Type I, Type II, and other types of errors in pattern analysis.

C. J. Krauskopf (1991) is to be commended for calling attention to the fact that pattern analysis is subject not only to Type I errors but also Type II errors, which were not even mentioned by A. B. Silverstein (1982). There are, however, a number of points on which the authors still differ. Most notably, Krauskopf's recommendation not only fails to solve the multiple-comparisons problem, it exacerbates that problem. Other possibilities are considered, including the possibility that the assumption on which pattern analysis is based, clinical meaningfulness, is itself an error. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Type IV errors revisited.

Regards J. R. Levin and L. A. Marascuilo's (see record 1973-05774-001) conception of Type IV errors in an analysis of variance as a dubious contribution since most of the examples they cite as errors are reasonable procedures. Their use of interaction estimates rather than simple effect tests on cell means is opposed since such estimates involve subtraction of meaningless main effects and, therefore, become meaningless themselves. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A quantum theoretical explanation for probability judgment errors.

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector spaces defined by features and similarities between vectors to determine probability judgments. On the other hand, quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of (von Neumann) axioms that relax some of the classic (Kolmogorov) axioms. The quantum model is compared and contrasted with other competing explanations for these judgment errors, including the anchoring and adjustment model for probability judgments. In the quantum model, a new fundamental concept in cognition is advanced—the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. We conclude that quantum information-processing principles provide a viable and promising new way to understand human judgment and reasoning. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Type IV errors and Games.

Replies to P. A. Games's (see PA, Vol. 51:Issue 3) criticisms of the authors' conception of Type IV errors in analyses of variance. It is argued that contrasts must be congruent with the mathematical model underlying the structure of the variable, while Games appears to believe that the latent structure is relatively unimportant since the interaction and simple effects models can be combined to form a cell means model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Type IV errors and interactions.

Extends L. A. Marascuilo and J. R. Levin's notion of Type IV errors, emphasizing the interpretation of interactions in factorial analysis of variance (ANOVA) designs. To help clarify what an interaction is and what it is not in terms of the ANOVA model, it is emphasized that (a) comparisons designed to explain an interaction are acceptable only if they reduce to comparisons involving interaction parameters exclusively; and (b) such comparisons may be both specified and directional, i.e., they may be defined to test an E's a priori hypotheses. (17 ref.) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Protecting the overall rate of Type I errors for pairwise comparisons with an omnibus test statistic.

Compares 2 procedures for protecting the number of false rejections for a set of all possible pairwise comparisons. The 2-stage strategy of computing pairwise comparisons, conditional on a significant omnibus test, is compared with the multiple comparison strategy that sets a "familywise" critical value directly. The ANOVA test, the Brown and Forsythe test, and the Welch omnibus test, as well as 3 procedures for assessing the significance of pairwise comparisons, are combined into 9 2-stage testing strategies. The data from this study establish that the common strategy of following a significant ANOVA F with Student's t tests on pairs of means results in a substantially inflated rate of Type I error when variances are heterogeneous. Type I error control, however, can be obtained with other 2-stage procedures, and the authors tentatively consider the Welch F″ Welch t″ combination desirable. In addition, the 2 techniques for controlling Type I error do not substantially differ as much as might be expected; some 2-stage procedures are comparable to simultaneous techniques. (18 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multiple testing and Type I errors: A reply in defense of multifactor designs.

Comments on R. Udolf and B. Raymond's (1973) article on multivariate analysis of variance (MANOVA) and confidence levels. Keselman argues that their article is a cursory and misleading presentation of the problem of the relationship between multiple testing and the Type I level of significance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Distributional versus singular approaches to probability and errors in probabilistic reasoning.

Four experiments examined differences in probabilistic reasoning as a function of whether problems were presented in a frequentist or case-specific form. The experiments demonstrated that these different forms influence the likelihood of Ss committing the conjunction and disjunction fallacies. The authors contend that these 2 forms elicit different approaches to probability. Frequency problems, it is argued, elicit a distributional approach in which probabilities are equated with relative frequencies, whereas case-specific problems elicit a singular approach in which probabilities are equated with the propensities or causal forces operating in an individual case. According to this account, distributional and singular approaches evoke different kinds of inferential rules and heuristic procedures, some of which are more closely aligned with extensional principles than others. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Meta-analysis for integrating study outcomes: A Monte Carlo study of its susceptibility to Type I and Type II errors.

