We use the functional data methodology to examine whether there are significant differences between two waves of contagion by COVID-19 in Colombia between 7 July 2020 and 20 July 2021. A pointwise functional t-test is initially used, then an alternative statistical test proposal for paired samples is presented, which has a theoretical distribution and performs well in small samples. Our statistical test generates a scalar p-value, which provides a global idea about the significance of the positivity curves, complementing the existing punctual tests, as an advantage.