It’s been a while since I’ve done any statistics. The material I've read online and in books seem to be conflicting - so I would love a sense check to ensure that I am using the appropriate method for the results I have collected and the question I am trying to answer.
I have recently conducted a questionnaire with likert-type items (available for reference here). I asked participants to rate from 1 to 5 the usefulness of different datasets they may use. I presented them with 16 different datasets to consider. Of the 189 responses, 123 were fully completed. I also ask them what sector they work in.
The question I want to answer is: Are there distinctive groups of people who find similar datasets useful?
I’ve therefore decided to run a simple k-means clustering to try and identify these groups. However, I’ve found it difficult to define a cluster number using the elbow method as well as the silhouette method. Using the elbow method, there is not a distinct "break". Likewise, for the silhouette coefficient, as we increase the number of clusters, the mean silhouette coefficient just hovers around 0.24 to 0.27.
I’ve also tried to run a factor analysis using Principal Axis Factoring and orthogonal Varimax rotation following the Yong & Pearce 2013 tutorial. This gave me three “factors” which the datasets could load to. Despite being interesting, I don’t think it helps to answer my question of finding the groups of people who find similar datasets useful.
Have I misused statistics? If you were to approach the results of my questionnaire from fresh, how would you analyse it? I apologise for any statistics naivety and thank you in advance for any advice.