Just as a rule of thumb, in general the most important assumption that is violated is independence. If the data is not independent and is instead positively cor

Just as a rule of thumb, in general the most important assumption that is violated is independence. If the data is not independent and is instead positively correlated (the most likely form of correlation in practice) most equations will overestimate statistical significance. A small amount of correlation can lead to very biased estimates of significance. Correlation between observations will generally appear in any time series data or data that is arranged spatially. Again, just a rule of thumb, but you should be very wary of the lack of independence between observations.