How would I interpret this TukeyHSD result in R?

Question

I'm comparing two systems to see whether there is a significant difference in being able to locate anomalies using System A and System B. I've run a t-test on both and have rejected the null hypothesis.

I then decided to run an ANOVA to confirm my findings and I was also able to reject the null hypothesis. I ran a further TukeyHSD test to see where the differences lay and got this:

        Tukey multiple comparisons of means
95% family-wise confidence level

 Fit: aov(formula = x_time_subtracted_from_y_time ~ system, data = data)

 $system
                 diff        lwr      upr    p adj
   SystemB-SystemA 0.03974616 0.02658632 0.052906     0

Am I reading this correctly as that System B averages 0.03974616 points higher than System A? If so does the below then mean that System A averages out 0.0004256548 higher than System B?

 Fit: aov(formula = y_time ~ system, data = data)

              diff           lwr            upr             p adj
 SystemB-SystemA -0.0004256548 -0.0008034504 -0.00004785925 0.0272384

Thanks in advance.

Answer 1

Yes, your interpretation is generally correct. TukeyHSD() is simply a Student's t-test, like you ran before, adjusted for multiple comparisons. Tukey's procedure assumes the following:

• Independence of observations
• Homoscedasticity

The Fisher's LSD test is a similar and useful analysis, though it does not correct for multiple comparisons like Tukey's. See here and here for more information on both.