General solution of the analysis of variance and covariance in the case of unequal or disproportionate numbers of observations in the subclasses

In this paper a preview of the problem is given. Then the mathematical solutions of estimating the sums of squares and products of different sources of variation under different assumptions are presented. Two kinds of populations from which our samples are supposed to be drawn are specified. One is defined as possessing approximately the same stratification as our sample; while the other is defined as having equal frequencies in the subclasses. For the first kind of population, we should use the restrictions of the weighted means. For the second kind, we should use the restrictions of the unweighted means. The assumptions of zero interactions and significant interactions are also considered. After working out the exact method, two approximate methods with appropriate statistical assumptions to be fulfilled are given.For a more complete account, see:Fei Tsao, General solution of the analysis of variance and covariance in the case of unequal or disproportionate numbers of observations in the subclasses. Ph.D. Thesis, University of Minnesota, 1945. Pp. 120.     

Note on the scaling of ratings or rankings when the numbers per subject are unequal

The average rating (or normalized rank) of a person rated by a larger number of judges will in general be closer to the group average than will the average rating of a person rated by a smaller number of judges, as a result of rating unreliability and regression. This note presents a technique for correcting that bias.     

Tests of two hypotheses on extraversion

Three samples give mixed results on a hypothesis that higher extraversion is associated with greater tendency to assume similarity between oneself and others. Results consistently support a second hypothesis that group judgements of the socially desirable personality on an American college campus will show that personality to be highly extraverted. The average actual student is in fact substantially less extraverted than what is considered desirable. These findings are discussed in terms of possible tensions produced by the discrepancy between the ideal and the real.     

Tests of three hypotheses regarding the predictors of delinquency

Three hypotheses regarding the predictors of criminal activity in children and adolescents were assessed. These dealt with family, peer, and attitudinal variables, and they were explored in relation to indices based on seriousness of criminal activity and reoffending. The data were based on a sample of 338 youths who had been convicted of crimes and received probation or custody dispositions. The results provided general support for a model implicating family, peer, and attitudinal variables in youthful criminal activity. They did not, however, provide support for hypothesized interactions between family relationship and family structuring dimensions or between family relationship and peer association variables. The results did support an hypothesis regarding the independent contribution of an antisocial attitudes variable to the prediction of criminal activity.Funding to support this research was provided by the Children's Services Branch of the Ministry of Community and Social Services (Ontario), Carleton University, and the London Family Court Clinic. Thanks are extended to Penny Faulkner, Mary Ann Robblee, Suzanne Bell, and Natalie Gabora for their assistance on the project. Members of the Ministry Research Advisory Committee are also thanked for their contribution.     

Some observations and hypotheses about the psychoanalytic theory of adult development.

The developmental framework, when applied to adulthood, emphasizes the continuing evolution of the personality at five or fifty and 'focuses on the formation of psychic structure in process and underscores the continuity of normal and pathologic outcomes.' (COPER 9, 1974, p. 14). Many of the events we have discussed here are experiences unique to the adult and outside the realm of the child. Their uniqueness and developmental significance need to be better accounted for in psychoanalytic theory. Confrontation with each adult developmental task or crisis produces basic change in the life of each individual. To quote Bibring (1959): 'We find them as developmental phenomena at points of no return between one phase and the next when decisive changes deprive former central needs and modes of living of their significance forcing the acceptance of highly charged new goals and functions.' (p. 119). One purpose of this paper has been to demonstrate that such developmental turning points of no return are not limited to childhood but occur throughout the life cycle.     

