Testing Mean Differences among Groups: Multivariate and Repeated Measures Analysis with Minimal Assumptions

To date, there is a lack of satisfactory inferential techniques for the analysis of multivariate data in factorial designs, when only minimal assumptions on the data can be made. Presently available methods are limited to very particular study designs or assume either multivariate normality or equal covariance matrices across groups, or they do not allow for an assessment of the interaction effects across within-subjects and between-subjects variables. We propose and methodologically validate a parametric bootstrap approach that does not suffer from any of the above limitations, and thus provides a rather general and comprehensive methodological route to inference for multivariate and repeated measures data. As an example application, we consider data from two different Alzheimer’s disease (AD) examination modalities that may be used for precise and early diagnosis, namely, single-photon emission computed tomography (SPECT) and electroencephalogram (EEG). These data violate the assumptions of classical multivariate methods, and indeed classical methods would not have yielded the same conclusions with regards to some of the factors involved.     

The China Puzzle: Falling Happiness in a Rising Economy

Over the 1990–2000 decade happiness in China plummeted despite massive improvement in material living standards. This finding contradicts the notion that income growth at low living standards leads to gains, not losses, in happiness. We explain this puzzle by drawing on a specific version of relative deprivation theory, the concept of “frustrated achievers.” Our major finding is that income inequality in China became increasingly skewed towards the upper income strata, so that related to the average income the financial position of most Chinese worsened. Consequently, financial dissatisfaction rose and became an increasingly important factor in depressing happiness. Other negative feelings emerging with rapid transitions, such as anomie and disaffection, show a less depressive effect on Chinese happiness. We conclude with some speculations about the applicability of our findings to transition economies in general.

Ensuring Liberties: Understanding State Restrictions on Religious Freedoms

Promises of religious freedoms have become the standard in national constitutions. Yet, despite these assurances, religious freedoms are routinely denied. Combining new data collections with expanded theoretical explanations, this research explores how dimensions of governance and measures of the religious economy contribute to government restrictions on religion. Consistent with recent work on the judicialization of politics, we find that the absence of an independent judiciary is an important predictor of government restrictions on religious freedoms, whereas free elections and government effectiveness are insignificant in our full models. Consistent with the religious economy theory, we find that social restrictions and government favoritism toward a religion(s) are persistent predictors of the government's restrictions. Although the proportion of the population Muslim holds a strong bivariate association with government restrictions (r = .57), the relationship is reduced to insignificance in our full models. We briefly discuss the implications of these findings.     

Food and water intake as functions of resource consumption costs in a closed economy.

In two experiments, rats living in a closed economy were offered continuous, concurrent access to four resources: food, water, a nest, and a running wheel. Costs of consuming food and water were imposed with bar-press requirements, and the price of either one or both resources was raised. As the consumption cost increased, less was consumed in each bout of resource use. Bout frequency increased, but not sufficiently to compensate for the fall in bout size, and total intake fell. Food and water tended to be complementary resources, in that as intake of one fell with its price, intake of the other also decreased. This interaction was accounted for by the defense of the ratio of body water to lean body mass. As amount consumed decreased, increases in feed efficiency (weight gain per unit of food ingested) and the use of stored calories compensated for the reduced energy intake. There was evidence of competition between feeding and drinking at the higher costs: When both commodities were expensive, the decline in the intake of each one was greater than when only one commodity was expensive. Although the time spent nesting, running, and in unmonitored activity was adjusted when feeding or drinking took more of the rat's day, there was no particular activity that was sacrificed.     

The K-BIT: A screen for IQ in six diverse populations

Performance data were collected on the Kaufman Brief Intelligence Test (K-BIT) from a total of 196 individuals from six diverse populations. College students did best, followed closely by closed head-injured adults and their controls; the order of performance then was learning-disabled children, psychiatric patients, and finally, neurosurgical patients in the acute stages of recovery.     

