# How understandable is this statistical hypothesis?

I am trying to get a statistical hypothesis translated to English as part of a paper to be submitted for peer review and am not sure whether what I came up with is the correct translation.

"It is assumed that there is no statistically significant difference in the measures of the variables within the XYZ dimension" Does this make sense?

I have asked around some people who are at home in statistics but none of them are native speakers. Basically, the thing is I am not 100% sure if "measures of the variables" is a valid term or if it is redundant whatnot.

To provide you with some more insight, here is a translated section on how the analysis of this particular hypothesis was conducted: For the analysis to answer the research sub-questions, frequency analysis was conducted by assessing the number and percentage distribution of respondents' answers. The data were then subjected to a detailed analysis of the normality of the data distribution by the Shapiro-Wilk normality test, which revealed that the data were not normally distributed according to a Gaussian curve. This result was expected, given the relatively small number of respondents and the wide range of ordinal responses.

• It is not possible to say if this a correct translation without comparing it to the original text. It may be well a correct translation of an incorrect statement. If it's the case, there will be an issue if you use the answer of Christian Hennig (+1) to correct the translation but not the original version, in particular if the two are meant to be published. Apr 24 at 16:12

The term "statistically significant" is used wrongly here. Significance can be a result of a statistical hypothesis test, but it cannot be part of the hypothesis itself.

If you say "no difference in the measures", it can be read as meaning that measurements should be identical, which chances are isn't what you want to express.

Also if you say "differences" I want to know between what and what (two terms are needed to define a difference, not just one). If it's about Shapiro-Wilk, chances are you just want to say that the null hypothesis is that the variable is normally distributed.

Edit: After comments it seems this is about Friedman's test. The Friedman null hypothesis says that the distributions of the different variables are the same.

• I'd go a step further and never use the word "significant" in a scientific paper. It often leads to confused thinking among statistical novices. Whatever you are trying to say, you can say it more clearly without that word Apr 24 at 16:08
• Thank you for the comments. Didn't really expect the hypothesis to be incorrect in that sense (and the unfortunate part is this was already peer reviewed). Yes, the null hypothesis was formulated as follows: "It is assumed that there is no statistically significant difference in the measures of the variables within the XYZ dimension". Friedman test was used to answer the hypothesis (p>0.05), so given that, does "difference in the measures" formulation make sense? I.e. "It is assumed that there is difference in the measures of the variables within the XYZ dimension" Apr 24 at 16:23
• Forgot to add: each dimension here consists of 4-5 categories which have 7-8 levels Apr 24 at 16:34
• If you say "difference" you've got to say between what. The Friedman null hypothesis says that the distributions of the different variables are the same. Apr 25 at 0:44
• Circling back: after some more looking, the best match trying to convey the original meaning while keeping it as true to the comments here as possible seems to be "There is no difference in the measures of the variables included within the XYZ dimension". I understand it would be better to list all the variables here but given what I found in the literature this seems to be something one can live with. I am really trying to kind of "reverse-engineer" the process here, given the original hypothesis weren't formulated correctly to begin with. Not really how it should be done, but it is smth Apr 26 at 18:12