The abundances of light elements based on the big bang nucleosynthesis model are calculated using the Tsallis non-extensive statistics .
The impact of the variation of the non-extensive parameter q from the unity value is compared to observations and to the abundance yields from the standard big bang model .
We find large differences between the reaction rates and the abundance of light elements calculated with the extensive and the non-extensive statistics .
We found that the observations are consistent with a non-extensive parameter q = 1 ^ { +0.05 } _ { -0.12 } , indicating that a large deviation from the Boltzmann-Gibbs statistics ( q = 1 ) is highly unlikely .