Suggestions for revised scoring of the Tower of Hanoi test

Detailed time and error analyses of the Tower of Hanoi (TOH) test was performed using four repeated assessments of eight children (ages 9-12 years), who had perceptual and problem solving deficits. The time before each move was measured. In addition to the traditionally counted time scores, new, relative time scores were computed in order to separate the planning time from the general reaction speed. New error scores were defined and sum scores of serious errors (perserative moves, illegal moves, and wrong results) and mild errors (self-corrected moves, almost performed moves, and interrupted trials) were computed. The relative planning time correlated positively with the achieved score, and negatively with the serious errors. The serious errors correlated negatively with the achieved score. The relative planning time seems to measure the quality of planning better than does the raw planning time, and it is a recommended score for TOH analysis. The value of new error scores requires additional research.     

Relationship between choice reaction time and the Tower of Hanoi test.

The aim of this study was to examine a possible relation between the speed of information processing, as measured by simple and choice visual RT, and problem-solving, as measured by the Tower of Hanoi test. For 20 normal teenagers, performing all tests, significant correlations were found between choice RT and both measures of performance on the Tower of Hanoi, number of disk moves, and time taken to complete the task. Simple RT was correlated with Completion time but not with the number of moves, while the reverse pattern was discerned for decision time. Choice movement time was also associated with both measures, but simple movement time was not. These results are consistent with the hypothesis of a common neurobiological basis to information-processing speed and executive functions.     

Tower of Hanoi: evidence for the cost of goal retrieval.

Past research on the Tower of Hanoi problem has provided clear evidence for the importance of goal-subgoal structures in problem solving. However, the nature of the traditional Tower of Hanoi problem makes it impossible to determine whether there is any special cost associated with storing or retrieving goals. A variation of the Tower of Hanoi problem is described that allows one to determine separately if there is an effect of how long a goal has to be retained on storage time or how long ago it was formed on retrieval time. This paradigm provides evidence for an effect of retention interval on retrieval time and not on storage time. An ACT-R (Adaptive Control of Thought-Rational) simulation of these data is described, which treats goal memory as no different from other memories.     

The computerized Tower of Hanoi: a new form of administration and suggestions for interpretation

A computerized version of the Tower of Hanoi with a new form of administration was administered to two different groups, 15 men and 22 women, who were university students reporting normal psychological histories, and 24 traumatically brain-injured patients (20 men and 4 women). Scores on this test for both groups can be interpreted as an index of ability to solve problems and of learning strategies. Men and women scored differently on the task, i.e., women used different strategies than men to solve problems.     

Adult Age Differences in Tower of Hanoi Performance: Influence From Demographic and Cognitive Variables

We examined performance in a five-disk version of the Tower of Hanoi (TOH) puzzle, assumed to reflect executive functioning, in population-based samples ranging in age from 35 to 85 years (N ?=?2798). Univariate analyses revealed significant age effects across three TOH measures as reflected by an age-related increase in moves to solution, a gradual slowing of performance, and an increase in rule violations with advanced age. The age-related influence was eliminated, or reduced considerably, when controlling for demographic and cognitive background variables. Across the dependent measures, Block Design and a measure of episodic memory (recall) were the consistent predictors. No effects of education were detected, while significant gender differences, favoring males, were observed for two TOH measures. Taken together, the results suggest that age-related deficits observed in TOH performance reflects an age-related impairment in visuospatial ability in addition to impairments in executive functions.     

Cross-sectional versus longitudinal age gradients of tower of Hanoi performance: the role of practice effects and cohort differences in education

We examined 5-year longitudinal changes in Tower of Hanoi (TOH) performance in a population-based sample of adults (35-85 years initially; n = 1480). An age-matched sample (n = 433) was included to estimate practice effects. The longitudinal age gradients differed substantially from the cross-sectional age gradients. This was the case even when practice effects, that were substantial in magnitude across the young/middle-aged groups, were controlled for. Instead of a continuous age-related deficit in performance from 35 and onwards, longitudinal data showed slowing of performance and increases of illegal moves past age 65. Cohort-related differences in educational attainment did not account for this discrepancy. Further analyses revealed a positive relation between practice-related gains and explicit memory of having performed the task at the first test occasion and a positive association between latent changes in TOH and Block Design, in line with cross-sectional findings. In conclusion, the results demonstrate a pattern of age-related changes indicating a late-onset decline of TOH performance and underscore the need to control for retest effects in longitudinal aging research.     

A longitudinal study of the performance of the elderly and young on the Tower of Hanoi puzzle and Rey recall

Normal performance on the Tower of Hanoi puzzle by amnesic patients has been taken as support for viewing this problem solving task as having a nondeclarative memory component. Individuals in each decade of life between the 20s and 80s were asked to solve this puzzle four times in four sessions with intersession intervals from 1 to 7 days (Davis & Keller, 1998). Participants in their 70s and 80s were significantly impaired compared to participants in their 20s and 30s. The elderly were also significantly impaired on five immediate trials of a 15 words verbal recall test. Participants were readministered these tests an average of 6.6 years later for the elderly (n = 12) and 7.7 years later for the young (n = 11). For the Tower of Hanoi, the performance of the elderly, but not the young individuals, was significantly poorer than their original performance. For the verbal recall test, no significant change over time was detected for the young or elderly participants. These findings support the view that some nondeclarative and/or problem solving tasks demonstrate as great or greater decline with age than some declarative tasks.     

