If we have 3 groups and we calculate the Tukey confidence interval for each pair of means difference and we reject \(\displaystyle{H}_{{{0}}}:μ_{{{1}}}=μ_{{{2}}}\) and \(\displaystyle{H}_{{{0}}}:μ_{{{1}}}=μ_{{{3}}},{W}{e}\neg\ne{c}{e}{s}{s}{a}{r}{i}{l}{y}{r}{e}{j}{e}{c}{t}{h}{y}{p}{o}{t}{h}{e}{s}{e}{s}{P}{S}{K}{H}_{{{0}}}:μ_{{{2}}}=μ_{{{3}}}\). We had in a, previous task this situation.

For example, if \(\displaystyleμ_{{{2}}}\) is very close to \(\displaystyleμ_{{{3}}}\) this means that \(\displaystyleμ_{{{2}}}\approxμ_{{{3}}}\approxμ\). So, since it would be almost the same value for both means, they will be different from ja1. But, also it can be that all three means are very different one from another.

For example, if \(\displaystyleμ_{{{2}}}\) is very close to \(\displaystyleμ_{{{3}}}\) this means that \(\displaystyleμ_{{{2}}}\approxμ_{{{3}}}\approxμ\). So, since it would be almost the same value for both means, they will be different from ja1. But, also it can be that all three means are very different one from another.