Percentage points of Wilks'L mvc andL vc criteria

Likelihood ratio tests have been proposed by Wilks for testing the hypothesis of equal means, variances, and covariances (H _mvc) and the hypothesis of equal variances and covariances (H _vc) in ap-variate normal distribution. Using exact distributions of the appropriate likelihood ratio statistics, tables of the .05 and .01 points of these distributions are constructed forp = 4, 5, 6, 7 and sample sizen = 25 (5) 60 (10) 100. A correction factor is recommended for largern. Two numerical examples illustrate use of the tables. A nonparametric test is proposed forH _mvc when the multivariate parent population is known to be non-normal.This research was supported partly by the Office of Naval Research under Contract No. Nonr-855(06) and partly by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. 18(600)-83. Reproduction in whole or in part for any purpose of the United States Government is permitted.     

An IBM method for computing intraserial correlations

A method for computing intraserial correlations using a 602-A Calculating Punch, an 077 Collator, a 513 Gang Punch, and a 403 Tabulator is described. An example of the use of the procedure and an estimate of the time needed with each machine are given. This procedure is compared with another method, which makes use of a more powerful IBM machine.This research was supported in part by the United States Air Force under Contract No. AF 33(038)-25726, monitored by the Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government.     

Testing message diffusion in harmonic logistic curves

The growth of a population of knowers of a message was studied to test a human interactance hypothesis. The conditions investigated involvedpeople interacting in time, with the population pairing off randomly (i.e., determined by many, small, different influences) and transferring an attribute (i.e., an all-or-none act) at either a steady rate or a waning rate, subsequent to the originating stimulus. The mathematical expressions for these pre-conditions were the differential equations for the linear logistic for steady acting and the harmonic logistic for waning acting. Variant forms of these curves were developed. Two exploratory experiments, or pretests, comprised launching a coffee slogan in a town and imitating a badge wearer in a boys' camp. Since the activity rate waned harmonically in both cases, the harmonic logistic fit best in both the town and the camp as expected by the hypothesis.A paper read before Section K sponsored by the Committee on Social Physics of the AAAS Conference in Boston, December 30, 1953. This research was supported in part by the United States Air Force under Contract AF 33(038)-27522, monitored by the Human Resources Research Institute (now, Officer Education Research Laboratory, Air Force Personnel and Training Research Center), Air Research and Development Command, Maxwell Air Force Base, Alabama. Permission is granted for reproduction, translation, publication and distribution in part and in whole by or for the United States Government.     

Maximizing the discriminating power of a multiple-score test

Maximizing the discriminating power of a multiple-score test involves maximizing the homogeneity of each subtest and minimizing the correlations between subtests. A method is presented for constructing such tests from items whose intercorrelations are not too high. Under certain restrictions the saturation, defined as the proportion of inter-item covariance to total variance, is maximized for each subtest. The nucleus of each subtest is three items with high covariancesinter se. All items which will lower the saturation are discarded; the one item is added which will maximize the saturation of the resultant test. This process is repeated until all the items are included or discarded for that subtest. If the correlation between any such subtests approaches the geometric mean of their saturations, their items form a new pool for one or more subtests. Formulas are presented for deciding which items to eliminate in order to reduce further the correlations between subtests.This research was supported in part by the United States Air Force under Contract AF 33(038)-10588 with Human Resources Research Center, Lackland Air Force Base, San Antonio, Texas. Permission is granted for reproduction, translation, publication use and disposal in whole and in part by or for the United States Government.     

Development and convergent validation of a methodology for estimating cross-job retraining times

Cross-jobtransferability of skills is defined in terms of the ease with which individuals can apply knowledge and skills acquired in a previous job in learning to perform a new job. This study reports the development of a prototype methodology for estimating retraining times based on analyses of transferability of skills. Using this methodology which assesses interjob similarity in task content and task learning time, times to retrain across 41 different U.S. Air Force enlisted jobs were estimated. Convergent validities of retraining time estimates were tested in terms of correlations with differences in jobs': (a) general job learning difficulty, and (b) aptitude requirements. Results supported predictions that cross-job retraining time would be longer (a)into jobs that generally aremore difficult to learn, (b)from jobs that generally areless difficult to learn, and (c) across jobs having different, rather than similar, aptitude requirements. Implications for training, human resources planning, and coping with increasingly rapid technological changes in the workplace are discussed.Research sponsored by the Air Force Office of Scientific Research/AFSC, United States Air Force, under contract F49620-87-R-0004. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.     

