Salomée Ruel, my hunch is that your options are at the ordinal level of measurement. However, the general view is that you can regard your data from a combination of a number of items (probably 3 or more items) as being at the interval level of measurement.

The bigger issue is probably what kind of statistics can be used with your data. Some/most people argue that only nonparametric statistics can be used with responses on individual items (I am personally not as "conservative" as that because, for example, I think that comparing the means and SDs on individual items can sometimes provide useful insights) and that parametric statistics can be used with composite scores as long as those composite scores have at least 3 items.

All the best with your research.

Dear Dr. Salomée Ruel , as per my limited understanding, the type of scale and data depend on the way you "defined" "company's digital tools adoption" in your study. If you measured the Perception of the employees regarding a company's adoption of digital tools (by providing some examples of the tools for clarification), then it is clearly Interval Scale and can be treated as continuous data type.

Actually the way you asked your respondents itself shows that you are measuring the perception of employees regarding the so-called "Perceived Digital Tools Adoption" in a company. However, the purpose and Nomological position of this variable in your study might be more important in deciding which statistical test should be applied. Regards.

Hello Robert. So one of my Idea would be to test the company size influence (respondents being seperated intro 3 groups) over the adoption level for each of the tools individually. Have you got any advice for a test to apply? Thank you so much Salomée

Salomée Ruel, I'm sorry, but I don't know enough about your research to provide a confident answer for you. To begin with, did you ask only one question about the level of adoption of digital tools, or did you have a number of items, about each of which you asked your participants to provide a response ranging from not started to advanced?

Hi again Robert. Thank you for your suprt. Very simple. For each digital tool individually, we asked respondents about the adoption level of this tool.

So for instance :

Big data from not started to avanced based on the définition of the 5 levels. There are not several items to measure the adoption level.

Idem with all the other tools.

Thank you

Salomée

Hello Salomée,

Sorry, your explanation isn't clear to me. I still can't get a good picture of what you asked. Might you be able to show me your survey.? You could do that on a private RG message if you didn't want to make it public.

Feel free to ask me how to do that (send a private RG message) if you want to do it but don't know how.

Your items could make up an ordinal scale because you are trying to measure participants’ competence/ability in “digital tools adoption,” with an implication of categorizing and ranking your data in order, and no established fixed interval between the rankings. Besides, the level of educational attainment (e.g., beginner-advanced) is a common example of the ordinal scale.

For further reading, you may check out the following.

Finch, W. H., & French, B. F. (2018). Educational and psychological measurement. Routledge.

https://books.google.com/books/about/Educational_and_Psychological_Measuremen.html?id=FUjpDwAAQBAJ&source=kp_book_description

Good luck,

Thank to all of you.

So my understanding till here is that I was right running a kruskall Wallis Test in order to know if there is any difference of adoption level for each digital tools between 3 groups (groups based on company size).

Robert has suggested that I run some bonferroni correction also. So, i Guess what I should do now is, for each kruskall Wallis Test significant, run some Mann Whitney U tests with bonferroni correction in order to check where différences really are : G1 vs G2, G1 vs G3 and G2 vs G3.

If anyone could confirm this to me, it would be great!

I am grateful for your kind support

Salomée

The Kruskal-Wallis test evaluates the differences between three/more independent/separate groups. The Mann‑Whitney test measures the difference between two independent/separate groups.

You might find the attached helpful.

Good luck,

Salomée Ruel, I'd really like someone with a solid background in stats to step in to provide advice. As you know, in our private communications, I recommended you factor analyse your data if that would be possible. It might not be possible, however, because I don't know how many participants you have, or how many items you had on your survey.

If you go ahead with the analyses you propose, my fears are that you could have Type 1 errors because you'll be doing so many individual analyses - and therefore there is the prospect of some findings being due to chance. Conversely, if you apply some kind of "correction" (e.g., of a Bonferroni type) for chance findings, as I recommended, you might end up with Type 2 errors because, with a lot of analyses, you will need to set a high hurdle in relation to attaining statistical significance. Therefore, some "real" differences might be missed.

It depends. What kind of research questions do you have? If, for example, it is about means, then that determines your so called level of measurement (see https://psycnet.apa.org/record/2005-07821-008). Whether this should matter for what statistical procedures you use is a different question. It is worth looking at https://www.jstor.org/stable/2684788.

