Visual representations of the p-value in ANOVA to assist intuitive understanding I'm a statistics newbie and I would like to make sense of the p-value with ANOVA, hopefully with a visual presentation. All online visual tools I've found so far only have MSB, MSE and F values visually presented (such as this here. I'm a very visual person and I would like to see how it works before I learn more about it. 
Do you have any suggestions for me? It could be a Matlab program as well, something where I play with the distributions and see the p value change. 
 A: There could possibly be a good reason why the MSB, MSE, and F values are only shown.  These are what is "actually important" in the analysis so to speak.  A p-value is just a sampling probability of some function of these three quantities (not sure of the specific function).
You don't need a p-value if you understand how to interpret these quantities.  p-value doesn't provide you with "extra" information, and it is so easy to mis-interpret (such as: probability for hypothesis, probability of eroneous conclusion, probability of type 1 error, etc.).  It can be quite fun to have a "p-value bash" every now and then :)
Much more useful and informative to look at effect sizes.  For if they are all pretty close - to within say plus/minus one standard error - then you already know without any need for hypothesis testing, that the data do provide support in favour of the hypothesis of equal means $H_0:\;\mu_0=\mu_1=\dots=\mu_k$.  You only need a hypothesis test, in the formal setting when it isn't "obvious" whether or not to accept or reject.  Say if one or two out of 20 means were between 2 and 3 standard errors away from the rest.  This is when the hypothesis test will help.  And also, if you see 10 out of the 20 groups over 3 standard errors apart, then you don't need the test: you know the null is not supported by the data.
