# Likert scale and yes/no calculation of one score

My survey is based on observations and interviews. The observation questions are yes/no type questions and interview questions are 4 points.

$1=$ never, $2=$ sometimes, $3=$ usually, and $4=$ always.
Yes $=1$, No $=0$.

If I add up all these with highest possible score and divide it by the total score received, I can then retrieve a total score for the survey.

For example, let's say I have 5 responses for the Likert and 5 for the yes/no. $5\times4$ $=20$ (with 4 being the highest possible score you can get on the Likert scale) and $5\times1$ $=5$ $(1$ being the highest possible score for yes/no question). I then add up both to find the highest possible score $=25$. If I get a combined score of $20$, do I divide it by the possible score, $20\div25=80$%? Can I build my questionnaire and calculations like this?

My main objective is to get one percentage / score for the entire questionnaire. I thought of accomplishing this in 2 ways:

1. Get the sum of earned score from both scales divided by total possible scores for both scales.
2. Get a percentage by using the above calculation for individual scales, which will give me two sets of percentages, and then take an average for those percentages.

I am not sure which way I should go with, or if this even makes sense doing it this way.

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Are all of the items (likert or yes/no) intended to measure the same underlying construct? Have you checked anything to determine if they do? – gung Dec 7 '12 at 19:21
All likert and yes/no questions are targeting the same dimension/composite. The address a specific area within the organization. For example, communication to clients have both yes/no and 4 point scale. – Newb Dec 7 '12 at 23:57

As long as you consider the weight of the response, e.g is each response to the question worth the same.

Example: Question 1 - No (0/1) Question 2 - 3 (3/5) Question 3 - 3 (3/5)

Total score=6/11 or ~ 54%
If they were weighted equally it would be (0+3/5+3/5)/3 = 0.4 or 40%

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The weight of the response is not equal because yes/no has a total weight of 1 and the likert scale is weighted with a highest possible score of 3. According to your last equation, I am dividing the total from the amount of responses? (0/1+2/3+2/3+1/3)/4 = 41.67% – user17616 Dec 8 '12 at 23:31
@Newb You appear to have two unregistered accounts. Could you confirm that the one you used to leave this comment is the same as the OP? A moderator can merge your accounts, but you'll need to register once and for all. – chl Dec 9 '12 at 10:11

The simple, "classical test theory" approach that weighs every item equally would probably have you just standardize all the items and average the $z$-scores, but I don't think that's a good idea, because four-point Likert scales may not approximate a continuous dimension well enough (and a binary item definitely won't; it might not even make sense), though the average of 12 polytomous items might be approximately continuous enough. I've seen it suggested that each item's Likert scale should have at least five items to approximate a continuous distribution, and at least five Likert scale items should measure the same scale if their simple sum / average is to approximate a continuous dimension. (Can't remember where, but I can look it up and edit it in if you want a source but can't find one yourself; just comment!)