AMonte Carlo study was conducted to determine Types I and II error rates of the Schmidt and Hunter (S&H) meta-analysis method and the U statistic for assessing homogeneity within a set of correlations. One thousand samples of correlations were generated randomly to fill each of 450 cells of an 18?×?5?×?5 (Underlying Population Correlations?×?Numbers of Correlations Compared?×?Sample Size Per Correlation) design. To assess Type I error rates, correlations were drawn from the same population. To assess power, correlations were drawn from two different populations. As compared with U, which was uniformly robust, the Type I error rate for the S&H method was unacceptably high in many cells, particularly when the criterion for determining homogeneity was set at a highly conservative level. Power for the S&H method increased with increasing size of population differences, sample size per correlation, and in some cases, number of correlations compared. The U statistic did more poorly in most conditions in protecting from Type II errors. (14 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the self-erasing nature of errors of prediction.

82 female undergraduates were assigned to 1 of 4 experimental groups—predict-request, information-request, predict only, and request only—in which requested tasks involved writing a counterattitudinal essay or singing over the telephone. In 3 experiments, Ss overpredicted the degree to which their behavior would be socially desirable and these errors of prediction proved to be self-erasing. Having mispredicted a given behavior, Ss were likely to have these predictions confirmed in later behavior, indicating that prediction of a behavioral sequence evokes a specific cognitive representation of that sequence which is subsequently accessed. Results demonstrate the strong effects on behavior of engaging in prebehavioral cognitive work. (27 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Type I and Type II Bias.

Errors in research do occur. Their prevalence should be viewed with alarm rather than passive acceptance as an essential concomitant of humans conducting research. The author looks at the discussion of errors in an article by Leroy Wolins (Amer. Psychologist, 1962, 17, 657-658) and an article by Emanuel Berger (Amer. Psychologist, 1962, 17, 657). The first article suggests that we may be quite unaware of the large proportion of the iceberg (erroneous research results) which is never perceived or reanalyzed. The second article pleads for experimental evaluation of research results. It would seem as though these two articles are both positively and negatively related. On the one hand, subjective evaluation and interpretation of research results may possibly expose inadvertent errors in computations (or in design, sampling, etc.). Thus, results which do not readily blend with an already established nomological network might call for statistical recomputations. On the other hand, subjective evaluation can become quite blinding when one identifies with or strongly favors certain results. In such cases, errors in computation would never be suspected, much less discovered. The author discusses experimental errors further, taking a look at Type I and Type II bias. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the probability of Neanderthal ancestry

PURPOSE: We describe a method to reduce the number of shocks necessary to fragment renal stones during extracorporeal shock wave lithotripsy by automatically taking into account stone movements. MATERIALS AND METHODS: Echotrack computer software was developed and implemented on a lithotriptor. One software module uses image processing to detect instantaneous stone location based on ultrasound images generated by the lithotriptor. A second module uses the detected location to control the shock wave generator position, and automatically adjusts it to improve coincidence between the focal volume and stone. The reliability of the tracking algorithm was clinically tested in 65 patients with renal stones. These in vivo tests were qualitative and the goal was to assess software ability to track stones during actual treatments. A quantitative evaluation of the reduction in shocks necessary for fragmentation was performed in vitro. Artificial stones were moved according to computer generated trajectories. Each trajectory was applied once with and once without automatic adjustment of the generator position. RESULTS: The in vivo tests demonstrated software ability to track stones as far as they were visible in the images. During in vitro tests automatic adjustments of the generator position reduced the number of shocks necessary to fragment stones completely by a factor of 1.64. CONCLUSIONS: Image based renal stone tracking software that automatically adjusts the shock wave generator position according to the displacement of renal stones is useful during extracorporeal shock wave lithotripsy. Treatment time was significantly shorter with this software.     

