Replication and p Intervals: p Values Predict the Future Only Vaguely, but Confidence Intervals Do Much Better

ABSTRACT— Replication is fundamental to science, so statistical analysis should give information about replication. Because p values dominate statistical analysis in psychology, it is important to ask what p says about replication. The answer to this question is "Surprisingly little." In one simulation of 25 repetitions of a typical experiment, p varied from <.001 to .76, thus illustrating that p is a very unreliable measure. This article shows that, if an initial experiment results in two-tailed p = .05, there is an 80% chance the one-tailed p value from a replication will fall in the interval (.00008, .44), a 10% chance that p < .00008, and fully a 10% chance that p > .44. Remarkably, the interval—termed a p interval —is this wide however large the sample size. p is so unreliable and gives such dramatically vague information that it is a poor basis for inference. Confidence intervals, however, give much better information about replication. Researchers should minimize the role of p by using confidence intervals and model-fitting techniques and by adopting meta-analytic thinking.     

The Decision-Theoretic Lockean Thesis

Abstract

Certain philosophers maintain that there is a ‘constitutive threshold for belief’: to believe that p just is to have a degree of confidence that p above a certain threshold. On the basis of this view, these philosophers defend what is known as ‘the Lockean Thesis’, according to which it is rational to believe that p just in case it is rational to have a degree of confidence that p above the constitutive threshold for belief. While not directly speaking to the controversy over the Lockean Thesis, this paper defends the general idea behind it—namely, the thesis that there is some threshold such that it is rational to believe that p if and only if it is rational to have a degree of confidence greater than that threshold. This paper identifies the threshold in question—not with the alleged constitutive threshold for belief—but with what I call ‘the practical threshold for rational belief’. Roughly, the thesis defended here is that it is rational to believe that p if and only if it is rational to have a degree of confidence that p that rationalizes engaging in certain types of practical reasoning.     

Knowledge requires commitment (instead of belief)

Philosophical Studies - I argue that S knows that p implies that S is properly committed to the truth of p, not that S believes that p. Belief is not required for knowledge because it is possible...     

What Mary Did Yesterday: Reflections on Knowledge-wh

Reductionists about knowledge- wh hold that " s knows- wh " (e.g. "John knows who stole his car") is reducible to "there is a proposition p such that s knows that p , and p answers the indirect question of the wh -clause." Anti-reductionists hold that " s knows- wh " is reducible to " s knows that p , as the true answer to the indirect question of the wh -clause." I argue that both of these positions are defective. I then offer a new analysis of knowledge- wh as a special kind of de re knowledge.     

Conditions for the acceptance of deontic conditionals.

Recent psychological research has investigated how people assess the probability of an indicative conditional. Most people give the conditional probability of q given p as the probability of if p then q. Asking about the probability of an indicative conditional, one is in effect asking about its acceptability. But on what basis are deontic conditionals judged to be acceptable or unacceptable? Using a decision theoretic analysis, we argue that a deontic conditional, of the form if p then must q or if p then may q, will be judged acceptable to the extent that the p & q possibility is preferred to the p & not-q possibility. Two experiments are reported in which this prediction was upheld. There was also evidence that the pragmatic suitability of permission rules is partly determined by evaluations of the not-p & q possibility. Implications of these results for theories of deontic reasoning are discussed.     

Phenomenal transparency in achromatic checkerboards.

The study explored the luminance relations that determine the occurrence of achromatic transparency in phenomenal surfaces on complex backgrounds. Let the luminances of the left and right parts of a transparent surface on a bipartite background and those of the left and right parts of the bipartite background be p and q and m and n, respectively. Metelli proposed that this surface looks transparent when the rule p < q if m < n (or p > q if m > n) is satisfied, and Masin and Fukuda that it looks transparent when the inclusion rule is satisfied, that is, when p epsilon (m, q) or q epsilon (p, n). These rules also apply to achromatic checkerboards formed by one checkerboard enclosed in another checkerboard. This study shows that only the inclusion rule correctly predicted the occurrence of transparency in these checkerboards.     

