Formula based on number of responses

**sleah** · 05-18-2005, 03:52 PM

Here is my problem:

I need a formula to calculate a score based on the number of reponses and score given for various features.

Total number of participants = 6
Total number of features = 15
Each participant rates ONLY 5 of the features, adding up to a score of 10 (Some features may not be rated at all).

My first thought (WRONG) was just to divide the sum of the scores by the number of respondents. Looked good at first, however, that was deceiving. Ex: if only 1 person rated feature A and gave it a score of 3, then the answer is 3. If 2 people rated feature B and each gave and score of 3 , then the answer would also be 3 (sum/repondents). Since 2 people rated feature B, it should clearly show more importance than feature A.

Any hints as to what the correct formula for this should be? Please.

**MrShorty** · 05-18-2005, 04:01 PM

Not a lot of detail, but my first thought would be to simply some the responses. So feature A would score a 3 and feature B scores 6. If feature C scored 1 by 5 people, it would score 5, placing it between A and B in importance.

Would that work?

**sleah** · 05-18-2005, 04:24 PM

Thank you for the suggestion, however that won't work. I guess I did leave some information out.

The final number has to also be on a scale of 1-10 and will be charted. If no responses, won't be charted.

**MrShorty** · 05-18-2005, 06:20 PM

Ok.

You don't give much detail on the survey's "rules." For example, does each respondent have to rate 5 features, or can they rate up to 5? In other words, could I select feature A, give it a score of 10, meaning that A is the only feature I deem important and leave zeroes in the other 14 features? Or would I have to give A a score of 6 and put 1's in four other features of secondary importance?

In the final analysis, what do you want a score of 10 to mean??

Basically, what I would propose next, if this will work. Figure out the theoretical maximum a given feature could "score" (as a sum of the total like I proposed above). 6*6=36? 6*10=60? or whatever you figure it is. Divide the "sumscore" proposed above by this theoretical maximum and multiply by 10. Essentially, I'm just taking the sum I previously proposed and normalizing it to a scale from 1 to 10.

Under this scenario, it isn't likely that any feature will score 10, but each feature's score will be between 0 and 10, and will indicate a relative ranking between the features. A score of 10 would mean that that feature is the only feature of any importance (or of any significant importance).

Is that going to work for you?

On Edit: Here's another possibility. Instead of referencing to the theoretical maximum score, reference to the feature that gets the highest "sumscore." In this case, divide a features sumscore by the maximum sumscore obtained for any feature and multiply by ten. Under this scenario, the highest scoring feature will yield 10, and the others will be less than 10.

**sleah** · 05-19-2005, 09:33 AM

Thank you for your help. The survey rules are that up to 5 can be scored but all 5 do not have to be.

I slept on it and hopefully came up with a solution. At this time, it seems to work out. I am taking the SUM of each feature and dividing it by the total less repondants SUM/(Total-Respondents). For those cases where the sum is the same, but the number of repondants is different, it gives a higher weight to those features with more responses, which just seems logical.

If anyone sees anything wrong with this logic, please let me know.

Thank you.

Formula based on number of responses

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