APPENDIX Y

DERIVATION OF SCORES FOR UNILATERAL ACTIONS

An appropriate score was needed to analyze unilateral actions. One alternative was to consider simply the intensity of the action on the side the action was requested. This score does not give any information about the asymmetry of the action or whether the action was unilateral. For example, two subjects might both have produced an intensity of 4 on the requested side, but one might have made a symmetrical action and the other a unilateral action. A better score should tell something about the symmetry or unilaterality of the action because there are no hypotheses about how the simple intensity scores are related to other variables.

Another alternative was to use the separate asymmetry scores for the right and left unilateral requests. The information these scores provide about an action that the subject was asked to make asymmetrical is minimal and depended upon the action requested. When a unilateral action is requested on the right, the asymmetry score should be right; when on the left, the score should be left. Table Y1 shows that this pattern was generally obtained. Only for brow actions did a large proportion of subjects seem unable to perform actions as requested. Over all the requests for unilateral actions in Table Y1, 69 percent had an asymmetry score consistent with the request. Of the brow actions alone (AUs 1,2, and 4), only 36 percent followed this pattern while 90 percent of the other actions followed it. A score was needed that could discriminate among the subjects who performed the action as requested.

Another reason for rejecting these separate asymmetry scores was that there were no hypotheses regarding them. For example, there was no hypothesis about how the asymmetry of a unilateral action requested for the left side would be related to the side subjects favored in making a unilateral request or the side they rated as easier to make it on. (There were only chance correlations between the separate asymmetry scores and other measures in this study.) There were hypotheses about which side subjects could do a better unilateral action on and which side they would rate easier or favor. What was needed was a score that would reveal the relative asymmetry of the two requests. This score would reflect how much better a unilateral action was performed when requested for one side than for the other. The score needed to be analogous to other scores that indicated how much stronger an action was on one side, how much easier an action was on one side, etc.

It will be helpful for discussing the derivation of such a score to introduce some terminology that describes unilateral actions. The subjects were asked to perform a unilateral action on one side, and, afterwards, on the other. The side on which the action was requested will be called here the "onside" because this is the side where the action should occur. The other side will be called the "offside" because no action should occur here. These distinctions were reflected in the instructions to subjects which explicitly stated that they should show the action on only one side and not on the other. Thus, for every requested unilateral action there was an offside intensity score and an onside intensity score, regardless of whether the request was for an action on the right or the left side.

The simplest score that might be considered is whether the subject could do a unilateral action on one side but not on the other. The separate asymmetry scores for each unilateral request reflect how well a subject could do the action on one side, but they do not indicate anything about how the well the request for the other side was performed. Again, in order to determine whether the subject could do an action on only one side of the face, one needs to know the scores for both sides. Using the asymmetry scores for each request separately will not suffice.

Table Y2 looks at asymmetry scores for both the right and left unilateral requests considered together. It shows how many subjects had asymmetry consisent with both requests or had only left, only right, or only symmetrical scores. Agreeing with Table Y1, most subjects could produce asymmetry that was consistent with both requests for most of the actions except the brow actions. Only for the brow actions did a large proportion of the subjects have difficulty producing asymmetry consistent with one or both requests. A better score would differentiate among subjects who had asymmetry consistent with both requests and thus retain more subjects in the analysis.

One approach would be to use only true unilateral actions as the criterion for whether a subject can do a unilateral action on the requested side of the face. A true unilateral action should have an intensity of zero on the offside, but movement could often be detected on the offside of both the right and left unilateral requests. Table Y3 shows for each action requested how many subjects did a right or a left unilateral action with an offside of zero intensity. For many of the actions, only a few subjects could do a true unilateral action on either side. This lack of actual unilateral movements would mean an unacceptable loss of subjects from the analysis of these actions if this criterion were used.

Table Y3 also shows that some subjects could do a truly unilateral action for both the right and the left unilateral requests. For example, the total of subjects who did a right unilateral plus those who did a left unilateral AU 20 exceeds the number of subjects, indicating that some subjects must have done both. For most of the AUs, it was obvious during scoring that some subjects could do a true unilateral for both requests. Some way was needed to decide which of the two unilateral actions was better.

One solution might be to chose the unilateral action that had a greater onside intensity. Suppose the request for a right action showed an onside intensity of 4 while the onside intensity for the left action was 3 with the offside intensities zero in both requests. The right unilateral action might be considered a more or better unilateral because more of the action could be shown or isolated on the right side than the left.

