Decisions are all about emotion, however, numbers are so very important. At the end of the day if the bank balance is zero, no amount of emotion is going to change that. 
When it comes to numbers and decision making there are essentially three positions people take. 

Believers 

These people believe numbers enhance decisions. In fact, decisions should be based on the numbers. The effort must be put in to find and assess the numbers. 
The problem for these people is that if they can’t find any numbers they can become indecisive or even distressed about the decision. And if they can’t find them, they may not believe anyone else can come up with reliable data. 

In this case apply the mantra – everything can be measured. Then go about showing them how this can be done. Remember, if it is observable it is measurable. 

Swingers 

These are the people that like the numbers when it suits them and not so when they don’t. They will jump on the bandwagon of the source of the affirming data and criticise the data that contradicts. 

The problem is identifying when they are letting their personal biases interfere with their decision making. 

In this case comparisons work well. Comparing the sources of data, how the data has been collected and analysed and comparing who is behind the data and the analysis. 

Non-Believers 

These are the gut feel decision makers. The ones that follow the mantra that there are three types of lies: “Lies, damned lies and statistics”. They simply don’t believe what comes from a “black box”. 

The problem here is that no amount of logic is going to change their mind. 

You have to appeal to their emotion. The best methodology for creating an emotional response that you are seeking is to tell a story. It does not have to be a personal one, it can be about any person or event that you believe will strike a chord with them and shift their mindset.