COLLEGE SENIORS DO NOT UNDERSTAND STATISTICS!!!
Now I am not a statistician nor do I have any real expertise in statistical analysis. In fact, I turn to statisticians when I need to do statistical analyses beyond student T-tests or analysis of variance. However, I think I know enough about statistics to not make the error of the p-value.
The p-value essentially tells you the probability that some event, data, occurrence is due to chance (generally referred to as the null hypothesis). So if you are hoping that the effect you are looking at is not due to chance you want a small p-value. The question, of course, then becomes 'how small'? The scientific community has generally agreed that a p-value of < 0.05 is a rigorous cut-off. A p-value > 0.05 is considered to be reasonable odds that your effect may be due to chance. However, this cut-off of 0.05 is arbitrary and indeed higher and lower cut-offs are used in some fields.
To be clear, p-values can range from 0 - 1, so you can consider a p-value of 0.05 to be analogous to a 5% chance that the effect you are looking at to be due to chance. That also means that your p-value of 0.06 means there is a 6% chance your data is due to chance and that is too high for most scientists to consider your data significant.