The counseling assignment problem

A disposition index, DI, which provides information about each possible placement to be considered in a personnel classification situation is discussed. The index is readily computed by machine methods and can be used by counselors required to make assignments. The use of the disposition index provides an adequate approximation to optimal solutions obtained by other methods.This report is based on work done under ARDC Project No. 7702, Task No. 17051, in support of the research and development program of the Air Force Personnel and Training Research Center, Lackland Air Force Base, Texas. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

The relationship between factorial composition of test items and measures of test reliability

For continuous distributions associated with dichotomous item scores, the proportion of common-factor variance in the test,H ², may be expressed as a function of intercorrelations among items.H ² is somewhat larger than the coefficienta except when the items have only one common factor and its loadings are restricted in value. The dichotomous item scores themselves are shown not to have a factor structure, precluding direct interpretation of the Kuder-Richardson coefficient,r _K-R, in terms of factorial properties. The value ofr _K-R is equal to that of a coefficient of equivalence,H ² , when the mean item variance associated with common factors equals the mean interitem covariance. An empirical study with synthetic test data from populations of varying factorial structure showed that the four parameters mentioned may be adequately estimated from dichotomous data.This study was supported in part by an Air Force project (Contract Number AF18(600-170), monitored by the Crew Research Laboratory, Air Force Personnel and Training Research Center, Randolph Air Force Base, Randolph Field, Texas. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government. Further support was given by the Northwestern University Graduate School. The computational assistance of Mr. Norman Miller is acknowledged. Professor Meyer Dwass provided mathematical advice both directly and indirectly relevant to the paper.     

Methods of solving some personnel-classification problems

The personnel-classification problems considered in this paper are related to those studied by Brogden (2), Lord (6), and Thorndike (8). Section 1 gives an approach to personnel classification. A basic problem and variations of it are treated in section 2; and the computation of a solution is illustrated in section 3. Two extensions of the basic problem are presented in section 4. Most of the methods indicated for computing solutions are applications of the simplex method used in linear programming (see 1, Chs. XXII, XXIII). The capabilities of a high speed computer in regard to the simplex method are discussed briefly (see section 1).This work was supported in part by the United States Air Force under Contract AF 33(038)-25192, monitored by the Personnel Research Laboratory of the Air Training Command Human Resources Research Center. Permission is granted for reproduction, translation, publication, use, and disposal in whole or in part by or for the United States Government.     

The estimation of the discriminal dispersion in the method of successive intervals

A new algebraic formula is derived for estimation of the discriminal dispersion in the method of successive intervals. The legitimate use of the formula requires that as many normal deviates as possible be present in the matrix. For this reason, it is recommended that deviates corresponding to the interval (0.01, 0.99) of the cumulative proportions be used, instead of those corresponding to (0.05, 0.95), the interval used by Edwards and Thurstone. Computations on data published by Edwards and Thurstone showed that when adjustment was made for variability in dispersions calculated by the formula of this paper, a reduction of fifty per cent in mean absolute discrepancy was produced. Since the formula is easy to use and avoids the disadvantages of its predecessors, it should have fairly wide applicability in psychological research.This research was supported in part by the United States Air Force under Contract No. AF 33(038)-25726 monitored by Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government. The writer is grateful to Dr. A. L. Edwards for a critical reading of an earlier version of this paper, and to Dr. L. H. Lanier and Dr. L. M. Stolurow for editorial advice on the present version, which was written at the University of Illinois. The editors ofPsychometrika have informed the writer that H. J. A. Rimoldi and M. Hormaeche (7) have independently derived the same formula for the discriminal dispersion from a different set of postulates using the law of comparative judgment.     