The assessment of cognitive procedural learning in amnesia: why the tower of Hanoi has fallen down

The Tower of Hanoi has been widely accepted as an evaluation of cognitive procedural learning in amnesia but inconsistent findings have raised questions about the nature of the learning process involved in this task. This article presents the performance of a hippocampal amnesic, MS, who, showing poor learning across daily sessions of a formal evaluation, subsequently solved the puzzle through spontaneous use of a declarative-level strategy (the odd-even rule), suggesting that his primary approach to the task was the deployment of declarative solution-searching strategies. The presented data suggest normal learning within daily sessions, but subnormal learning across daily sessions due to the forgetting of acquired declarative information. It is suggested that tasks that are potentially solvable by an algorithm or rule, as is the Tower of Hanoi, be regarded as inappropriate for use in cognitive procedural assessments.     

Test reliability and effective test length

Measures of effective test length are developed for speeded and power tests, which are independent of the number of items in the test or of the time required for administration. These measures are used in determining reliability for (1) speeded and power tests, where a separately timed short parallel form is administered in addition to the full-length test; (2) power tests, where a subset of items is imbedded within the total test, parallel to the total test; and (3) power tests, where the subset of items is correlated with the complementary parallel subset in the test.     

Personality test reliability: correlates for older subjects

This study reports the findings of an investigation of psychological and social factors related to test-retest stability and change in scores on the Eysenck Personality Inventory given to 167 older men and women. Higher reliability coefficients on the Eysenck were associated with better scores on a measure of well being and higher levels of education.     

Artifact, bias, and complexity of assessment: the ABCs of reliability

Interobserver agreement (also referred to here as "reliability") is influenced by diverse sources of artifact, bias, and complexity of the assessment procedures. The literature on reliability assessment frequently has focused on the different methods of computing reliability and the circumstances under which these methods are appropriate. Yet, the credence accorded estimates of interobserver agreement, computed by any method, presupposes eliminating sources of bias that can spuriously affect agreement. The present paper reviews evidence pertaining to various sources of artifact and bias, as well as characteristics of assessment that influence interpretation of interobserver agreement. These include reactivity of reliability assessment, observer drift, complexity of response codes and behavioral observations, observer expectancies and feedback, and others. Recommendations are provided for eliminating or minimizing the influence of these factors from interobserver agreement.     

A neuropsychological study of dissociation in cortical and subcortical functioning in obsessive-compulsive disorder by Tower of Hanoi task

Several biological models of Obsessive-Compulsive Disorder (OCD) have focused on the roles frontal cortex and basal ganglia dysfunctions play in the expression of the disorder. From a neuropsychological point of view, previous reports have underlined the possible involvement of the prefrontal cortex in declarative functions and the basal ganglia in procedural ones. A possible dissociation of cortical and subcortical functioning has been studied using the Hanoi Tower Task to explore different neuropsychological aspects of problem-solving procedures. Our results indicate that differential cortical and subcortical dysfunctions could contribute to OCD pathophysiology and that procedural and declarative forms might be independent of each other.     

The theory of the estimation of test reliability

The theoretically best estimate of the reliability coefficient is stated in terms of a precise definition of the equivalence of two forms of a test. Various approximations to this theoretical formula are derived, with reference to several degrees of completeness of information about the test and to special assumptions. The familiar Spearman-Brown Formula is shown to be a special case of the general formulation of the problem of reliability. Reliability coefficients computed in various ways are presented for comparative purposes.     

Working memory, inhibition, and fluid intelligence as predictors of performance on Tower of Hanoi and London tasks

The contributions of working memory, inhibition, and fluid intelligence to performance on the Tower of Hanoi (TOH) and Tower of London (TOL) were examined in 85 undergraduate participants. All three factors accounted for significant variance on the TOH, but only fluid intelligence accounted for significant variance on the TOL. When the contribution of fluid intelligence was accounted for, working memory and inhibition continued to account for significant variance on the TOH. These findings support argument that fluid intelligence contributes to executive functioning, but also show that the executive processes elicited by tasks vary according to task structure.     

Tower of Hanoi performance of retarded young adults and nonretarded children as a function of solution length and goal state

Three experiments were conducted with the Tower of Hanoi task to assess problem solving ability in 6-, 7-, 8-, and 10-year-old nonretarded children and mentally retarded young adults of varying maturational ages. In Experiment 1 we gradually reduced the number of moves required for solution until subjects could solve the 3-disk tower-ending problem. Although all groups experienced difficulty with the standard 7-move problem, all but the trainable retarded group readily solved the 6-move problem. The trainable group did not reach a comparable level of success until the 4-move problem. On the 7-move problem the retarded groups performed at the level of nonretarded groups that were maturationally $\text{1}\text{1}\text{2}$ to 3 years younger. An analysis of first moves indicated that subject groups differed in the strategies they used to solve the problems. In Experiment 2, practice effects were ruled out as a source of the superior performance on the 6- than on the 7-move problem. In Experiment 3, 7- and 10-year-old nonretarded children and mentally retarded young adults did not differ on 5-move problems in which configuration of the goal states was varied. A comparison of all 5-move problems judged to have the same depth of search requirements indicated that the tower-ending problems were significantly easier to solve than the partial-tower-ending problems, which in turn were easier than the flat-ending problems. A limited depth of search capacity sets boundaries on the use of sophisticated strategies and, to a large extent, accounts for the retarded groups' maturational lag.     

PET studies of language: An assessment of the reliability of the technique

In order to understand the basis of language in the brain, we must be able to describe the neurological systems that are used in language comprehension and production. In this paper, one technique for functional neuroimaging is discussed: measurement of blood flow change using positron emission tomography (PET). Two experiments were carried out investigating the usefulness of this method. One experiment examined the intrinsic time limitations of blood flow change as a measure of cognitive activity. A second issue considered is the replicability of the results obtained using this method. A comparison of two experiments containing the same conditions suggests that the results are replicable, when the experiments and method are similar. One case is discussed where the experiments differ; it is suggested that this is due to a difference in the materials used in the experiments, and that the difference has a principled basis.