Memory as a Generative Epistemic Source

It is widely assumed that memory has only the capacity to preserve epistemic features that have been generated by other sources. Specifically, if S knows (justifiedly believes/rationally believes) that p via memory at T2, then it is argued that (i) S must have known (justifiedly believed/rationally believed) that p when it was originally acquired at T1, and (ii) S must have acquired knowledge that p (justification with respect to p/rationality with respect to p) at T1 via a non-memorial source. Thus, according to this view, memory cannot make an unknown proposition known, an unjustified belief justified, or an irrational belief rational–it can only preserve what is already known, justified, or rational. In this paper, I argue that condition (i) is false and, a fortiori , that condition (ii) is false. Hence, I show that, contrary to received wisdom in contemporary epistemology, memory can function as a generative epistemic source.     

The negated conditional: a litmus test for the suppositional conditional?

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability [P(q/p)]. In this paper, the authors examine a further implication of this analysis with respect to the wide-scope negation of conditional assertions, "it is not the case that if p then q." Under the suppositional account, nothing categorically follows from the negation of a conditional, other than a second conditional, "if p then not-q." In contrast, according to the mental model theory, a negated conditional is consistent only with the determinate state of affairs, p and not-q. In 4 experiments, the authors compare the contrasting predictions that arise from each of these accounts. The findings are consistent with the suppositional theory but are incongruent with the mental model theory of conditionals.     

Conditionals and directionality: On the meaning of if vs. only if

The aim of this study was to test the predictions of the current theories of reasoning about the comprehension of conditional statements. We used two types of conditional statement that are logically equivalent: if p then q and p only if q . The model theory of reasoning considers that these conditional forms differ in their initial meaning, because the negative contingency is considered only in the p only if q form. Mental-rule theories maintain that the interpretation of p only if q depends on a rephrasing of the statement as: if not q then not p . Alternatively, a directional bias may explain the differences between if p then q and p only if q . We report three experiments that demonstrate the existence of a directional bias in the comprehension of the conditionals. The results were not predicted by either the mental-rules theories or the model theory; they could, however, be easily assimilated by the model theory.     

The probability of causal conditionals

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.     

Introspection and inference

In this paper I develop the idea that, by answering the question whether p, you can answer the question whether you believe that p. In particular, I argue that judging that p is a fallible yet basic guide to whether one believes that p. I go on to defend my view from an important skeptical challenge, according to which my view would make it too easy to reject skeptical hypotheses about our access to our minds. I close by responding to the opposing view on which our beliefs themselves constitute our only source of first-person access to our beliefs.     

Refinement of the MMPI-2 F(p) scale is not necessary: a response to Gass and Luis

Gass and Luis (2001) reported that four MMPI-2 Lie scale items contained on the F(p) scale do not measure symptom exaggeration but measure defensiveness. They hold that elimination of the four Lie scale items improves the utility of the F(p) scale in the identification of exaggeration in VA samples. To directly address the assertion that removal of the L scale items from the F(p) scale enhances the predictive validity of F(p), data derived from a previously published study where 74 psychiatric inpatients were asked to retake the MMPI-2 and either feign psychopathology or respond in an honest manner were reanalyzed. The intact F(p) scale demonstrated a stronger correlation with group membership, increased incremental validity, and superior classification rates compared with the F(p) scale without the 4 Lie scale items. Consequently, the F(p) refinement recommended by Gass and Luis is unnecessary.     