General resolution of correlation matrices into components and its utilization in multiple and partial regression

The derivation of multiple and partial regression statistics from uniqueness-augmented factor loadings, presented in the literature for orthogonal factor solutions, is generalized to oblique solutions. A mathematical rationale for the general case, without restriction to uncorrelated factors, is presented. Use of the general formulation is illustrated with a two-factor, seven-variable example.This report is based on work done under ARDC Project 7702, in support of the research and development program of the Air Force Personnel and Training Research Center, Lackland Air Force Base, Texas. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

Can I see the real me? Leadership ability and the better-than-average effect

Military organizations typically emphasize the importance of leadership. The quality of military leadership might be inhibited because individuals tend to overestimate their respective leadership abilities. We hypothesized that military professionals generally overestimate how well they lead compared to their peers (Hypothesis 1). We also hypothesized that an egocentric bias, where self-ratings are weighted more strongly than other-ratings, contributes to this better-than-average effect (Hypothesis 2). The results obtained across two studies supported both hypotheses. Most notably, 242 of 251 United States Air Force Academy cadets and 31 of 34 United States Air Force officers rated themselves as above average compared to their peers. The obtained results have important implications for understanding the better-than-average effect generally and leadership in military and nonmilitary organizations.     

The stability of the factorial pattern of aircrew classification tests in four analyses

This study consists of four factor analyses of the Army Air Forces Aircrew Classification Batteries. The first was an analysis of the 1945 wartime battery, while the other three were analyses of the 1947 postwar battery, consisting of essentially the same variables, but using different samples. Eleven factors were found which had been identified and reported in previous analyses. An additional factor, possibly an artifact, was identified as an age-education doublet. The only factor which differed significantly in the analyses was pilot or flying interest. These factor analyses show that the factorial content of the tests remains quite similar in both wartime and postwar populations.The data reported in this study were collected as part of the United States Air Force Human Resources Research and Development Program and described in Research Bulletin 52-16. The opinions or conclusions contained in this report are those of the authors. They are not to be construed as reflecting the view or indorsement of the Department of the Air Force.     

A method for clustering eigenvalues

A method of computing communalities is presented which attempts to cluster eigenvalues about zero. Results are exhibited which show reduction of rank using computed communalities.This paper is based on work performed under Contract AF 30(602)-3300 monitored for the U. S. Air Force by Mr. Rocco Iuorno, Rome Air Development Center. The use, under the above contract, of the IBM 7094 computer located at Aeronautical Systems Division, Wright-Patterson Air Force Base, is gratefully acknowledged. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

Application of the quartimax method of rotation to Thurstone's primary mental abilities study

This study compares a quartimax rotation of the centroid factor loadings for Thurstone's Primary Mental Abilities Test Battery with factorings of the same correlation matrix by Thurstone (simple structure), Zimmerman (revised simple structure), Holzinger and Harman (bi-factor analysis), and Eysenck (group factor analysis). The quartimax results agree very closely with the solutions of Holzinger and Harman and of Eysenck, and reasonably well with the two simple structure analyses. The principal difference is the general factor provided by the quartimax solution. Reproduction of the factorial structure is sufficiently good to justify its use at least as the first stage of rotation. More extensive trial of the method will be needed with more varied data before it will be possible to decide whether quartimax factors meet psychological requirements sufficiently well without further rotation.We wish to thank Professor L. G. Henyey and the University of California Computer Center for making the IBM 701 electronic computer available for this study, and the National Science Foundation for its support of the work of the Computer Center. Professor H. F. Kaiser of the University of Illinois has made helpful criticisms of the paper, and Mr. Louis S. Davis of the University of California has assisted with preparation of the tables. The research was supported in part by the United States Air Force under Contract No. AF 33 (038)-25726 monitored by the Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government.A 701 program for calculation of the quartimax and varimax loadings, prepared by Professor H. F. Kaiser, is available in the library of computer programs held by the Computer Center at the University of California (Program No. 464). Mr. J. O. Neuhaus and Mr. K. W. Dickman have prepared a quartimax program for Illiac at the University of Illinois. This Illiac program will be usable on three other computers recently built or under construction: Mistic (Michigan State University), Silliac (University of Sydney), and the machine being constructed by Iowa State College.     

Should knowledge entail belief?

The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. While the entialment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas.Research sponsored in part by the Air Force office of Scientific Research (AFSC), under Contract F49620-91-C-0080. The United States Government is authorized to reproduce and distribute reprints for governmental purposes.     

