In my first post on piano competition statistics, I made a few interesting observations relating countries to number of prizes won (per capita) in piano competitions:

- Of all Western European countries, Italy wins most prizes in piano competitions.
- Belgium scores substantially better than the Netherlands (my home country).
- Many top-scoring countries are Eastern European countries (top 7), and more specifically former Soviet states, excluding Russia itself.
- The top Eastern Asian country is South Korea.
- China ranks very low, so the large numbers of Chinese pianists may currently still be explained by China’s huge population.

These are observations *aggregated* across the years 2000 – 2015. But what about *trends* across 2000 – 2015? Are some countries up-and-coming, winning more and more prizes each year? Are other countries in decline? The above observations do not say anything about this. To gain more insight into trends, we need to look at the prizes won in each individual year, without aggregating across all years. As an example, have a look at the prizes won by American contestants across the years 2000 – 2015, visualized as a fraction of the total number of prizes awarded each year:

You can see that the general trend is that Americans are winning increasingly many prizes. This increasing trend can be summarized in a single number, the correlation coefficient, which we will denote by *r*. The correlation coefficient *r* can take on any value between -1 and 1, with

*r*= -1: meaning a clear trend of fewer prizes in recent years,*r*= 0: meaning no discernible trend,*r*= 1: meaning a clear trend of more prizes in recent years.

In the above plot, *r* = 0.62, indicating a pretty strong positive trend of winning more and more prizes. Moreover, this trend cannot be explained by random chance, as demonstrated by the significantly low p-value (p = 0.001. It can thus be considered a ‘real’ trend. (Technical note; thus feel free to skip: the figure uses the Mann-Kendall test for monotonic trend detection).

Now you are probably curious to see this number *r* for all individual countries, and not just for the United States, so that you can see which countries are up-and-coming, and which are on the decline. This is precisely what the barplot below shows: for each country, the trend in prize-winning between 2000 and 2015 is summarized in a single correlation coefficient *r*, and a bar is colored red if the trend is significant (p < 0.05), i.e. can be considered a ‘real’ trend.

How does the above plot compare to the five observations stated at the beginning of this post?

**Top Western European prize-winner Italy is on the decline.**The original observation was that, when*aggregating*across the years 2000 – 2015, Italy has won most prizes per capita. The above barplot additionally shows that, when looking at the*trend*across the years 2000 – 2015, Italians have however been winning fewer prizes in recent years (*r*< 0; p < 0.05).**Are the Netherlands overtaking Belgium?**The original observation was that, when*aggregating*across the years 2000 – 2015, Belgium has won more prizes per capita than the Netherlands. The above barplot additionally suggests that, when looking at the*trend*across the years 2000 – 2015, the Netherlands may however have been improving a bit throughout the years, although the improvement is not significant (*r*< 0; p > 0.05).**Top prize-winner Estonia is on the decline.**The original observation was that, when*aggregating*across the years 2000 – 2015, of any country Estonia has won most prizes (per capita). The above barplot additionally shows that, when looking at the*trend*across the years 2000 – 2015, Estonia is however on the decline and has been winning fewer prizes in recent years (*r*< 0; p < 0.05).**South Korea is the strongest up-and-coming country.**The original observation was that, when*aggregating*across the years 2000 – 2015, of any Eastern Asian country South Korea has won most prizes per capita. The above barplot additionally shows that, when looking at the*trend*across the years 2000 – 2015, South Korea can be identified as the strongest up-and-coming country, winning more and more prizes each year (*r*> 0; p < 0.05).**Beware of China with its huge population.**The original observation was that, when*aggregating*across the years 2000 – 2015, China ranked very low due its large population. The above barplot additionally makes clear that, when looking at the*trend*across the years 2000 – 2015, the Chinese are however winning more and more prizes (*r*> 0; p < 0.05).

Finally, a minor note of caution with respect to the interpretation of the above results: It may be that in some cases a small part of the increase in number of prizes can be explained by population growth, which was not taken into account. On a related note: Population size itself is not relevant in this analysis, as we are only looking at the increase (or decrease) in number of prizes, regardless of the population size.