Omission of Outliers

In homogeneity analysis, outliers are objects that have too many unique features. As noted earlier, SCREW1 might be considered an outlier.

To delete this object and run the analysis again, from the menus choose:

Data > Select Cases...

Figure 1. Select Cases dialog box
Select Cases dialog box
  1. In the Select Cases dialog, select If condition is satisfied.
  2. Click If.
    Figure 2. If dialog box
    If dialog box
  3. In the If dialog, Type object ~= 16 as the condition.
  4. Click Continue.
  5. Click OK in the Select Cases dialog box.
  6. Finally, recall the Multiple Correspondence Analysis dialog box, and click OK.
Figure 3. Model summary (outlier removed)
Model summary (outlier removed)

The eigenvalues shift slightly. The first dimension now accounts for a little more of the variance.

Figure 4. Discrimination measures
Discrimination measures

As shown in the discrimination plot, Indentation of head no longer discriminates in the second dimension, whereas Brass changes from no discrimination in either dimension to discrimination in the second dimension. Discrimination for the other variables is largely unchanged.

Figure 5. Object scores labeled with Brass (outlier removed)
Object scores labeled with Brass (outlier removed)

The object scores plot labeled by Brass shows that the four brass objects all appear near the bottom of the plot (three objects occupy identical locations), indicating high discrimination along the second dimension. As was the case for Thread in the previous analysis, the objects do not form compact groups, but the differentiation of objects by categories is perfect.

Figure 6. Object scores labeled with Indentation of head (outlier removed)
Object scores labeled with Indentation of head (outlier removed)

The object scores plot labeled by Indentation of head shows that the first dimension discriminates perfectly between the non-indented objects and the indented objects, as in the previous analysis. In contrast to the previous analysis, however, the second dimension cannot now distinguish the two categories.

Thus, the omission of SCREW1, which is the only object with a star-shaped head, dramatically affects the interpretation of the second dimension. This dimension now differentiates objects based on Brass, Head form, and Length in half-inches.