# Visualization of an Order Verified by Wilcoxon

The background: After I've conducted a survey about preferences of users in ridesharing, I now want to construct an order of importance of these preferences (this is to answer one of my research questions). For instance price might be more important than comfort of the vehicle might be more important than the played music. I collected the data based on a five-point likert-scale.

My procedure so far:

1. Of course clearing the data
2. Generate an order via a simple approach: very important gets $$4$$, important gets $$3$$ and so on. Then I build a sum over all answers and I sort the preferences based on their sums.

The second step provides me with an order, which is not statistically verified. Therefore,

1. I perform a one-sided Wilcoxon signed-rank test for each pair of preferences.

The resulting p-values are in the following matrix:

The visualization can be read as follows: preference a is statistically proven to be not less important than preference d to j for all common significance levels. (The order of preferences comes from the second step.)

The problem is, I've collected $$42$$ preferences and the corresponding visualization has the following problems:

• $$42$$ is quite a lot and the visualization gets confusing.
• Moreover, to understand what is shown in the graphic a lot of brain work is needed, especially for an unexperienced user.

Do you have an idea how to visualize the result better?

I do not have a good way to answer your question since I do not know who your audience is, what actions/understandings are you trying to drive from your analysis, etc.

I think that is where you need to start. If your audience is executives in charge of revenue, perhaps showing the difference in revenue where the top n preferences are in a car vs n-1, n-2, .... Or frequency of the top preferences.

Given the audience and the action/understanding you may not need to show all 42 preferences in the mainline of your presentation.

You can also look for inspiration on your audience/action from traditional statistical methods for this type of analysis. Namely conjoint part of choice modeling. Take a look at some of those public analysis or classes and maybe an idea will take hold that is similar to your audience/action.

This is more of a path forward rather than an answer but I do not see the question as answerable right now.

• I'm doing research, so in the audience are mostly other researchers. By the way: I did not use a conjoint analysis in the first place because there are also other research objectives. Because I cannot simply conduct a second survey with a feasible number of participants, I have to use my current data.
– So S
Sep 17 '19 at 20:09