P-values are more informative than the reject-or-not result of a fixed level α test. Beware of placing too much weight on traditional values of α, such as α=0.05.
Very small effects can be highly signifcant (small P), especially when a test is based on a large sample. A statistically signifcant effect need not be practically important. Plot the data to display the effect you are seeking, and use confidence intervals to estimate the actual value of parameters.
Many tests run at once will probably produce some signifcant results by chance alone, even if all the null hypotheses are true.