How to interpret grouping result in Tukey's HSD test

Assuming there are three methods to kill bugs, and we want to know whether their performance differs. The Tukey's HSD test gives the following grouping results:

\$groups
trt means  M
1   1  1.96  a
2   3  1.88 ab
3   2  1.68  b


If we need suggest some methods to use, can we say method 1 and 3 can both be used as they are either better than or equal to method 2 (both have the grouping letter 'a')?

• What is the actual scientific question here? What are you going to use the treatments for? – mdewey Aug 4 '17 at 15:23

Since treatment 3 shares a subscript with treatment 2, treatment 3 is not more than the expected standard error greater than treatment 2.
You would be able to conclude, however, that treatment 1 is significantly greater than treatment 2.