This solution suggests that using the onside intensities alone might provide the basis for determining which side showed the better unilateral, regardless of whether the actions were truly unilateral or not. If there was a greater onside intensity for either the right or left request, that would be the better unilateral. For example, suppose the score for a right unilateral request had an onside intensity of 4 and an offside intensity of 1, while the request for a left action had the corresponding intensities of 3 and 1. The right requested action would be called the better unilateral, and this is sensible because it is the more asymmetrical.

This formula works well when the offside intensities are constant (e.g., both 0 or both 1, etc.), but there are problems when the offside intensities vary as they do in this study. For example, suppose the request for a right unilateral produced an onside intensity of 5 and an offside intensity of 5, while the request for a left unilateral produced an onside intensity of 4 and an offside intensity of 1. Simply considering the onside intensities would select the right performance as the better unilateral , but this would be misleading because this action was not only bilateral, it could have been symmetrical while the requested left unilateral was quite asymmetrical. Consider also the case where both onside intensities are the same, but the offside intensities vary. It would be useful to use the offside intensities to decide which was the better try for the unilateral action, but using the offside intensities alone would result in the same kinds of difficulty as using the onside alone.

The examples above illustrate a host of problems that result from considering only the onside intensity and ignoring the offside intensity (or vice-versa) when deriving a score for unilateral actions. It suggests that a better approach would be to consider the difference between the onside and offside intensities. If the right or left requested performance had a bigger difference, that would be the better unilateral. However, there is a more refined measure of the difference between these intensities: the asymmetry score. Thus, in this study, the better unilateral action is defined as the requested unilateral performance which showed the greater asymmetry. Furthermore, a scalar value was calculated to reflect how much better one request was by taking the difference between the asymmetry scores for the two requests. This method of calculating a score for unilateral movements allowed all of the subjects who showed an action to be included in the analysis. All the subjects who showed only a right or only a left asymmetry in Table Y2 were assigned this score, and all the subjects who showed asymmetry consistent with both requests were assigned a score based on the difference in scores for the two sides. Subjects who showed only symmetrical actions were assigned a better unilateral score of zero.

Some difficult conceptual issues are handled better by defining the better unilateral as the more asymmetrical action. For example, consider the request for a right unilateral as having an onside intensity of 1 and an offside intensity of 0 and the left request having a 5 and 1, respectively. Even though the right request was a true unilateral, it would be misleading to call it the better unilateral because the left performance showed a greater ability to isolate much action on one side and little action on the other. When scoring these rare events, it seemed clear that the subject could easily turn on the one side that was scored as a big asymmetrical action (left in this example), but could not do the same when the other side was requested, as though the offside would move if too much were attempted on the onside.

Having defined the better unilateral as the more asymmetrical attempt to perform a unilateral action, it is instructive to compare relative intensities for the onside and offside between the better and poorer attempt. The strong relationship between these measures is reported in the results (Table 11), and should provide confidence in the final definition because it is highly related to the other scores that were rejected above.

TABLE Y1

NUMBERS OF UNILATERAL ACTIONS WHICH WERE RIGHT, LEFT, AND SYMMETRICAL FOR BOTH THE RIGHT AND LEFT REQUESTS

TABLE Y2

COMPARISON OF ASYMMETRY SCORES FOR THE RIGHT AND THE LEFT UNILATERAL REQUESTS SHOWING HOW MANY SUBJECTS PRODUCED ACTIONS CONSISTENT WITH BOTH REQUESTS OR HAD ONLY LEFT OR ONLY RIGHT OR NO ASYMMETRICAL SCORES FOR EITHER REQUEST

	Asymmetry Consistent With Both Requests	Only Showed Left Asymmetry	Only Showed Right Asymmetry	Showed No Asymmetrical Actions	Total
Action
AU 1	2	8	9	9	28*
AU 2	3	7	16	4	30
AU 1+2	4	7	17	3	31
AU 4	0	8	4	16	28*
AU 6/7	27	2	4	0	33
AU 9	16	7	6	0	29
AU 10	19	7	2	1	29
AU 12	30	2	1	0	33
AU 20	27	1	2	0	30*
AU 45	28	2	3	0	33 *

A total of 5 events across 3 AUs did not fit into the categories of this table.

TABLE Y3

NUMBER OF SUBJECTS WHO PERFORMED TRUE UNILATERAL ACTIONS WITH AN OFFSIDE OF ZERO INTENSITY FOR THE RIGHT AND LEFT UNILATERAL REQUESTS