Solved – How to Normalise data on a Likert scale 1-7

likertnormalization

I'm looking to create environmental and social sustainability values for countries, similar to what is carried out here.

http://reports.weforum.org/global-competitiveness-report-2014-2015/appendix-a/#view/fn-a

In the first step, the individual indicators in each area are normalized on a 1-to-7 scale and aggregated by averaging the normalized scores, such that a social sustainability score and an environmental sustainability score are calculated for each country.

In the second step, these scores are normalized again on a 0.8-to-1.2 scale,a which is based on the distribution of each of the two sustainability components. The purpose of this methodology is to reward the countries attaining a relatively good performance on the two sustainability components while penalizing those that register a poor performance. Applying this methodology corresponds to transforming actual averages into coefficients ranging from 0.8 to 1.2. For example, the worst performer on the social sustainability pillar obtains a score of 0.8 and the best performer a 1.2. The same calculation is conducted for the environmental sustainability pillar.

$$X_{i,\text{0 to 1}} = \frac{X_i-X_\min}{X_\max-X_\min}$$

I believe the above represents the formula to normalise data? Let us just take for example the following.

Income inequality amongst a sample of countries in 2012 ranged from a min of 20.5 to 88.2. In France the GINI score was 40.6.

Therefore normalising this data would produce a score for France of 0.2968. However, how would I then transform this into a 1-7 Likert scale, with 1 being the best and 7 the worst?

Best Answer

$$ 7-6 * \frac{X_i-X_{min}}{X_{max}-X_{min}} $$

normalizes to a continuous 1-7 scale, mapping $X_{min}$ to 7 and $X_{max}$ to 1.

Some problems creep in at this point ...

  1. Likert scales are usually used to capture respondent input, not as a way to present computational results. Why do you want to convert from a continuous scale to a discrete ("Likert") scale?
  2. The procedure described in the linked article - normalize individual items to a fixed finite scale, then aggregate - creates interpretational problems. For example, the order of the aggregated results can be different based on the total number of cases. That's like saying that the order of the first three finishers in a race can depend on who comes in last. Sometimes that's exactly the behavior you want, but many times it isn't.
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