Tukey Test

A display of the Bonferroni test results from Table 12-1 (which is part ofthe Chapter Problem) is provided on page 577. Shown on the top of the next page is the SPSS-generated display of results from the Tukey test using the same data. Compare the Tukey test results to those from the Bonferroni test.

Here, the single factor of lead is considered, which is further divided into low, medium and high levels.

Refer to table 12-1 for the Bonferroni test results. Also, Tukey test results are also provided.

The Bonferroni and Tukeys test is to be performed for three different possible pairs.

So, the null hypothesis is:

\[\begin{aligned}{l}{H_0}:{\mu _1} = {\mu _2}\\{H_0}:{\mu _1} = {\mu _3}\\{H_0}:{\mu _2} = {\mu _3}\end{aligned}\]

Where, \[{\mu _1}\] represents the mean low lead levels, \[{\mu _2}\] represents the medium lead level and \[{\mu _1}\] represents the mean high lead levels.

The SPSS table displays 3 levels of blood lead. Low lead levels are represented by 1, medium levels are represented by 2, and high levels are represented by 3.

For the first pair (1 - 2):

The p-value of the Tukey test is 0.067and the p-value of the Bonferroni test is 0.079. Both p-values are not small \(\left( {p > 0.05} \right)\). So, the null hypothesis fails to be rejected. There is no significant difference between the means of low lead level and medium lead level.

For the second pair (1 - 3):

The p-value of the Tukey test and Bonferroni test is 0.076 and 0.090. These p-values are also not small \(\left( {p > 0.05} \right)\). So, the null hypothesis fails to be rejected. There is no significant difference between the means of low lead level and high lead level.

For the third pair (2 - 3):

The p-value of the Tukey test and Bonferroni test are 1.000 and 1.000. These p-values are also not small \(\left( {p > 0.05} \right)\). So, the null hypothesis fails to be rejected. There is no significant difference between the means of medium lead level and high lead level.

The conclusion drawn from the Tukey test and Bonferroni test are the same; however, the p-values are different in both the tests.