A simple duality principle in test theory

It is demonstrated that theorems in test theory have corresponding dual theorems which are obtained by exchanging true scores and error scores, as well as reliability coefficients and their complements, in both the hypothesis and the conclusion. A formula that does not conform to the principle cannot be an identity in the test-theory model, but must be based on additional assumptions in the hypothesis tht perhaps are not immediately apparent. The usefulness of this principle is indicated, and its origin in the mathematical formalism underlying the theory is discussed.     

Processing of natural images is feedforward: A simple behavioral test

Natural images can be classified so rapidly that it has been suggested that their analysis is based on a first single pass of processing activity through the visuomotor system. We tested this theory in a visuomotor priming task in which speeded pointing responses were performed toward one of two target images containing a prespecified stimulus (e.g., animal vs. nonanimal, ellipse vs. rectangle). Target pictures were preceded by prime pictures of the same or an opposite category, linked to either the same or an opposite pointing response. We found that pointing trajectories were initially controlled by the primes alone, but independently of information in the actual targets. Our data indicate that prime and target signals remained strictly sequential throughout all processing stages, meeting unprecedentedly stringent behavioral criteria for feedforward processing (rapid-chase criteria). Our findings suggest that visuomotor priming effects capture the output of the very first pass of information through the visuomotor system, before output is affected by recurrent information.     

A comparison of three simple test theory models

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of minimal models available to test analysts.This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.     

A simple syllogism-solving test: Empirical findings and implications for g research

It has been reported that the ability to solve syllogisms is highly g-loaded. In the present study, using a self-administered shortened version of a syllogism-solving test, the BAROCO Short, we examined whether robust findings generated by previous research regarding IQ scores were also applicable to BAROCO Short scores. Five syllogism-solving problems were included in a questionnaire as part of a postal survey conducted by the Keio Twin Research Center. Data were collected from 487 pairs of twins (1021 individuals) who were Japanese junior high or high school students (ages 13–18) and from 536 mothers and 431 fathers. Four findings related to IQ were replicated: 1) The mean level increased gradually during adolescence, stayed unchanged from the 30s to the early 50s, and subsequently declined after the late 50s. 2) The scores for both children and parents were predicted by the socioeconomic status of the family. 3) The genetic effect increased, although the shared environmental effect decreased during progression from adolescence to adulthood. 4) Children's scores were genetically correlated with school achievement. These findings further substantiate the close association between syllogistic reasoning ability and g.     

Children read normal and reversed letters: A simple test of reading skill

Above- and below-average readers in grades 3, 5 and 7 named letters under two conditions. In one condition, letters were presented in normal orientation. In the other condition, letters were presented in left-right mirror image orientation. The ratio of (1) naming time on normal letters to (2) naming time on mirror image letters was calculated for each child. Good readers had lower ratios than poor readers. This was due primarily to the faster naming of normal letters by good readers. Good and poor readers named mirror image letters at similar speeds. Two possible explanations for the results are discussed. One explanation is that the skilled readers have a better memory for the normal orientation of the letter shapes. A second explanation is that skilled readers process more peripheral information, when naming, than their less skilled counterparts, but that this peripheral processing is curtailed when transformed text is presented.     

Emotional triangles: A test of emotion-based attentional capture by simple geometric shapes

Previous work has proposed that simple geometric shapes, carrying the features present within negative or threatening faces are especially effective at capturing or guiding attention. Here we test this account and provide converging evidence for a threat-based attentional advantage. Experiment 1 found that downward-pointing triangles continue to be detected more efficiently than upward-pointing triangles when: (i) both overall RT and search slope measures are obtained; and (ii) when the set size is varied and the stimuli are presented in random configurations. Experiment 2 tested and ruled out an alternative account of the selection advantage, based on differences between triangle shape consistencies with scene perspective cues. Overall, the data provide converging evidence that simple geometric shapes, which might be particularly important in providing emotional signals in faces, can also attract attention preferentially even when presented outside of a face context.     

A simple scoring weight for test items and its reliability

It is pointed out that the scoring weights for test items should be approximations to regression-equation weights. For this reason any estimate of reliability of the weight should not be permitted to influence the size of the weight but should be used in determining the limit of acceptability of an item. A simple approximation weight is recommended for general use, and anabac is provided for the estimation of it when the correlation between item and criterion is the phi coefficient. A formula for the standard error of this weight is derived and tables of significant and very significant weights are presented in terms of deviations from the median weight.     

