Ranald R. Macdonald

COPING WITH THE OCCUPATIONAL STRESSORS OF POLICE WORK: A STUDY OF SCOTTISH OFFICERS

The Coping Scale of the Occupational Stress Indicator (OSI)16 was administered to a group of serving Scottish police officers (N=699) in order to examine the coping skills they might employ in dealing with routine police work. Differences in coping style according to age, gender and rank were observed. Overall, a preference for more problem-focused, direct action coping strategies was apparent. In particular, officers displayed a preference for balancing the demands of work and home as a means of coping with the self-perceived stressors of routine police work. No significant correlation was found between the OSI coping scales and psychological distress as measured by the GHQ-28; however, some small effects were apparent in relation to rank, gender and age.

Statistical inference and Aristotle's Rhetoric

Formal logic operates in a closed system where all the information relevant to any conclusion is present, whereas this is not the case when one reasons about events and states of the world. Pollard and Richardson drew attention to the fact that the reasoning behind statistical tests does not lead to logically justifiable conclusions. In this paper statistical inferences are defended not by logic but by the standards of everyday reasoning. Aristotle invented formal logic, but argued that people mostly get at the truth with the aid of enthymemes--incomplete syllogisms which include arguing from examples, analogies and signs. It is proposed that statistical tests work in the same way--in that they are based on examples, invoke the analogy of a model and use the size of the effect under test as a sign that the chance hypothesis is unlikely. Of existing theories of statistical inference only a weak version of Fishers takes this into account. Aristotle anticipated Fisher by producing an argument of the form that there were too many cases in which an outcome went in a particular direction for that direction to be plausibly attributed to chance. We can therefore conclude that Aristotle would have approved of statistical inference and there is a good reason for calling this form of statistical inference classical.

The limits of probability modelling: A serendipitous tale of goldfish, transfinite numbers, and pieces of string

This paper is about the differences between probabilities and beliefs and why reasoning should not always conform to probability laws. Probability is defined in terms of urn models from which probability laws can be derived. This means that probabilities are expressed in rational numbers, they suppose the existence of veridical representations and, when viewed as parts of a probability model, they are determined by a restricted set of variables. Moreover, probabilities are subjective, in that they apply to classes of events that have been deemed (by someone) to be equivalent, rather than to unique events. Beliefs on the other hand are multifaceted, interconnected with all other beliefs, and inexpressible in their entirety. It will be argued that there are not sufficient rational numbers to characterise beliefs by probabilities and that the idea of a veridical set of beliefs is questionable. The concept of a complete probability model based on Fishers notion of identifiable subsets is outlined. It is argued that to be complete a model must be known to be true. This can never be the case because whatever a person supposes to be true must be potentially modifiable in the light of new information. Thus to infer that an individuals probability estimate is biased it is necessary not only to show that the estimate differs from that given by a probability model, but also to assume that this model is complete, and completeness is not empirically verifiable. It follows that probability models and Bayes theorem are not necessarily appropriate standards for peoples probability judgements. The quality of a probability model depends on how reasonable it is to treat some existing uncertainty as if it were equivalent to that in a particular urn model and this cannot be determined empirically. Bias can be demonstrated in estimates of proportions of finite populations such as in the false consensus effect. However the modification of beliefs by ad hoc methods like Tversky and Kahnemans heuristics can be justified, even though this results in biased judgements. This is because of pragmatic factors such as the cost of obtaining and taking account of additional information which are not included even in a complete probability model. Finally, an analogy is drawn between probability models and geometric figures. Both idealisations are useful but qualitatively inadequate characterisations of nature. A difference between the two is that the size of any error can be limited in the case of the geometric figure in a way that is not possible in a probability model.

The effect of sequential dependencies on some signal detection parameters

The values of various sensitivity and response criterion parameters were calculated under different experimental conditions for both detection and recognition tasks. The effects of feedback and stimulus probability were found to be consistent with previous studies. When the values of the parameters were computed depending on the nature of the immediately preceding trial, the criterion parameters were found to be dependent on the identity of the preceding response, while those measuring sensitivity were dependent on its correctness. The dependence of the sensitivity parameters could be explained as an artifact of statistical bias, while the effect on the criterion parameters appears genuine. The nature of the phenomenon of statistical bias is discussed.

Intertrial dependence in detection and recognition tasks

Abstract A Markov analysis revealed the existence of 1st order intertrial dependence in error and response sequences from both detection and recognition tasks. Both feedback and the introduction of a burst of white noise between trials reduced intertrial dependencies in the error sequences. Task difficulty and intertrial periods affected intertrial dependence in the response sequence.

Effect of Distance on Heterochromatic Matching

The brightness of colors in a number of paintings by Francis Pratt appeared to vary as a function of the viewing distance. These pictures were composed of narrow strips of different colors varying in brightness and saturation. Five experiments were undertaken to replicate and study this effect under controlled conditions using heterochromatic brightness matching of various pairs of colored stimuli. The subjects were first-year students in psychology, participating as a course requirement. The number of subjects varied in the different experiments, between 6 and 9. The relative brightness of blue as compared to red, orange, and yellow-green varied as a function of viewing distance. The relative brightness of the blue decreased as distance increased. By varying the physical size of the stimuli it was possible to keep the angle subtended at the retina constant for two distances and the effect remained. Any explanation must therefore account for the finding that the effect is not due to the apparent size of the stimuli.

Isotonic Regression Analysis and Additivity

Abstract This paper reviews the literature on isotonic regression with a view to finding tests for additivity in data whose population values are unique only up to a monotonic transformation. Several approaches are considered and a sequential one is recommended-first testing monotonicity, and then testing the double cancellation axiom. Two tests are presented for testing monotonicity and an algorithm for detecting significant departures from double cancellation is outlined.

EFFECTS OF VIEWING DISTANCE AND VISUAL ANGLE ON METAMERIC MATCHES

A metameric matching task was used to study the effect of viewing distance and visual angle on the appearance of bichromatic stimuli. Increasing the viewing distance resulted in a shift towards the longer wavelength component. Effects of visual angle were also found.