The KAM uses variables that are measured in different units and on different scales. To calculate aggregate knowledge economy indexes, as well as to simplify graphic representation of countries’ comparative performance, we bring all the indicators to the same standard of measurement through the process known as normalization.
First, countries are ranked in order from “best” to “worst” using their actual scores on each variable. Then, their scores are normalized on a scale of 0 to 10 against all countries in the comparison group. (see the formula below) 10 is the top score for the top performers and 0 the worst for the laggards. The top 10% of performers gets a normalized score between 9 and 10, the second best 10% gets allocated normalized scores between 8 and 9 and so on. In other words, the 0-10 scale ranks the performance of each country on each variable relative to the performance of the other countries in the sample.
The default comparison group is “all countries” (146). The country can also be compared to others in the relevant region or income category. In this case, the data will be ranked and normalized only against the selected comparison group. A country will get different normalized scores depending on what group it is compared against.
The ability to use both the actual and the relative (normalized) results together gives more insight into what is happening in a particular country or variable. For example, a chart may show that a country’s relative position has worsened between 1995 and 2000, or between 2000 and the most recent period, or 1995 and the most recent period. This means that either country’s absolute performance on the relevant indicator has actually deteriorated or the absolute performance has improved but not by as much as in the comparator countries. These are two quite different situations and it is very important to know which is happening.
It merits attention that an economy should not necessarily aim for a perfect score of 10 on all variables and be on the outer edges of the scorecard. Some variables reflect performance; others reflect trade-offs which characterize different development strategies; still others reflect the particular structural characteristics of an economy.
The normalization procedure used in the KAM is as follows:
1. The actual data (u) is collected from World Bank datasets and international literature for all the variables and countries.
2. Ranks are allocated to countries based on the absolute values (actual data) that describe each and every one of 148 variables (rank u). Countries with the same performance are allocated the same rank. Therefore, the rank equals 1 for a country that performs the best among the countries in our sample on a particular variable (that is, it has the highest score), the rank equals to 2 for a country that performs second best, and so on.
3. The number of countries with higher rank (Nh) is calculated for each country.
4. The following formula is used in order to normalize the scores for every country on every variable according to their ranking and in relation to the total number of countries in the sample (Nc) with available data :
Normalized (u) = 10*(1-Nh/Nc)
5. The above formula allocates a normalized score from 0 to 10 for each country.