What are the best ways to support your reasoning with evidence?

Yes, I agree with this point. Supporting your reasoning with convincing evidence requires you to resonate on the same level with your audience. The starting point is for you to be understood. So, you need to understand their perspectives and be up to date on the subject matter. When you know your audience, you communicate your reasoning with terminologies seamlessly that they can easily relate with. That way, your evidence is understood even when the audience disagree.

First, think why are you reasoning with the audience anyway ? To convince them ? To rile them up ? ... Pure logic does not work with humans. Connecting real-life examples with your argument helps the audience relate to your message. If you can't find good evidence/examples, and it is an interactive discussion, ask the listener what can they share that would justify your point. You may be surprised at their willingness to help you make a point to them ! Good luck.

I agree to the fact that you need to evaluate the evidence that needs to be used based on the persona. Emotion will work on certain audiences but using hard facts and firm evidences are ways to convincely portray your thoughts. Personal stories will work in some industries such as Healthcare and Hospitality but other industries will be trickier such as Finance or Retail

In case anyone didn't know, this is what any experienced speaker does every time. Knowing your audience and crafting your content to be group appropriate and engaging is THE foundation for future benefit.

When preparing to present material which draws directly from a study or some other work, at a bare minimum, you must understand how this source exists in the family of similar sources: you must understand the context of its existence in the greater body of knowledge. Equally important, you must rigorously examine what you want it to say to your audience. What is your stake in this? Why and how are you presenting this information?

One thing I have found helpful when presenting evidence for acceptance is to clearly spell out the significance and the limitations of your evidence. This allows you open to a third opinion on a matter, gives new insights and opportunities for more collaborations.

Evidence is of course important, but evidence is to a good argument as paint in a tube is to a beautiful oil painting. The evidence must be used to support or refute claims and, often, arguments are deficient because the premises or co-premises connecting the claims to the evidence are left unstated. I believe this happens because many premises or co-premises are taken for granted by the reasoner forwarding an argument. The reasoner may have a meta-cognitive blind spot being unaware of the implicit knowledge (or assumptions) he or she takes for granted, but which may be unavailable to the receivers of the argument. Accordingly, the reasoning may make much less sense to the receiver than to the sender.

Try and recognize your transparent emotions, they are your bias. Imagine scenarios playing out in a variety of ways and those transparent feelings will weigh in. Just as quickly they will dissolve in to the periphery and continue framing your lens in to new experiences. It is time well spent to purposefully coax them out and become familiar.