Anchoring errors in clinical judgments: Type I error, adjustment, or mitigation?

The nature of anchoring errors in clinical judgments was clarified. Study 1 tested if gender mediates the occurrence of anchoring errors. Judgments from 103 undergraduate psychology students evidenced neither anchoring errors nor gender differences. Given the inability to replicate M. L. Friedlander and S. J. Stockman's (see record 1983-31114-001) study, two rival hypotheses were advanced: the adjustment hypothesis (practitioners adjust appropriately their clinical judgments after receiving new client information) and the adjustment mitigation hypothesis (initial anchoring effects are mitigated by an adjustment effect). The judgments from 157 psychologists in Study 2 affirmed the adjustment and mitigation hypotheses over the anchoring hypothesis alone. The mitigation process appears adaptable in clinical judgments. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the functional relationship between word identification and letter probability.

Investigated whether words made up of probable letters and probable letter combinations are more accurately recognized than words made up of improbable letters and improbable letter combinations. The experimental method corrected shortcomings in previous research which has shown accuracy of word recognition to be affected only by word probability and not by letter probability. The shortcomings were the confounding of different letter probability dimensions within one another. In the present investigation with 40 19-43 yr old adults, 100 words were assessed with respect to the probabilities of their letters and, independently, the conditional probabilities of their letters. Subsequent tests of recognition accuracy in a brief presentation showed accuracy to be greatest for words made up of letters having either high simple probabilities or high conditional probabilities. It is concluded that word recognition is an active, perhaps serial, process which makes liberal use of individual letter statistics to facilitate accurate recognition. (French summary) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multiplicity, directional (Type III) errors, and the Null Hypothesis.

L. V. Jones and J. W. Tukey (2000) pointed out that the usual 2-sided, equal-tails null hypothesis test at level ot can be reinterpreted as simultaneous tests of 2 directional inequality hypotheses, each at level α/2, and that the maximum probability of a Type I error is α/2 if the truth of the null hypothesis is considered impossible. This article points out that in multiple testing with familywise error rate controlled at ot, the directional error rate (assuming all null hypotheses are false) is greater than α/2 and can be arbitrarily close to α. Single-step, step-down, and step-up procedures are analyzed, and other error rates, including the false discovery rate, are discussed. Implications for confidence interval estimation and hypothesis testing practices are considered. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multivariate analysis and the problem of Type I error.

Discusses the recommendation by M. R. Leary and E. M. Altmaier (see record 1981-02539-001) that MANOVA should be used with several dependent variables in order to control for overall Type I error rate. This paper calls attention to limitations and dangers in routine application of MANOVA, describes some alternative procedures, and laments the necessarily pervasive character of the problem of statistical error. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the making of new men: Some extrapolations from research.

Analyzes Soviet and American patterns of socialization and their effects. Results indicate that Soviet society devotes more attention to problems of child rearing than does that of the United States, where socialization is disrupted by an accelerating trend toward segregation by age, contributing to increasing alienation, apathy, and juvenile delinquency. As a basis for developing appropriate countermeasures, research literature is presented regarding the major forces which shape the behavior and development of the child. Practical implications of these principles are examined in the contexts of family, school, and community. (French summary) (17 ref.) (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Statistical methods in epidemiology: I. Statistical errors in hypothesis testing

PURPOSE: Although scientific journal editors are making use of statisticians in the review process, the quality of statistical reporting in many journals remains poor. In many cases the problem for the scientist would appear to be a lack of understanding of basic statistics. The focus of the scientist is on showing 'p < 0.05', when what is actually required is a statement about effect size and interval estimation. The aim of this paper is to show the inadequacy of reporting of results using p-values alone. This paper is the first in a series detailing common statistical methods, with a view to aiding potential authors in their statistical presentation of data. METHOD: A review of the basic hypothesis test, using examples from the author's own teaching experiences. RESULTS: Type I and type II errors are defined; the problem of multiple comparisons is highlighted; interval estimation is introduced. CONCLUSIONS: The case for considering the p-value as an error probability is made which suggests ways of improving statistical presentation and thus expediting the statistical review process.