You can use a graph to help you examine whether your data are evenly distributed on both sides of the center or skewed in one direction. When data are skewed, which is common when the data are not normal, the mean and median have different values. If your sample is small and the data are skewed, the validity of a parametric test, such as a t-test, may be questionable. In this case, you may want to use a nonparametric test, which is not based on the normal distribution.
If you know the order of data collection, you can use a scatterplot or time series plot of the data against time to reveal nonrandom patterns. If your data show a nonrandom pattern over time, a hypothesis test may be less appropriate than an analysis that evaluates the data in relation to time.