It looks to me it will be maximally ordinal. And I do not think the categories are 'clearly defined'. The only one having an exact meaning is 'not started'. This will be an anchor. Could you set limits to the other categories? For instance, 'basic' could be between 0 and maximally 10% of adoption level or something similar? If the values can be changed, it is not clear and may completely depend on the one given the answer. If an novice would answer, he/she might think the company is 'advanced' as he/she might be impressed, but an expert, knowing what is out there, might also answer basic, but it means something different.

Hi Peter, a definition of each level is given in the survey. I haven't stated them here for the sake of brievety. Thank you again for confirming the scale is ordinal.

Salomée Ruel, please be aware that it's useful to be clear about the definitions of words. You have a number of ITEMS on each of which participants choose a RESPONSE OPTION, and the whole set of items (with their responses) might be regarded as comprising a SCALE.

Because I understand you intend to analyse your items one-by-one, you don't have a scale, and I think that your response options should be regarded as at the ordinal level of measurement.

I hope that's helpful.

This is very helpful Robert. After 10 years of conducting only qualitative research, I am lnow learning statistics so I do not master the vocabulary.

Also, I totally consider the Idea to run a factorial analysis among the 15 items (15 digital tools) to avoid the type I error you mentionned to me. I am trying to figure out why knowing the potential impact of firm size on a "group" of digital tools would be a greater contribution than for each of them one by one. I have 320 complete surveys so I guess this is enough.

I am extremely grateful for your support.

Salomée

Salomée Ruel, if you do want to try factor analysis, I'm happy to help you. Again, as happened between you and me earlier, if you don't want to make your concerns and analyses public, feel free to contact me privately through RG.

Robert

It is good that all of us have agreed that our lady's scale is ordinal. That's consensus.

Good luck, Salomée!

Dear Salomée Ruel,

I would like to add the possibility of Mokken analysis. Please see van der Ark (2007) for a dedicated and accessible software package in R (link below).

The advantage of mokken is that it provides tests whether responses given to a set of items can be treated as an ordinal scale.

In my experience mokken can add information over factor analyses. the latter can be complex and has no single/uniform approach (e.g., I am now thinking: what correlations to give to the factor analysis... Biserial, polychoric?). But many more technical issues need to be solved. Mokken is more straightforward to start with, I would say.

Good luck with your research!

https://www.jstatsoft.org/article/view/v020i11

Mohialdeen Alotumi, forgive me if I sound contentious, but I certainly haven't indicated that I think Salomée's scale is ordinal. I would argue that she doesn't really have a scale, but, rather, she has a collection of items. In my view, she has a set of response options for those items, and those response options are ordinal in nature..

Robert Trevethan, she stated in her question that they were following a 5-point scale. However, I believe all points of concern/suggestions raised by you and others are valid. When considered, they might be conducive to a better ordinal scale.

Best,

Besides, since their items seem ordinal in nature, their scale should be an ordinal one. Accordingly, they can opt for ordinal scale stats tests.

She can try out the following stats test tool.

http://methods.sagepub.com/which-stats-test

Best,

Dear all, I have spent a nice Sunday afternoon :)

So that you know:

After factorial analysis, the tools are divided into two dimensions. 1 tool is exluded. 1 dimension with 8 tools, the other with 6. There seem to be a way to explain those two dimensions so this is fine to me.

I have calculated cronbach alpha for those two SCALES, they are fine (respectively 0.868 and 0.861).

Then I have run the shapiro test which shows that data are not normal.

I have applied the Kruskall wallis tests on the two scales, both tests are significant.

Then, I have calculated the bonferonni correction in order to know what mann whitney tests will be signficant or no.

Then I have run all the mann whitney tests, so since I have 3 groups, I had 3 mann whitney tests to run for each SCALE of digital tools.

Now I know precisely, depending on the type of digital tools, between which groups of company size some differences are significant or not!

Thank you, this could not happen without you all!

Salomée

Salomée Ruel, thank you for the feedback - and congratulations. I'm really glad that you pursued my suggestion that you factor analyse your data.

Every good wish as you continue with your research.

Do you think your latent variables are dimensions, or do you think that they may be more assigning people to different groups?