Signal detectability in the presence of monotic or dichotic noise bands of equal or unequal levels

The application of the power-spectrum model of masking to the detectability of a signal masked by dichotic noise was investigated in three experiments. In each experiment, the signal was a 2-kHz sinusoid of 400-msec duration, masked by either one or two 800-Hz wide bands of noise presented singly or in pairs. In Experiment 1, we compared the detectability of a diotic signal masked by dichotic noise with the detectability of a monaural signal masked by each of the noises separately. The spectrum level of the noise was 35 dB SPL. For dichotic presentations, the signal was sent to both ears while pairs of noise bands, one below and one above the signal frequency, were presented together, one band to each ear. Threshold levels with the dichotic stimuli were lower than or equal to the thresholds with either ear's stimulus on its own. Similar dichotic stimuli were used in Experiment 2, except that the signal frequency was nearer to one or the other of the bands of masking noise, and the noise had a spectrum level of 50 dB SPL. In Experiment 3, thresholds were obtained with two sets of symmetrically and asymmetrically placed notched-noise maskers. For one of these sets, the spectrum level of both noise bands was 35 dB SPL; for the other set, interaural intensity differences were introduced in the form of an inequality in the levels of the noise bands on either side of the signal. In one ear, the spectrum level of the lower frequency noise band was 35 dB SPL and the spectrum level of the higher frequency noise band was 25 dB SPL, whereas in the other ear, the allocation of noise level to noise band was reversed. The dichotic thresholds obtained with the unequal noise maskers could be predicted from the shapes of the auditory filters derived with equal noise maskers. The data from all three experiments suggest that threshold signal levels in the presence of interaural differences in masker intensity depend principally on the ear with the higher signal-to-masker ratio at the output of its auditory filter, a finding consistent with the power-spectrum model of masking.     

The within-list distributed practice effect: Tests of the varied context and varied encoding hypotheses

The present studies provided separate tests of the varied context and varied encoding hypotheses of the MP-DP effect. The investigation of varied encoding used an incidental learning procedure in which the nature of the orienting task was manipulated such that the subject attended to different attributes of words (varied encoding) or only one attribute (same encoding). While the prediction that the recall of MP-DP items should be comparable under comparable levels of encoding was not supported, differences were obtained in recall of items under same and variable orienting task conditions. An MP-DP effect was obtained under the incidental learning procedure. Tests of varied context involved the presentation of target items in list contexts which were the same or different from list contexts on previous occurrences of the item. The prediction that recall of items surrounded by different context should exceed that of items surrounded by the same context was not supported.     

Power of pairwise comparisons in the equal variance and unequal sample size case

A Monte Carlo simulation was conducted to compare five, pairwise multiple comparison procedures. The number of means varied from 4 to 6 and the sample size ratio varied from 1 to 60. Procedures were evaluated on the basis of Type I errors, any‐pair power and all‐pairs power. Four procedures were shown to be conservative, while the fifth provided adequate control of Type I errors only for restricted values of sample size ratios. No procedure was found to be uniformly most powerful. The Tukey‐Kramer procedure was found to provide the best any‐pair power provided it is applied without requiring a significant overall F test. In most cases, the Hayter‐Fisher modification of the Tukey‐Kramer was found to provide very good any‐pair power and to be uniformly more powerful than the Tukey‐Kramer when a significant overall F test is required. A partition‐based version of Peritz's method usually provided the greatest all‐pairs power. A modification of the Shaffer‐Welsch was found to be useful in certain conditions.     

Towards refinement of abductive or inductive hypotheses through propagation

In this paper we address the problem of distributed sources of information, or agents, that observe the environment locally and have to communicate in order to refine their hypothesis regarding the actual state of this environment. One way to address the problem would be to centralize all the collected observations and knowledge, and to centrally compute the resulting theory. In many situations however, it would not be possible to adopt this centralized approach (e.g. for practical reasons, or privacy concerns). In this paper, we assume that agents individually face abductive or inductive tasks in a globally coherent environment, and we show that general mechanisms can be designed that abstractly regard both cases as special instances of a problem of hypothesis refinement through propagation. Assuming that agents are equipped with some individual revision machinery, our concern will be to investigate how (under what conditions) convergence to a consistent state can be guaranteed at more global levels: (i) between two agents; (ii) in a clique of agents; and (iii) in general in a connected society of agents.     