Evaluation of an Air Force Child Physical Abuse Prevention Project Using the Reliable Change Index

Three hundred and seventy-nine parents at 25 Air Force bases participated in a collaborative child physical abuse prevention project designed by the United States Air Force Family Advocacy Program and Father Flanagan's Boys' Home (Boys Town). These participants were active duty or civilian employee parents and their spouses who completed the Boys Town Common Sense Parenting ® program as part of a comprehensive prevention effort. We hypothesized that participants would report decreased child behavior problems, improved relationships with family members, and reduced risk for child physical abuse after attending parenting sessions. Results supported this hypothesis. The data were also analyzed to determine the frequencies of individual parents who made statistically reliable changes on the dependent measures using Jacobson's Reliable Change Index. Nineteen to 30% of the participants reported significant improvement in the areas assessed. Parents who improved in abuse risk were at a higher level of risk and were less satisfied with family relationships prior to their participation than those who did not change. Implications for prevention of child physical abuse and future directions for research are discussed.     

Two models of group behavior in the solution of eureka-type problems

A study by Shaw (7) some twenty years ago is frequently cited by social scientists to support the generalization that groups are superior to individuals in problem-solving. Shaw suggests that personal interaction within the group is responsible for the superior performance of groups. This article re-examines her data in the light of two models which propose that the difference in quality of solution between group and individual performance is solely a matter of ability. It is shown that Shaw's data may be considered to have been an outcome of behavior postulated by the models. Since Shaw's observations relate to a special population and to special kinds of problems, the proposed models may not be appropriate under differing experimental conditions. In fact, Lorgeet al. (4) have indicated that experimental demonstration of the superiority of groups over individuals in problem-solving depends not only on the kind of group but also on the kind of problem to be solved. In addition, the diversity of transfer of training for groups and for individuals is considered.Supported in part by the Office of Naval Research under Contract N6 onr 266 (21) and the Air Force Personnel and Training Research Center under Contract AF 18(600)-341.     

The development of hierarchical factor solutions

Although simple structure has proved to be a valuable principle for rotation of axes in factor analysis, an oblique factor solution often tends to confound the resulting interpretation. A model is presented here which transforms the oblique factor solution so as to preserve simple structure and, in addition, to provide orthogonal reference axes. Furthermore, this model makes explicit the hierarchical ordering of factors above the first-order domain.Grateful acknowledgment is given to Dr. Lloyd G. Humphreys for his encouragement and valuable suggestions in the development of this task. This investigation was carried out under the Air Force Personnel and Training Research Center program in support of Project Nos. 7702 and 7950. Permission is granted for reproduction, translation, publication, and use or disposal in whole or in part by or for the United States Government.     

The Impact of the United States Air Force Deployment Transition Center on Postdeployment Mental Health Outcomes

The United States Air Force Deployment Transition Center (DTC) operates a 2-day third-location decompression program that commenced operations during the summer of 2010 in Ramstein, Germany, with the aim to assist Air Force service members (AFSMs) who are returning from deployment as they prepare to reintegrate back into their home lives and work stations. The present study evaluated the impact of DTC attendance on later mental health outcomes. Because participants are not randomly assigned to attend the DTC, propensity score weighting was used to compare DTC participants (N = 1,573) to a weighted control group of AFSMs (N = 1,570) in the same job specialties who returned from deployment during the same time period. Rates of endorsement to items on the Postdeployment Health Reassessment were examined and compared, as were rates of mental health diagnoses from AFSMs’ official medical records. Key findings indicate that DTC participants reported lower levels of depressive and posttraumatic stress symptoms and lower levels of relationship conflict following return from deployment, as compared to weighted control participants. Mental health diagnostic rates were comparable for the 2 groups during the first 6 months following return from deployment. These findings suggest that participation in the DTC program had notable benefits for redeploying AFSMs and support the continued use of the program.     

The role of collateral information about examinees in item parameter estimation

Standard procedures for estimating item parameters in item response theory (IRT) ignore collateral information that may be available about examinees, such as their standing on demographic and educational variables. This paper describes circumstances under which collateral information about examineesmay be used to make inferences about item parameters more precise, and circumstances under which itmust be used to obtain correct inferences.This work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the United States Government. We are indebted to Tim Davey, Eugene Johnson, and three anonymous referees for their comments on earlier versions of the paper.