Tukey test help!

Question

Hey,

I don't understand what this Tukey test shows. Can someone help me?

$`species:treatment`

diff lwr upr p adj

saureus:TreatA-ecoli:TreatA 1.246667 -1.4747115 3.968045 0.6212974

ecoli:TreatB-ecoli:TreatA -7.693333 -10.4147115 -4.971955 0.0000000

saureus:TreatB-ecoli:TreatA -5.380000 -8.1013782 -2.658622 0.0000150

ecoli:TreatB-saureus:TreatA -8.940000 -11.6613782 -6.218622 0.0000000

saureus:TreatB-saureus:TreatA -6.626667 -9.3480449 -3.905288 0.0000002

saureus:TreatB-ecoli:TreatB 2.313333 -0.4080449 5.034712 0.1222784

treatment and species alone were significant.

Thanks

Answer 1

A Tukey test is what's called a "post-hoc" test. In your statistical test you had two independent variables (species and treatment) and you also looked for an interaction between species and treatment. The interaction variable explores the question of whether the the value of one independent variable affected the other in its effect on the respobse. So your test looked something like:

Response = Species + Treatment + Species*Treatment

The original ANOVA could only tell you if there was a significant effect of the interaction of species and treatment. The Tukey test gives you specific information about exactly which combinations of your 2 variables had an effect on the response.

The treatments with very low p-values are significant and the ones with high p-values are not. A p-value captures the probability that the effect you observed occurred by chance alone, so very low p-values suggest that it's highly probable that the variable in question caused the response you observed.