Multiple Comparisons

 Tukey's multiple comparison
ANOVA: Analysis Of Variance is a statistical analysis tool for more that TWO sets of data
How about comparison amongst the groups?
Use Tukey’s Test for Multiple Comparison
Assumptions of Tukey's test
•The observations being tested are independent
•There is equal within-group variance across the groups associated with each mean in the test (homogeneity of variance)

 Data Analysis Plus Excel Add-in
 Bring your laptop as we shall have hands-on exercises in class.
You should also install Data Analysis Plus Excel Add-in software in your computer.

TUKEY’S TEST
When more than two sample means are being compared
The formula for Tukey's test is:

where YA is the larger of the two means being compared, YB is the smaller of the two means being compared, and SE is the standard error of the data in question.
(We will only be concerned with the absolute difference, so, you can ignore any negative signs)
If the qs( shown in the following table) value is larger than the Tukeyqcriticalvalue (omega ‘ɯ’) obtained from the distribution
the two means are said to be significantly different.

Sample data for Tukey’s Test analysis

Feed 1Feed 2Feed 3Feed 4
60.8    68.7    62.6    87.9
67.0    67.7    62.1    84.2
65.0    74.0    70.2    83.1
68.6    66.3    76.5    85.7
61.7    69.8               90.3
•Use Tukey’s test to make all pairwise comparisons among the four population mean weights.
•Use p = 0.05.

MultipleComparisons
Choose:Add-Ins>DataAnalysisPlus>MultipleComparisons>OK
Enter:Inputrange:(A1:D6orselectedcells)
Select:Labels
Enter:AlphaforLSDmethod:
(Note:AlphavalueforTukey’smethodisfixed)
Enter:OK