A Nonrandomized,Nonconservative Version of the Fisher Exact Test

The Fisher exact test has been unjustly dismissed by some as ‘only conditional,’ whereas it is unconditionally the uniform most powerful test among all unbiased tests, tests of size α and with power greater than its nominal level of significance α. The problem with this truly optimal test is that it requires randomization at the critical value(s) to be of size α. Obviously, in practice, one does not want to conclude that ‘with probability x the we have a statistical significant result.’ Usually, the hypothesis is rejected only if the test statistic's outcome is more extreme than the critical value, reducing the actual size considerably.

The randomized unconditional Fisher exact is constructed (using Neyman–structure arguments) by deriving a conditional randomized test randomizing at critical values c(t) by probabilities γ(t), that both depend on the total number of successes T (the complete-sufficient statistic for the nuisance parameter—the common success probability) conditioned upon.

In this paper, the Fisher exact is approximated by deriving nonrandomized conditional tests with critical region including the critical value only if γ (t) > γ₀, for a fixed threshold value γ₀, such that the size of the unconditional modified test is for all value of the nuisance parameter—the common success probability—smaller, but as close as possible to α. It will be seen that this greatly improves the size of the test as compared with the conservative nonrandomized Fisher exact test.

Size, power, and p value comparison with the (virtual) randomized Fisher exact test, and the conservative nonrandomized Fisher exact, Pearson's chi-square test, with the more competitive mid-p value, the McDonald's modification, and Boschloo's modifications are performed under the assumption of two binomial samples.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

Underestimating busyness: Indications of nonresponse bias due to work-family conflict and time pressure

International research shows that both work-family conflict and time pressure are increasing in Western societies. With these increased pressures, precisely those people who are combining work and family obligations may be missing from survey estimates. This study investigates whether the measurement of work-family conflict (WFC) and time pressure is influenced by nonresponse bias. Using the Flemish “Work, Family and Time use in Flanders”-survey and the Basic Question survey for nonrespondents of this survey, we investigate whether nonrespondents score higher on subjective and objective indicators of WFC and time pressure than respondents. Results show that nonrespondents are indeed those sample units who experience significantly more WFC and time pressure, demonstrating that WFC and time pressure related nonresponse biases exist. Implications and suggestions to reduce bias in data collections are discussed.     

Income inequality and participation: A comparison of 24 European countries

Previous research suggests that when there is a high level of inequality, there is a low rate of participation. Two arguments are generally offered: First, inequality depresses participation because people from different status groups have fewer opportunities to share common goals. Second, people may participate more in civic and social life when they have more resources. However, until now, these explanations have not been separated empirically. Using EU-SILC data for 24 European countries, we analyze how income inequality is related to civic and social participation. Our results indicate that the main effects of inequality manifest via resources at the individual and societal level. However, independent of these resources, higher inequality is associated with lower civic participation. Furthermore, inequality magnifies the relationship between income and participation. This finding is in line with the view that inter-individual processes explain why inequality diminishes participation.     

Foreign-born emigration: A new approach and estimates based on matched CPS files

The utility of postcensal population estimates depends on the adequate measurement of four major components of demographic change: fertility, mortality, immigration, and emigration. Of the four components, emigration, especially of the foreign-born, has proved the most difficult to gauge. Without "direct" methods (i.e., methods identifying who emigrates and when), demographers have relied on indirect approaches, such as residual methods. Residual estimates, however are sensitive to inaccuracies in their constituent parts and are particularly ill-suited for measuring the emigration of recent arrivals. Here we introduce a new method for estimating foreign-born emigration that takes advantage of the sample design of the Current Population Survey (CPS): repeated interviews of persons in the same housing units over a period of 16 months. Individuals appearing in a first March Supplement to the CPS but not the next include those who died in the intervening year, those who moved within the country, and those who emigrated. We use statistical methods to estimate the proportion of emigrants among those not present in the follow-up interview. Our method produces emigration estimates that are comparable to those from residual methods in the case of longer-term residents (immigrants who arrived more than 10 years ago), but yields higher--and what appear to be more accurate--estimates for recent arrivals. Although somewhat constrained by sample size, we also generate estimates by age, sex, region of birth, and duration of residence in the United States.