Labor supply and consumption of food in a closed economy under a range of fixed- and random-ratio schedules: tests of unit price

The behavioral economic concept of unit price predicts that consumption and response output (labor supply) are determined by the unit price at which a good is available regardless of the value of the cost and benefit components of the unit price ratio. Experiment 1 assessed 4 pigeons' consumption and response output at a range of unit prices. In one condition, food was available according to a range of fixed-ratio schedules, whereas in the other condition, food was available according to a range of random-ratio schedules. Consistent with unit price predictions, consumption and response output were approximately equivalent across schedule types within the lower range of unit prices. However, at Unit Prices 64 (ratio value = 192) and greater, considerably more consumption and response output were observed in the random-ratio condition. Experiment 2 replicated these findings with 4 pigeons using the rapid demand curve assay procedure that is commonly used in the behavioral economics literature. Findings are integrated with two mathematical models of behavior under variable reinforcer delays.     

Variable-interval schedule performance in open and closed economies

In two experiments, pigeons obtained food according to variable-interval schedules. In the first experiment, equivalent variable-interval schedules with average interreinforcer intervals ranging between 10 and 80 s in different conditions were studied in both open and closed economies. Response rates increased as reinforcement frequency decreased in the closed economy. By contrast, in the open economy response rates decreased for 1 bird and were variable for the other as reinforcement frequency decreased. The second experiment showed that the differences in the functions between responding and reinforcement frequency in the two types of economies were not due to changes in deprivation level. These results suggest that open and closed economies yield different behavioral effects. This conclusion is supported further by a reconsideration of previous findings that appear counter to the conclusion.     

The economics of the law of effect.

A corollary of the law of effect predicts that the larger the reinforcement, the greater the rate of responding. However, an animal must eat more small portions than large portions to obtain the same daily intake, and one would predict, therefore, that when eating smaller portions an efficient animal would eat less (conserving time and energy) and/or respond faster (conserving time). The latter of these predictions was supported by the present experiments with free-feeding rats for which portion size (pellet size or duration of feeder presentation) and portion price within meals were varied. Response rate was a function of the unit price (responses/g) of food: Rats responded faster when portions were smaller or when prices were higher. Meal size and frequency were relatively unaffected by unit price, but were influenced by the price of meal initiation. The results are discussed in relation to the economic differences between traditional operant and free-feeding paradigms and to both traditional and more recent formulations of the law of effect.     

Responding on concurrent-chains schedules in open and closed economies.

Pigeons' key pecks were reinforced according to concurrent-chains schedules of reinforcement. The programmed average time from the onset of the initial links to a terminal link entry was held constant across conditions while the value of variable-interval schedules in the terminal links was varied. Performance was assessed under two economic conditions: (a) an open economy in which session duration was limited to 1 hr and subjects were maintained at 80% of their free-feeding body weights with postsession food when necessary; and (b) a closed economy in which sessions were 23.5 hr long and no deprivation regimen was in effect. In all cases, the relative rate of responding in the initial links matched the reduction in overall delay to primary reinforcement correlated with entry into one terminal link relative to the reduction in delay correlated with entry into the other terminal link. Although the sum of responses made in the initial links and terminal links was found to increase, then decrease, as the rate of food presentation decreased in the closed economy, there was no consistent effect of overall rate of food presentation on total responding in the open economy. The choice data suggest that relative delay reduction predicts choice accurately, regardless of economic context.     

THE TOKEN ECONOMY: A DECADE LATER

In the last decade, the token economy has been extended widely across populations and behaviors in treatment, rehabilitation, educational, and community settings. Outcome research has expanded as well to include large-scale program evaluations and comparative and combined treatment studies of the token economy. In a previous review (Kazdin & Bootzin, 1972), several obstacles were identified for the effective application of the token economy. These included identifying procedures to enhance program efficacy, to train staff, to overcome client resistance, and to promote long-term maintenance and transfer of training. The present paper discusses recent advances in research and reviews progress on the major issues identified previously. New issues have become salient in the last decade that pertain to the extension of the token economy to institutional settings. The demands for maintaining the integrity of treatment, the ability to integrate token economies within existing institutional constraints, and the disseminability of the procedures on a large scale are major issues that may dictate the future of the token economy.