Statistics Toolbox

Example: Multiple Comparisons

You can perform a multiple comparison test using the multcompare function and supplying it with the stats output from anova1.

• [c,m] = multcompare(stats)
  c =
      1.0000    2.0000    2.4953   10.5000   18.5047
      1.0000    3.0000    4.1619   12.1667   20.1714
      1.0000    4.0000    6.6619   14.6667   22.6714
      1.0000    5.0000   -2.0047    6.0000   14.0047
      2.0000    3.0000   -6.3381    1.6667    9.6714
      2.0000    4.0000   -3.8381    4.1667   12.1714
      2.0000    5.0000  -12.5047   -4.5000    3.5047
      3.0000    4.0000   -5.5047    2.5000   10.5047
      3.0000    5.0000  -14.1714   -6.1667    1.8381
      4.0000    5.0000  -16.6714   -8.6667   -0.6619
  m =
     23.8333    1.9273
     13.3333    1.9273
     11.6667    1.9273
      9.1667    1.9273
     17.8333    1.9273
  

The first output from multcompare has one row for each pair of groups, with an estimate of the difference in group means and a confidence interval for that group. For example, the second row has the values

• 1.0000    3.0000    4.1619   12.1667   20.1714
  

indicating that the mean of group 1 minus the mean of group 3 is estimated to be 12.1667, and a 95% confidence interval for this difference is [4.1619, 20.1714]. This interval does not contain 0, so we can conclude that the means of groups 1 and 3 are different.

The second output contains the mean and its standard error for each group.

It is easier to visualize the difference between group means by looking at the graph that multcompare produces.

The graph shows that group 1 is significantly different from groups 2, 3, and 4. By using the mouse to select group 4, you can determine that it is also significantly different from group 5. Other pairs are not significantly different.

Multiple Comparisons

Two-Way Analysis of Variance (ANOVA)