This could be because the sample size was too small. For statistical significance, I might need to shoot several people. My crime has no statistically significant effect on life-span because it is common for people to die younger than my victim. In fact, any difference, no matter how tiny, will be statistically significant if the sample size is large enough. Probability and the accuracy of estimates.
Small samples provide a lower probability of being close to the sample mean.
This spread forms the basis of measures like standard error of the mean . In inferential statistics, 'p' values express the probability that samples are consistent with the null hypothesis. When using 'p' values as the criteria for accepting or rejecting hypotheses, there are two types of error. This is incorrectly deciding that the samples are not from the same population. This can arise by choosing too high a 'p' value.