Median decision techniques as an alternative to the classical statistical inference test

In the research area, the criterion to test a hypothesis is frequently the distance of each subject from the mean of the distribution. This concept of distance is constantly used and re-used as a source of evidence in the search for significant contrasts with respect to models of theoretical probability. This paper proposes a number of ideas regarding the use of new distance indicators related to statistics that rely less heavily on parametric assumptions, in particular, the use of median confidence intervals. We have simulated via EXCEL different data samples for a design of two independent groups under 15 different conditions in two different situations: mean equality and mean differences. The results showed the high sensitivity of the comparison of the confidence intervals, especially if a strict decision criterion is used. However, we did not obtain good results for sensitivity. In fact, in some cases, the comparison of the confidence intervals of the mean worked better than those of median.     

Decision making, movement planning and statistical decision theory

We discuss behavioral studies directed at understanding how probability information is represented in motor and economic tasks. By formulating the behavioral tasks in the language of statistical decision theory, we can compare performance in equivalent tasks in different domains. Subjects in traditional economic decision-making tasks often misrepresent the probability of rare events and typically fail to maximize expected gain. By contrast, subjects in mathematically equivalent movement tasks often choose movement strategies that come close to maximizing expected gain. We discuss the implications of these different outcomes, noting the evident differences between the source of uncertainty and how information about uncertainty is acquired in motor and economic tasks.     

Truth and consequences of ordinal differences in statistical distributions: toward a theory of hierarchical inference

A theory is presented that establishes a dominance hierarchy of potential distinctions (order relations) between two distributions. It is proposed that it is worthwhile for researchers to ascertain the strongest possible distinction, because all weaker distinctions are logically implied. Implications of the theory for hypothesis testing, theory construction, and scales of measurement are considered. Open problems for future research are outlined.     

Ranald Macdonald and statistical inference

Ranald Roderick Macdonald (1945–2007) was an important contributor to mathematical psychology in the UK, as a referee and action editor for British Journal of Mathematical and Statistical Psychology and as a participant and organizer at the British Psychological Society's Mathematics, statistics and computing section meetings. This appreciation argues that his most important contribution was to the foundations of significance testing, where his concern about what information was relevant in interpreting the results of significance tests led him to be a persuasive advocate for the ‘Weak Fisherian’ form of hypothesis testing.     

On objectivity and subjectivity in statistical inference: A response to Mayo

In this paper we respond to the article An Objective Theory of Statistical Testing by D. G. Mayo (1983). We argue that the theory of testing developed by Mayo, NPT*, is neither novel nor objective. We also respond to the claims made by Mayo against Bayesian theory.     

A pseudoperceptual display system for investigating human statistical decision processes

A CRO display system is described in which a random sequence of dots appears on the CRO derived from a Gaussian distribution with a specified mean and standard deviation. Os are required to make judgments about the statistical parameters of the distributions.     

Beyond accuracy: Epistemic flaws with statistical generalizations

What, if anything, is epistemically wrong with beliefs involving accurate statistical generalizations about demographic groups? This paper argues that there is a perfectly general, underappreciated epistemic flaw which affects both ethically charged and uncharged statistical generalizations. Though common to both, this flaw can also explain why demographic statistical generalizations give rise to the concerns they do. To identify this flaw, we need to distinguish between the accuracy and the projectability of statistical beliefs. Statistical beliefs are accompanied by an implicit representation of the statistic's modal profile. Their modal profile determines the circumstances in which they can legitimately be projected to unobserved instances. Errors in that implicit content can be compatible with the accuracy of the “bare” statistic, whilst systematically leading to downstream errors in reasoning, in a manner which reveals an epistemic flaw with an important aspect of the belief state itself.     

Decisional separability, model identification, and statistical inference in the general recognition theory framework

Recent work in the general recognition theory (GRT) framework indicates that there are serious problems with some of the inferential machinery designed to detect perceptual and decisional interactions in multidimensional identification and categorization (Mack, Richler, Gauthier, & Palmeri, 2011). These problems are more extensive than previously recognized, as we show through new analytic and simulation-based results indicating that failure of decisional separability is not identifiable in the Gaussian GRT model with either of two common response selection models. We also describe previously unnoticed formal implicational relationships between seemingly distinct tests of perceptual and decisional interactions. Augmenting these formal results with further simulations, we show that tests based on marginal signal detection parameters produce unacceptably high rates of incorrect statistical significance. We conclude by discussing the scope of the implications of these results, and we offer a brief sketch of a new set of recommendations for testing relationships between dimensions in perception and response selection in the full-factorial identification paradigm.     

BayesSDT: Software for Bayesian inference with signal detection theory

This article describes and demonstrates the BayesSDT MATLAB-based software package for performing Bayesian analysis with equal-variance Gaussian signal detection theory (SDT). The software uses WinBUGS to draw samples from the posterior distribution of six SDT parameters: discriminability, hit rate, false alarm rate, criterion, and two alternative measures of bias. The software either provides a simple MATLAB graphical user interface or allows a more general MATLAB function call to produce graphs of the posterior distribution for each parameter of interest for each data set, as well as to return the full set of posteriorsamples.     

Beyond Structural Realism: pluralist criteria for theory evaluation

In this paper I argue that singularist approaches to solving the Pessimistic Induction, such as Structural Realism, are unacceptable, but that when a pluralist account of methodological principles is adopted this anti-realist argument can be dissolved. The proposed view is a contextual methodological pluralism in the tradition of Normative Naturalism, and is justified by appeal to meta-methodological principles that are themselves justified via an externalist epistemology. Not only does this view provide an answer to the Pessimistic Induction, it can also accommodate our strongest intuitions regarding the progress of science.