Question

I interpret the data using scatter plot graph and Tukey’s test and it seems that they yield a different result. Tukey says that each variable(A,B,C,D) are not significantly different while it can clearly be seen in the graph that one of the variable(B) is lying higher above other. Which method should I trust? Is Tukey’s more reliable than the graph because it has changed the significant level so there’s lower chance of making type I error? Or is there a limitation for using Tukey’s ie. sample size?

the data is about different operating crews vs the production yield in manufacturing

Answer 1

Yes, your approach is correct. Since Tukey is used to make multiple comparisons, it is more reliable than the graph. The graph only gives an idea about the type of relationship but we cannot interpret significance on the basis of graphs. Hence you should rely on Tukey's test.