A free and simple computerized screening test for visual field defects

About 30–40% of stroke patients suffer from visual field defects following injury. These can interfere with the standard neuropsychological assessment and complicate the interpretation of tests that use visual materials. However, information about the integrity of a patient's central visual field is often unavailable. We, therefore, designed a screening tool, the computerized visual field test (c‐VFT), specifically targeted at providing easily available, but rough, information about patients' central visual field. c‐VFT was tested in two samples of stroke patients. Eleven patients were tested on c‐VFT and on the Esterman test. Five patients were tested on c‐VFT and the Humphrey Visual Field Analyzer (HFA), central 10‐2. Criterion validity of the c‐VFT was investigated by calculating quadrantwise intraclass correlation for both comparisons. For the HFA comparison, we also calculated point‐to‐point intraclass correlation, sensitivity, and specificity. Analyses revealed moderately good correspondence between c‐VFT and the Esterman test, and between c‐VFT and HFA 10‐2, respectively. When looking specifically at test points within one degree of visual angle apart in the two tests, intraclass correlation increased. For these points, the sensitivity of c‐VFT was 0.89 and specificity was 0.97. While the c‐VFT is not designed to be diagnostic nor to replace the detailed visual field analysis, this study shows that it provides a reasonable screening of the central visual field. The test can easily be used and will be made freely available to neuropsychological clinicians and researchers.     

A simple test for heterogeneity of variance in complex factorial designs

A simple procedure for testing heterogeneity of variance is developed which generalizes readily to complex, multi-factor experimental designs. Monte Carlo Studies indicate that the Z-variance test statistic presented here yields results equivalent to other familiar tests for heterogeneity of variance in simple one-way designs where comparisons are feasible. The primary advantage of the Z-variance test is in the analysis of factorial effects on sample variances in more complex designs. An example involving a three-way factorial design is presented.     

A simple proof of the spearman-brown formula for continuous test lengths

A direct proof is given for the generalized Spearman-Brown formula for any real multiple of test length.     

A simple but powerful test of perseverative search in dogs and toddlers

Perseverative (A-not-B) errors during the search of a hidden object were recently described in both dogs and 10-month-old infants. It was found that ostensive cues indicating a communicative intent of the person who hides the object played a major role in eliciting perseverative errors in both species. However, the employed experimental set-up gave rise to several alternative explanations regarding the source of these errors. Here we present a simplified protocol that eliminates the ambiguities present in the original design. Using five consecutive object hiding events to one of two locations in a fixed order (“AABBA”), we tested adult companion dogs and human children (24 months old). The experimenter performed the hiding actions while giving ostensive cues in each trial and moved the target object to the given location in a straight line. Our results show that in the B trials, both 24-month-old children and dogs could not reliably find the hidden object, and their performance in the first B trials was significantly below that of any of the A trials. These results are the first to show that the tendency for perseverative errors in an ostensive-communicative context is a robust phenomenon among 2-year-old children and dogs, and not the by-product of a topographically elaborate hiding event.     

A simple and powerful test for autocorrelated errors in OLS intervention models

The important assumption of independent errors should be evaluated routinely in the application of interrupted time-series regression models. The two most frequently recommended tests of this assumption [Mood's runs test and the Durbin-Watson (D-W) bounds test] have several weaknesses. The former has poor small sample Type I error performance and the latter has the bothersome property that results are often declared to be "inconclusive." The test proposed in this article is simple to compute (special software is not required), there is no inconclusive region, an exact p-value is provided, and it has good Type I error and power properties relative to competing procedures. It is shown that these desirable properties hold when design matrices of a specified form are used to model the response variable. A Monte Carlo evaluation of the method, including comparisons with other tests (viz., runs, D-W bounds, and D-W beta), and examples of application are provided.     

Independence and nonindependence: A simple method for comparing groups using multiple measures and the binomial test

Existing methods for conducting analyses of small group data are either highly complicated or yield low power. Both of these limitations provide disincentives for the progress of research in this field. An alternative method modelled on the sign (binomial) test which involves comparing the differences of distributions based on multiple observations of each of the groups is presented. The calculations involved in the procedure are extremely simple. It is suggested that because the method enhances researchers' ability to make sound statistical inferences easily this should stimulate research on group‐level processes and on social interaction more generally. Copyright © 2004 John Wiley & Sons, Ltd.     

