I'm writing a software algorithm at the moment which compares survey answers. Questions have 5 possible answers, and a respondent could choose between 1 and 5 answers. What I'd like to do, for each respondent, for each question, is calculate how strongly they feel about their answer. I propose to do this by counting the number of answers they selected. For example, suppose the question was: Which of these colours do you like? And the possible answers were: a) Blue b) Red c) Green d) Orange e) Purple Then someone who answers only b), feels more strongly about their answer than someone who selected all 5. What I'm having trouble with, is how to account for the different numbers of possible answers. If a question has a yes or no answer, and the respondent only chooses one answer, we want to

Jairo Decker

Jairo Decker

Answered question

2022-10-29

I'm writing a software algorithm at the moment which compares survey answers.
Questions have 5 possible answers, and a respondent could choose between 1 and 5 answers.
What I'd like to do, for each respondent, for each question, is calculate how strongly they feel about their answer.
I propose to do this by counting the number of answers they selected.
For example, suppose the question was:
Which of these colours do you like?
And the possible answers were:
a) Blue b) Red c) Green d) Orange e) Purple
Then someone who answers only b), feels more strongly about their answer than someone who selected all 5.
What I'm having trouble with, is how to account for the different numbers of possible answers. If a question has a yes or no answer, and the respondent only chooses one answer, we want to consider this as being less significant than if they only choose one answer on a question with more possible options.
So the more options to choose from, the higher the importance of each answer selected.
So far, I've come up with this:
i = max ( g n max )
Where:
i (importance)
max (maximum importance %) =100
p (possible answers)
g (given answers)
Can anybody suggest how I could approach this problem differently or improve the formula?

Answer & Explanation

silenthunter440

silenthunter440

Beginner2022-10-30Added 19 answers

You could try using a weighting system based on the user's choices.
The weights would be from high to low and give you a scaling factor to account for the significance of their choice.
For example:
w n = 6 n (where n = number of color choices, that is 1 to 5)
So, if a user choose a single color, she would get a weight, w=5, since she had a very strong preference for a single color. However, she would get a weight of, w=4 if she had a preference for two and only a weight, w=1 if she chose them all. Of course, a weight of zero if she did not answer is assumed.
Use this to generate a score for each user. However, you may also want your stats to come out a certain way and to be inclusive of trends and predilections and bias to the choice of colors given.
This could be used with some nonlinear characteristics and weighting function to determine appropriate weight values based on user choices.

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