I measured a variable $X$ and estimated the error bars on my measurement with the objective of testing if $X$ is significantly different from zero. I concluded that $X$ is different from zero only at 2$\sigma$. Following this, I applied the same technique and made use of an (arguably) more precise instrument, and made a second independent measurement. Unfortunately, I concluded that this second measurement is different from zero only at 2$\sigma$ as well.
Is it legit to combine the two consecutive measurements? How can this be done?