Heterogeneity #4, Deviation from the type -> #10, Participatory restructuring of the dynamics that generated the data
(From an unfinished 2008 thought-piece)
While preparing to teach a course on epidemiology for non-specialists I made a websearch for a simple teaching example on the t-test for comparing the means (averages) of two groups for some measurement. The first example I found compared the mean productivity for two groups of workers, one group of 40 workers averaging 4.8 (in some unspecified units) with a standard deviation of 1.2 and the other group of 45 averaging 5.2 a standard deviation of 2.4. Thinking about this example led me to articulate the sequence of thoughts and questions that follow about the foundations of statistical analysis. In particular, my inquiry explores contrasts between: the statistical emphasis on averages or types around which there is variation or noise; variation as a mixture of types; the dynamics (or heterogeneous mix of dynamics) that generated the data analyzed; and participatory restructuring of these dynamics in the future. A key issue is who is assumed to be able to take action—who are the “agents”—and who are the subjects that follow directions given by others.
…[Basic sections on t-test omitted here]
3. There is something else I didn’t yet mention: in the original example there was actually only one workplace—the first group in the example is made up of workers measured on one day; the second group is made up of workers measured on a later day when the music was playing. The different size of the groups is simply related to different numbers of missing measurements on the two days. We could, therefore, look at the change in productivity for individual workers who were measured on both days. Suppose that we go back to the first example and find that this change averaged 0.5 with a standard deviation of 1.3 for the 36 workers measured on both days (Figure 2). The chance of a mean difference of this size if the workers actually came from the same population—that is, if music playing had no systematic effect on individuals’ productivity, whether good or bad—is 0.01… Given that the mean difference is positive, again the obvious thing to do is for the employer to play the music.
4. Yet, given that the mean difference is 0.5 and the standard deviation is 1.5, there must be many individuals who show a negative difference, that is, whose productivity declined when music was playing. In fact, this was the case for 12 of the 36 (see Figure 2). Should they oppose the playing of music, even though they are in the minority? If they do, should the employer ignore their opposition given that the firm’s average individual productivity increases? Does the employer have to power to ignore any opposition? If so, the employer’s power to switch on the music comes at the expense of one third of the workforce. In effect, the employer treats them as part of a music-enhances-productivity population, even though they don’t fit this type.
5. The employer, faced with competition from other firms and cognizant of obligations to shareholders, might justify playing music by pointing to the increase in average productivity of the workers, which translates into an increase in overall productivity of the firm. There are, however, other paths to higher overall productivity that the employer could consider. The employer might start by asking individuals in the minority why their productivity decreased when the music played. Suppose it turned out that the tasks of those whose productivity decreased required greater concentration than the tasks of their fellow workers, or that the music chosen is not to their liking. The employer might then rearrange the workplace so that music was not played in areas where workers had to concentrate hard. Or, using headphones linked to airplane-style audio-systems, individual workers might choose from a selection of musical styles. Once the employer starts consulting individual workers, the employer might go on to ask individuals whose productivity increase was well above the mean increase to explain why. It might turn out, for example, that the music countered the tedium of their work and made them less likely to take extended bathroom breaks. By learning about the different individuals, the employer is able, in effect, to dividing the range of individuals into a set of types in relation to working when music is playing. Actions taken by the employer can then be customized accordingly. Such actions might even lead to a higher overall productivity for the firm than switching on music for all. Of course, switching on music for all is simpler and probably less expensive, but it is a matter of empirical investigation whether the firm’s net profit would increase more through the customized changes or the simpler one-size-for-all action.
6. There are other things to consider about the one-size-for-all action by the employer. It keeps our focus on productivity in relation to playing music or not, and thereby keeps attention away from the dynamics (or mechanisms or causal connections) through which factors in addition to music influence productivity. We are left to hope that whatever the dynamics are, the addition of music does not lead to any long-term shifts in them. In other words, whatever dynamics generated the data we analyze, we assume that these same dynamics continue into the future even after playing music is added to them. Perhaps, however, a number of workers, including even some who like music, react negatively to the employer exerting the power to pipe in music, worrying, say, that this opens the door to advertizing, anti-union messages, and so on. Moreover, to some extent, a similar assumption about the continuation of past dynamics underlies the customized actions. For example, if headphones were used so as to allow choice of music, would the quality of intra-office communication continue as before? However, there is one difference between the one-size-for-all and customized actions. The latter, by acknowledging the range of circumstances underlying the increases and decreases in individuals’ productivity, opens the door to further attention to the dynamics through which factors in addition to music influence productivity. Of course, much more data is needed to investigate these dynamics and the employer might judge as unwarranted the cost of collecting and analysing the data and acting on any results.
7. Imagine, however, an employer who consults workers, acknowledges the range of circumstances influencing productivity, and worries about whether past dynamics continue even after an intervention (here: switching on music) into them. These steps open the door to the employer mobilizing the workers in a participatory planning process. Skilful facilitators can lead participants through processes that elicit diverse items of knowledge about the current circumstances, generate novel proposals for improvement, and ensure that the participants are invested in collaborating to bring the resulting plans to fruition (Stanfield 2002). If this collaborative change happens, it would matter less whether the past dynamics continued as before because the workers would have become agents in the ongoing assessment and reorganization of their work lives. Moreover, improvement in productivity could result from plans unrelated to the initial issue about having music played. Of course, this scenario assumes that the employer and workers can all be brought together and kept interacting despite differences and tensions until plans are developed in which all are invested…