Measuring originality of a person on a sentence completion task I conducted an experiment where I had 20 people complete 100 sentences with only one word. They had to come up with their completion independently of others and could give any answer they thought was suitable. 

Here's a sample question with responses from 20 people: 

Yesterday I bought a: 


House
(No answer)
Sandwich
Car
Ticket
Sandwich


...


Car
Sandwich


I now need to measure, how creative every participant was, meaning I want to rate each participant on a certain scale from completely uncreative to absolutely creative (let's say 0 is uncreative, sticks to popular answers and 100 is highly creative with unique answers to every question). 

Please help me find suitable formula for rating each participant's originality of responses. 

Crucially important: some sentences were left unanswered by some people, meaning total number of answers for a question was smaller. 

Thank you.
First, I am a bit worried about your comment:


  (a) They are told to finish a sentence differently of others.


Are they given any other instructions? Do the answers have to "make sense" somehow? What's to stop someone from answering "yesterday I bought a stomach" for instance? That would certainly be unique. You do say they had to have answers they thought were "suitable" but, still, that's a huge range! Maybe not "stomach" but what about "heart lung machine"?

Second, I think you have to precisely define what you mean by "creative". You say (also in a comment) that "least used words mean higher creativity" but I am not so sure that I agree.

But, if you want the least used word and you want to account for the "no answers" then one way is:


All no answers get a 0 score on creativity.
Call the number of answers (excluding those with no answers) $N$
For each answer, call the number of people who gave that answer $Q_i$ where i ranges from 1 to the number of different answers. 
The creativity score of each answer is $N/Q_i$


The key is step 4. There are certainly other formulas you could use. Which one to choose depends on what you want the distribution of creativity to look like and whether you thing "only person with this answer" is twice as creative as "one of two people with this answer".

But, again, I'd hesitate to call this creativity.