Morse-Code: Configuration Analysis

Inspection of the configuration (Figure 6.1(a)) without any particular em- phasis reveals only a few basic observations. The numbers are clearly dis- tinguishable as they form a line on the outskirts of the configuration. The letters T and E are also observed to be more removed from the main cluster- ing than any other points. It is however clear that some form of classification of the points is necessary to aid the interpretation process.

The first attempted classification is in defining the categories of the points as the type of symbol that they are. Specifically, the three categories are ‘Number’, ‘Consonant’ and ‘Vowel’. The data file will then include an additional column representing the Categories of the data. The data is up-

(a) Non-Metric SMACOF: Shepard Plot

(b) Non-Metric SMACOF: Scree Plot

Figure 6.3: Morse-Code Data: Diagnostic Plots

loaded once more into the MDS-GUI and the box is checked, in the New Active Similarity Matrix Options window, indicating that a column of cate- gories is present. Each point is then automatically colour coded according to its respective category. The updated Non-Metric SMACOF result is shown

in Figure 6.4.

Figure 6.4: Morse Code: Symbol Categories

The categorised version provides a slightly better idea of the composition of the configuration. The numbers are again clearly defined and interesting the majority of the consonants are grouped tightly towards the center of the configuration. The vowels are not clearly grouped together, but it is noticed that each vowel is located on the outskirts of the configuration, indicating that in general they were perceived as non-similar to the majority of the other points. A more detailed category system is then undertaken in order to identify a more profound interpretation and understanding of the MDS result. In order to do this, a more detailed look is required at the composition of the Morse code symbols themselves. Table A.3 of the appendix provides the codes for each of the 36 symbols. It is noticed that each symbol is represented by a series of between 1 and 5 dashes and/or dots. A reasonable hypothesis is that, when determining the similarity between

two simultaneous sequences, the length of the two will be significant to the result. Each point of the data set is now provided with a category indicating whether its Morse-Code sequence is comprised of 1,2,3,4 or 5 elements. The reloaded data in the MDS-GUI produces Figure 6.5. The background colour of the Main Plotting Area of the MDS-GUI is adjusted to a gray so as to emphasize the difference in colour of points.

Figure 6.5: Morse Code: Length Categories

This result produces a far better depiction of how the respondents of the investigation responded. The configuration is very clearly influenced by the length of the code, with each length category grouped together. To be specific: sequences with five elements are red; with four elements are white; with three elements are black; with two elements are yellow; and with one element is green. We therefore see that not only are the categories grouped, but the groups are arranged such that they are ordered. That is, the single element group is furthest from the five element group, and so on.

(a) Morse-Code: Shepard Diagram with Labeled Points

(b) Morse-Code: Configuration with Labeled Points

Figure 6.6: Morse-Code Data: Labeled Points

Some point pairings require detailed analysis. Figure 6.6 shows the label- ing of two points on the Shepard Diagram, with the corresponding distance illustrated on the configuration mapping. These points were added by se-

lecting the Label Specific Point option of the Shepard Plot right click menu. The first pairing is that of N0 :N5, which has the Shepard point and line coloured ‘red’. Each of the ten number sequences are comprised of five el- ements (letters contain up to four elements). Of these ten sequences, one would expect the N0 :N5 combination to be perceived as the least similar numbers, as the N5 sequence consists of five dots and N0 consists of five dashes. This prediction is confirmed as the two points are the furthest apart of all the numbers. All other number combinations consist of different com- binations of dots and dashes and are therefore more easily confused. In particular, the N2 sequence consists of two dots and three dashes, while the N8 sequence is three dashes and two dots. These two are often con- fused, and therefore are the closest of the number pairings. This pairing is coloured blue on the Shepard Plot and configuration. Finally, the N0 :E combination should be of interest as one would expect it to be the two least similar objects of the data. N0, as described, consists of five dashes, while E has only one single dot. The result (colour coded green) however reveals that the MDS procedure did not capture the extent of this distance. The Shepard Plot reveals this point to indeed have one of the highest observed distances, yet is far from the highest ordination distance. The interest- ing point here is that while the ordination distance of the point is not the greatest of all the ordination distances, it is still far higher than its specific observed distance, meaning that some lesser observed distance pairings have been exaggerated even more drastically than N0 :E. This further confirms the conclusions drawn about the Shepard Plot in that the majority of points have been severely overstated by the Non-Metric SMACOF procedure.