Hail the impossible: p-values, evidence, and likelihood

Significance testing based on p-values is standard in psychological research and teaching. Typically, research articles and textbooks present and use p as a measure of statistical evidence against the null hypothesis (the Fisherian interpretation), although using concepts and tools based on a completely different usage of p as a tool for controlling long-term decision errors (the Neyman-Pearson interpretation). There are four major problems with using p as a measure of evidence and these problems are often overlooked in the domain of psychology. First, p is uniformly distributed under the null hypothesis and can therefore never indicate evidence for the null. Second, p is conditioned solely on the null hypothesis and is therefore unsuited to quantify evidence, because evidence is always relative in the sense of being evidence for or against a hypothesis relative to another hypothesis. Third, p designates probability of obtaining evidence (given the null), rather than strength of evidence. Fourth, p depends on unobserved data and subjective intentions and therefore implies, given the evidential interpretation, that the evidential strength of observed data depends on things that did not happen and subjective intentions. In sum, using p in the Fisherian sense as a measure of statistical evidence is deeply problematic, both statistically and conceptually, while the Neyman-Pearson interpretation is not about evidence at all. In contrast, the likelihood ratio escapes the above problems and is recommended as a tool for psychologists to represent the statistical evidence conveyed by obtained data relative to two hypotheses.     

Luck,propositional perception,and the Entailment Thesis

Looking out the window, I see that it’s raining outside. Do I know that it’s raining outside? According to proponents of the Entailment Thesis, I do. If I see that p, I know that p. In general, the Entailment Thesis is the thesis that if S perceives that p, S knows that p. But recently, some philosophers (McDowell, in Smith (ed.) Reading McDowell on mind and world, 2002; Turri, Theoria 76(3):197–206, 2010; Pritchard, Philos Issues (Supplement to Nous) 21:434–455, 2011; Pritchard, Epistemological disjunctivism, 2012) have argued that the Entailment Thesis is false. On their view, we can see p and not know that p. In this paper, I argue that their arguments are unsuccessful.     

Material Implication and General Indicative Conditionals

This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten , provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – assumed to be merely ( p ⊃ q ) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q.     

On differentiating embarrassment from shame

Four experiments were conducted to demonstrate that embarrassment and shame are distinct emotions that result from violations of different types of internalized standards. Embarrassment results from violating one's particular persona; shame results from violating a shared, objective ideal. Subjects vividly imagined themselves in situations and indicated their emotional reactions. In Experiment I, we demonstrate that people differentiate between embarrassment and shame systematically (F(1,27) = 74.4, p < 0.001). In Experiments 2 and 3, we demonstrate that embarrassment results from violating a persona (n = 34, p < 0.001; n = 23, p < 0.001), and shame results from violating an objective ideal (n = 34, p < 0.001; n = 23, p < 0.001). In Experiment 4, we demonstrate that it is the type of standard that is violated (n = 30, p < 0.001), not whether or not the violation was intentional, that determines whether one experiences embarrassment or shame. We argue that both shame and embarrassment play an important role in maintaining personal identity.     

Letter Writing and the Performativity of Intimacy in Female Pedagogical Relations: Recuperating Derridean Amnesia,Writing Back to Madame de Maintenon

Performativity and performance of language are the subject of this re-writing of Derrida's position on the gift. Here the source of performativity is Althusser's while the source of the gift is not only Marcel Mauss, but also both the opening of Derrida's Given Time: I, Counterfeit Money and the signing through letters of Madame de Maintenon, wife of Louis XIV and founder of a school for girls. A third writing plays a role, that of a 1910 biography of Madame. The paper is a relay, a re-play of the positions of the central characters, -- Derrida and Maintenon -- and a semiology of their writings. Out of this a new gift of pedagogy is evoked in a conception of pedagogical retreat.     

Christ’s faith,doubt, and the cry of dereliction

According to accounts of the Passion, Christ cries out from the cross, “My God, my God, why have you forsaken me?” The cry, I argue, manifests that Christ lacks a belief that God is with him. Given the standard view of faith—belief that p is required for faith that p—it would follow that Christ lost his faith that God is with him just before he died. In this paper, I challenge the standard view by looking at the cognitive requirement of faith. Although faith that p requires some positive cognitive orientation toward p, that orientation need not be belief. I show that reliance is an alternative stance that fulfills the cognitive requirement of faith. Reliance aims at providing sensible guidance for action that is in accord with one’s values/ends. Thinking of the cognitive component of Christ’s faith in terms of reliance makes sense of the doubt manifested in his cry.