In this post, I will investigate whether a county's team score in IMO is dependent (or independent) on translating IMO contest questions into one's native language.
The null hypothesis is:
Ho: Team Points in Math Olympiad is independent of Language (With Translation to Native Language) of Contest Question
The alternative hypothesis is:
H1: Team Points in Math Olympiad is NOT independent of Language (With Translation to Native Language) of Contest Question
The following tables are derived from IMO 2007 data:
Table 1. Observed frequencies by Team Points Interval by IMO Questions with/without translation to Native Language: IMO 2007
Table 2. Expected frequencies by Team Points Interval by IMO Questions with/without translation to Native Language: IMO 2007
Computing the test statistic yields the following:
Table 3. Results of Chi-Square computation: IMO 2007
Since the Computed Chi-square statistic (16.94) is greater than the Tabular Chi-square value at α = 0.05 (9.448) and α = 0.01 (13.277), we reject the null hypothesis.
We conclude that the each country's score at the Math Olympiad is NOT independent of the language (whether Translated to native tongue or not) of the contest question.
In plain language, the Math Olympiad team scores are dependent on whether the contest questions are translated into the native language of participating countries. For an insight on whether translation of IMO questions to native language affects the team scores in positive or negative manner, let’s take a look on the mean scores.
Table 4. Count and Average Score for IMO Questions with or without translation: IMO 2007
The difference in average team score of countries with translation and those that don’t is 36 points. It is likely that translating IMO questions to one’s native tongue could significantly increase team scores.