about the grounds for it. – Scortchi - Reinstate Monica Dec 07 '23 at 17:48

2 Answers2

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You can't even calculate p values without a null hypothesis, because this is a crucial ingredient that goes into all tests, along with data and a model specification.

For instance, for a t test for a regression coefficient, you typically test against the null hypothesis that $b=0$, and this is frequently not spelled out. But you can certainly test against other null hypotheses.

So the question really is whether these "default" hypotheses make sense in your case. This is something you could discuss with your advisor. Very often, we know that this kind of null hypothesis is trivially or at least very highly likely wrong before even looking at the data.

Stephan Kolassa
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    We were typing simultaneously. I'm glad our answers agree! – Peter Flom Dec 06 '23 at 13:43
  • I will probably delete the whole test since it's not applicable in my case. Do you have any suggestions on what other tests I could use (apart from normality and Cronbach's alpha since I already did them) that are typical for a descriptive statistical analysis? – Mel Dec 06 '23 at 14:42
  • Thank you for answering! – Mel Dec 06 '23 at 14:42
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    @PeterFlom: great minds type alike. – Stephan Kolassa Dec 06 '23 at 15:19
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    @Mel: if you are mainly interested in descriptive and exploratory analyses, then there are lots of descriptive statistics you could report, from the mean and the SD to ranges. However, I would always try to visualize as much as possible - a violin or beanplot of your raw data is much more informative than the mean and the SD. There are many possible visualizations. Which one is best depends on your situation, your data and what is interesting about both. Good luck! – Stephan Kolassa Dec 06 '23 at 15:21
  • Thanks, will do so! – Mel Dec 06 '23 at 15:34
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Why do you even want a p value when you don't have a hypothesis?

But, in short, the answer is "no". I mean, you can't stop the computer from outputting a p value, but, every p value has an inherent null hypothesis, usually that something isn't happening (e.g. that $\beta = 0$ or that $\mu = 0$ or that the OR is 1).

P values answer this question:

If, in the population from which my sample was randomly drawn, the null was true, what is the chance of getting a test statistic at least as extreme as the one I got, in a sample the size of the one I have?

This is not nearly as useful a question as many people think, but without a null, it's really pretty meaningless.

iff_or
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Peter Flom
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    To be honest, I didn't think it would be a problem to have a hypothesis if it was only in my empirical research, but it is, so now I will most probably delete it after consulting with my Mentor. Thank you for answering! – Mel Dec 06 '23 at 14:44
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    Feel free to accept one of the answers here if you felt it answered your query (by hitting the checkmark next to the answer) @Mel – Shawn Hemelstrand Dec 07 '23 at 08:12