Why are these comparisons considered non-significant in R-Studio? (Simple Two-way ANOVA) I am wondering why these means are considered non-significantly different in the TukeyHSD post-hoc--particularly the means between treatment types within respective fields. The only comparison which is considered significant is HSP:TR-H:TR. Clearly in the graph they differ within fields. This difference is huge when considering we are talking about grain yield for small sections (1x1m plots) of a field.
I know I don't have many reps (3 reps per treatment, 3 levels of treatment, 2 levels of field). They are both fixed factors. I have on outlier that I didn't remove to keep a balanced design. 
Let me know what you think guys because I am stumped! thanks! 
Alex 

 A: 
"Clearly in the graph they differ within fields"

You're presumably looking at the fact that some of the samples don't overlap but your samples are tiny. It's certainly not clear to me that they're different. 
The chance at least one sample of size n=3 doesn't overlap another (out of 6 such samples) is not small. 
Here's a random set of 6 boxplots with n=3, all drawn from the same distribution:

Indeed a quick simulation suggests this (at least one pair of completely non-overlapping samples of size 3 with 6 groups) will happen about 57%-58% of the time, give or take (this would work for any continuous distribution, since whether or not two samples overlap is invariant to monotonic transformation).
Looking at notched boxplots may help give a better sense (but n is so small the calculations are very rough), and then consider you have 15 pairwise comparisons so you should expect to see perhaps one or two of them (give or take) significant at the 5% level (no overlap in notches) even if nothing is going on. 
Your judgement that there's an outlier is similarly likely to be a misjudgement -- e.g. with 6 normal samples and n=3 you see an "outlier" like that quite often, so even with a fairly light tailed distribution it's not out of the ordinary.
A: The graph are showing the median score not the mean...mean values can be highly affected due to outliers. Looking at your mean differences in the output, are they too large compared to a very wide scale these scores are on? you can maybe compare two of the treatments at a time using t-test to see if you see a significant mean difference or not?