A reanalysis of Lord’s statistical treatment of football numbers

Stevens’ theory of admissible statistics [Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677680] states that measurement levels should guide the choice of statistical test, such that the truth value of statements based on a statistical analysis remains invariant under admissible transformations of the data. Lord [Lord, F. M. (1953). On the statistical treatment of football numbers. American Psychologist, 8, 750-751] challenged this theory. In a thought experiment, a parametric test is performed on football numbers (identifying players: a nominal representation) to decide whether a sample from the machine issuing these numbers should be considered non-random. This is an apparently illegal test, since its outcomes are not invariant under admissible transformations for the nominal measurement level. Nevertheless, it results in a sensible conclusion: the number-issuing machine was tampered with. In the ensuing measurement-statistics debate Lord’s contribution has been influential, but has also led to much confusion. The present aim is to show that the thought experiment contains a serious flaw. First it is shown that the implicit assumption that the numbers are nominal is false. This disqualifies Lord’s argument as a valid counterexample to Stevens’ dictum. Second, it is argued that the football numbers do not represent just the nominal property of non-identity of the players; they also represent the amount of bias in the machine. It is a question about this property-not a property that relates to the identity of the football players-that the statistical test is concerned with. Therefore, only this property is relevant to Lord’s argument. We argue that the level of bias in the machine, indicated by the population mean, conforms to a bisymmetric structure, which means that it lies on an interval scale. In this light, Lord’s thought experiment-interpreted by many as a problematic counterexample to Stevens’ theory of admissible statistics-conforms perfectly to Stevens’ dictum.     

Etiological hypotheses in a time-series case study of multiple behavior problems

A 15-year-old male was treated over a 20-month period for multiple behavior problems, including social isolation, family conflict, classroom behavior problems, scholastic underachievement, and impulsivity. Initial assessment data suggested that the problems were the result of a complex, interacting set of environmental, cognitive, and psychophysiological factors. Treatment was delivered and validated using a time-series design to test hypotheses generated by etiological theory. Discussion addresses the need for better use of psychopathological principles and etiological theory in clinical practice. The success of the case study suggests that this can be done by combining behavioral and psychometric clinical assessment, idiographic application of theory, an hypotheticodeductive approach to intervention, and time-series methodology.This study was supported in part by the University of Nebraska — Lincoln College of Arts and Sciences, by the UN-L Research Council, and by a George C. Holmes Fellowship granted to the senior author.The authors wish to acknowledge the assistance of Ms. Dorie Reed.     

Power and Type I errors for pairwise comparisons of means in the unequal variances case

A Monte Carlo simulation was conducted to compare pairwise multiple comparison procedures. The number of means varied from 4 to 8 and the sample sizes varied from 2 to 500. Procedures were evaluated on the basis of Type I errors, any‐pair power and all‐pairs power. Two modifications of the Games and Howell procedure were shown to make it conservative. No procedure was found to be uniformly most powerful. For any pair power the Games and Howell procedure was found to be generally most powerful even when applied at more stringent levels to control Type I errors. For all pairs power the Peritz procedure applied with modified Brown–Forsythe tests was found to be most powerful in most conditions.     

Estimating the reliability of a test split into two parts of equal or unequal length

When the reliability of test scores must be estimated by an internal consistency method, partition of the test into just 2 parts may be the only way to maintain content equivalence of the parts. If the parts are classically parallel, the Spearman-Brown formula may be validly used to estimate the reliability of total scores. If the parts differ in their standard deviations but are tau equivalent, Cronbach's alpha is appropriate. However, if the 2 parts are congeneric, that is, they are unequal in functional length or they comprise heterogeneous item types, a less well-known estimate, the Angoff-Feldt coefficient, is appropriate. Guidelines in terms of the ratio of standard deviations are proposed for choosing among Spearman-Brown, alpha, and Angoff-Feldt coefficients.