# Likert scale categories and composite scores

I have used the following Likert scale for a series of questions in a survey:

• $0=$ Not Important
• $1=$ Slightly Important
• $2=$ Moderately Important
• $3=$ Very Important
• $4=$ Extremely Important

As I understand it, this is a 5-point Likert scale. (Unsure, though!)

I have then used a weighting formula that has resulted in final (composite) scores as follows: $0.2, 1.4, 2.3, 3.4, 4.6$, etc.

Example: If a person has indicated "moderately important" to three questions, it is $2+2+2=6$. I have then multiplied $6$ by a constant, e.g. $6\times.33=1.98$. The constant is derived from theory and represents percentage contribution of a variable.

Questions:

1. How do I represent the composite scores on the above Likert scale (i.e. what does a score of $1.98$ mean?)
2. Is it possible for composite scores to be greater than the last category, e.g. if a person has chosen "extremely important" for four questions, is it $(4 + 4 + 4 + 4 = 16)\times.33=5.28$?
3. When we talk about a 5-point Likert scale, do we mean the distance between the response categories (e.g. between $0$ and $1$ or $1$ and $2$ on the above scale), or just the category numbers (e.g. $0, 1, 2, 3, 4$)?
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Where does the weighting scheme comes from? –  chl Dec 31 '11 at 23:57
It's not clear at all how you're calculating this score. The only example you've given is when you observe (2,2,2). How would you summarize (0,2,3)? How about (1,4,3)? It seems to be some kind of weighted product (which is unusual). If that's the case, the labeling of levels becomes crucial - If you label 0-4 (as above), anyone saying 'Not Important' will make the composite score 0 whereas something completely different happens if you label 1-5. Composite scores which depend heavily on the labeling system are usually undesirable. A weighted sum might make more sense. –  Macro Jan 1 '12 at 4:43
Thanks. I would do the following with your example: add them and multiple by the constant. e.g. (0 + 2 + 3) X .33 = 1.65. Yes, this is a weighted product: the first level is the aggregation (I have edited the question above) and the second is the multiplication by the constant). Isn't 0-4 and 1-5 the same five point Likert scale (i.e. where 0 in the first is equal to 1 in the second scale) –  Adhesh Josh Jan 1 '12 at 6:09
You described a scale that is a weighted average where all of the weights are $1/3$ (not a weighted product). In that case, yes, 0-4 and 1-5 are effectively the same. The weighted average only has to be $\leq$ to highest level observed if the sum of the weights is $\leq 1$. In your first example in the question, the sum of the weights is 1, but in the second example, the sum of the weights is $4/3$. –  Macro Jan 1 '12 at 7:17
If you want the multiplier to represent percentage contribution, then your example with $(4+4+4+4) \cdot 1/3$ doesn't make sense because each of the 4 variables contribute $33\%$, making the total contribution $132\%$, explaining why that example leads to a number greater than 4. This is the problem with your weighting scheme. –  Macro Jan 1 '12 at 9:25

Regarding your question about the composite score being greater than the last category, I think it is important to differentiate between the outcome space of your items (in this case 0 to 4) and your "scale".

In the case of your example, the procedure for aggregating the scores is producing a 'scale' that goes from 0 (when a person answers the four questions as 0,0,0,0) and 5.28 (when the answers to the questions are 4,4,4,4). [Note: I noticed that your questions indicates that you are aggregating answers across persons. I am not sure about the context of your analysis, but usually Likert scales are aggregated within subjects.]

In sum, the outcomes in the questions need not coincide with the scale that is created by aggregating them, however, this might make the interpretation of the aggregated scale more difficult. As a final note, it is worth considering that you are assuming that there is an equal spacing between the response categories, not a trivial assumption, and the aggregation method that you are using assumes this interval scale in the response categories.

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Thank you for the thoughtful reply, David. Welcome to our site! –  whuber Jan 2 '12 at 15:46
Thanks for pointing out that Likert scales are usually aggregated within subjects. This is the case for me too. I have edited the question above. –  Adhesh Josh Jan 2 '12 at 23:46