Exploring data: graphs and numerical summaries

# 2.7 Surgical removal of tattoos

The final data set in this section is different from the others in that the data are not numerical. So far you have only seen numerical data in the form of measurements or counts. However, there is no reason why data should not be verbal or textual. Table 7 contains clinical data from 55 patients who have had forearm tattoos removed. Two different surgical methods were used; these are denoted by A and B in the table. The tattoos were of large, medium or small size, either deep or at moderate depth. The final result is scored from 1 to 4, where 1 represents a poor removal and 4 represents an excellent result. The gender of the patient is also shown.

## Table 7 Surgical removal of tattoos

Method | Gender | Size | Depth | Score |  | Method | Gender | Size | Depth | Score
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
A | M | Large | deep | 1 |  | B | M | medium | moderate | 2
A | M | Large | moderate | 1 |  | B | M | large | moderate | 1
B | F | Small | deep | 1 |  | A | M | medium | deep | 2
B | M | Small | moderate | 4 |  | B | M | large | deep | 3
B | F | Large | deep | 3 |  | A | F | large | moderate | 1
B | M | Medium | moderate | 4 |  | B | F | medium | deep | 2
B | M | Medium | deep | 4 |  | A | F | medium | deep | 1
A | M | Large | deep | 1 |  | A | M | medium | moderate | 3
A | M | Large | moderate | 4 |  | B | M | large | moderate | 3
A | M | Small | moderate | 4 |  | A | M | medium | deep | 1
A | M | Large | deep | 1 |  | A | F | small | deep | 2
A | M | Large | moderate | 4 |  | A | M | large | moderate | 2
A | F | Small | moderate | 3 |  | B | M | large | deep | 2
B | M | Large | deep | 3 |  | B | M | medium | moderate | 4
B | M | Large | deep | 2 |  | B | M | medium | deep | 1
B | F | Medium | moderate | 2 |  | B | F | medium | moderate | 3
B | M | Large | deep | 1 |  | B | M | large | moderate | 2
B | F | Medium | deep | 1 |  | B | M | large | moderate | 2
B | F | Small | moderate | 3 |  | B | M | large | moderate | 4
A | F | Small | moderate | 4 |  | B | M | small | deep | 4
B | M | Large | deep | 2 |  | B | M | large | moderate | 3
A | M | Medium | moderate | 4 |  | B | M | large | deep | 2
B | M | Large | deep | 4 |  | B | M | large | deep | 3
B | M | Large | moderate | 4 |  | A | M | large | moderate | 4
A | M | Large | deep | 4 |  | A | M | large | deep | 2
B | M | Medium | moderate | 3 |  | B | M | medium | deep | 1
A | M | Large | deep | 1 |  | A | M | small | deep | 2
B | M | Large | moderate | 4 |  |  |  |  |  |

(Lunn, A.D. and McNeil, D.R. (1988) The SPIDA manual. Statistical Computing Laboratory, Sydney.)

What are the relative merits of the two methods of tattoo removal? Is one method simply better, or does the quality of the result depend upon the size or depth of the tattoo?

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