Aparametric investigation of multiletter matches

Proctor (1981) presented a theoretical framework that distinguishes factors contributing to disparities in time to classify physical-same, name-same, and different letter pairs as a function of three variables: method of presentation (simultaneous vs. successive), case relationship (samecase vs. opposite-case pairs), and blocking (blocked vs. mixed presentation of same-case and opposite-case pairs). He also argued that these variables were critical in multIletter matches, and performed a between-study comparison of existing data to support his contention. Because comparison across studies is always a tenuous process and because the absence of several relevant conditions precluded a complete analysis of predictions, a within-experiment manipulation of the three relevant variables was desirable. The present study reports such an experiment. In general, the factorial manipulation of variables supported predictions of Proctor’s framework and indicated that many phenomena of multiletter matching, including the widely studied fast-“same” phenomenon, are attributable primarily to differences in the rate at which component letter pairs are matched.     

Measurement of active rotation in standing: reliability of a simple test protocol

Interrater and intrarater reliability were evaluated for a test measuring active rotation range in a standing position. Subjects stood with their feet comfortably apart while a horizontal bar rested on their shoulders. A plumb bob attached to the end of the bar was allowed to drop to the floor, indicating maximal rotation range achieved. Two raters measured 24 subjects (M age = 35 +/- 14 yr.), who were sedentary office workers and active recreational golfers, on two occasions separated by two weeks to obtain values for left and right trunk rotation range. The test had good intrarater and interrater reliabilities, with standard error of measurement values varying from 5.6 degrees to 8.6 degrees against an overall mean range of 128 degrees. This simple active rotation test requires inexpensive equipment and could be incorporated into clinical examinations when there is a need to assess active rotation in standing with minimal constraints.     

Emotional triangles: a test of emotion-based attentional capture by simple geometric shapes

Previous work has proposed that simple geometric shapes, carrying the features present within negative or threatening faces are especially effective at capturing or guiding attention. Here we test this account and provide converging evidence for a threat-based attentional advantage. Experiment 1 found that downward-pointing triangles continue to be detected more efficiently than upward-pointing triangles when: (i) both overall RT and search slope measures are obtained; and (ii) when the set size is varied and the stimuli are presented in random configurations. Experiment 2 tested and ruled out an alternative account of the selection advantage, based on differences between triangle shape consistencies with scene perspective cues. Overall, the data provide converging evidence that simple geometric shapes, which might be particularly important in providing emotional signals in faces, can also attract attention preferentially even when presented outside of a face context.     

On predicting exponents for cross-modality matches

Mashhour and Hosman used magnitude estimations to scale seven continua: line length, time duration, finger span, loudness of noise, weight, gray reflectance, and surface area. The first four continua also served as the adjusted stimuli in 17 cross-modality matches among the various continua. Contrary to the view expressed by Mashhour and Hosman, the results appear to support the psychophysical power law. A reanalysis of the data shows that the exponents of the power functions obtained in cross-modality matches agree with the exponents of the power functions produced by magnitude estimations, provided correction is made for the regression effect. The measured discrepancies between the exponents predicted and those actually obtained show scatter that is consistent with that of other experiments. In particular, the scatter accords well with the distribution of 68 exponents predicted by Moskowitz from experiments in which Os matched both number and loudness to various taste concentrations.     

A simple and effective decision rule for choosing a significance test to protect against non-normality

There is no formal and generally accepted procedure for choosing an appropriate significance test for sample data when the assumption of normality is doubtful. Various tests of normality that have been proposed over the years have been found to have limited usefulness, and sometimes a preliminary test makes the situation worse. The present paper investigates a specific and easily applied rule for choosing between a parametric and non-parametric test, the Student t test and the Wilcoxon-Mann-Whitney test, that does not require a preliminary significance test of normality. Simulations reveal that the rule, which can be applied to sample data automatically by computer software, protects the Type I error rate and increases power for various sample sizes, significance levels, and non-normal distribution shapes. Limitations of the procedure in the case of heterogeneity of variance are discussed.