Analysis of residuals in contingency tables: another nail in the coffin of conditional approaches to significance testing.

Omnibus tests of significance in contingency tables use statistics of the chi-square type. When the null is rejected, residual analyses are conducted to identify cells in which observed frequencies differ significantly from expected frequencies. Residual analyses are thus conditioned on a significant omnibus test. Conditional approaches have been shown to substantially alter type I error rates in cases involving t tests conditional on the results of a test of equality of variances, or tests of regression coefficients conditional on the results of tests of heteroscedasticity. We show that residual analyses conditional on a significant omnibus test are also affected by this problem, yielding type I error rates that can be up to 6 times larger than nominal rates, depending on the size of the table and the form of the marginal distributions. We explored several unconditional approaches in search for a method that maintains the nominal type I error rate and found out that a bootstrap correction for multiple testing achieved this goal. The validity of this approach is documented for two-way contingency tables in the contexts of tests of independence, tests of homogeneity, and fitting psychometric functions. Computer code in MATLAB and R to conduct these analyses is provided as Supplementary Material.

Standardized environmental management systems as an internal management tool

In a principal-agent model we analyze the firm’s decision to adopt an informal or a standardized Environmental Management System (EMS). Our results are consistent with empirical evidence in several respects. A standardized EMS increases the internal control at the cost of introducing some degree of rigidity that entails an endogenous setup cost. Standardized systems are more prone to be adopted by big and well established firms and under tougher environmental policies. Firms with standardized EMS tend to devote more effort to abatement although this effort results in lower pollution only if public incentives are strong enough, suggesting a complementarity relationship between standardized EMS and public policies. Emission charges have both a marginal effect on abatement and a qualitative effect on the adoption decision that may induce a conflict between private and public interests. As a result of the combination of these two effects it can be optimal for the government to distort the tax in a specific way in order to push the firm to choose the socially optimal EMS. The introduction of standardized systems can result in win-win situations where firms, society and the environment get better off.