Many would say this is a philosophical question rather than a statistical one. But it is one statisticians are called upon to answer.
Here are several kinds of issues to ponder:
1st, was a diverse group of people randomized into treatment and control groups. If so, this helps to eliminate disease status, age, gender, education, income, etc, as 'lurking' explanatory variables. (Rich people can afford to take better care of themselves, and there were more rich people in the experimental group; what do you expect?")
2nd, was the treatment specifically designed to achieve the observed effect, or is this a surprise? (What factors led to expecting the observed result?)
3rd, was the study double-blind, thus eliminating various kinds of bias?
("The doctors took better care of subjects in the treatment group because they wanted to show the treatment works.")
4th, were the instruments used to get data on success relevant, reliable and established ones? (Are the data you put into your t test obviously relevant and established lab results? Are any patient surveys you analyzed well-vetted instruments for reliably detecting exactly what is relevant?)