Some properties of the communality in multiple factor theory

Several theorems concerning properties of the communaltiy of a test in the Thurstone multiple factor theory are established. The following theorems are applicable to a battery ofn tests which are describable in terms ofr common factors, with orthogonal reference vectors.1. The communality of a testj is equal to the square of the multiple correlation of testj with ther reference vectors.2. The communality of a testj is equal to the square of the multiple correlation of testj with ther reference vectors and then—1 remaining tests. Corollary: The square of the multiple correlation of a testj with then—1 remaining tests is equal to or less than the communality of testj. It cannot exceed the communality.3. The square of the multiple correlation of a testj with then—1 remaining tests equals the communality of testj if the group of tests containsr statistically independent ests teach with a communality of unity.4. With correlation coefficients corrected for attenuation, when the number of tests increases indefinitely while the rank of the correlational matrix remains unchanged, the communality of a testj equals the square of the multiple correlation of testj with then—1 remaining tests.5. With raw correlation coefficients, it is shown in a special case that the square of the multiple correlation of a testj with then—1 remaining tests approaches the communality of testj as a limit when the number of tests increases indefinitely while the rank of correlational matrix remains the same. This has not yet been proved for the general case.The author wishes to express his appreciation of the encouragement and assistance given him by Dr. L. L. Thurstone.     

Multiple rectilinear prediction and the resolution into components

It is assumed that a battery ofn tests has been resolved into components in a common factor space ofr dimensions and a unique factor space of at mostn dimensions, wherer is much less thann. Simplified formulas for ordinary multiple and partial correlation of tests are derived directly in terms of the components. The best (in the sense of least squares) linear regression equations for predicting factor scores from test scores are derived also in terms of the components. Spearman's single factor prediction formulas emerge as special cases. The last part of the paper shows how the communality is an upper bound for multiple correlation. A necessary and sufficient condition is established for the square of the multiple correlation coefficient of testj on the remainingn—1 tests to approach the communality of testj as a limit asn increases indefinitely whiler remains constant. Limits are established for partial correlation and regression coefficients and for the prediction of factor scores.I am indebted to Professor Dunham Jackson for helpful criticism of most of this paper.     

Estimation of other coefficients of correlation from the phi coefficient

Formulas are developed for estimating a point-biserialr or a tetrachoricr from an obtained phi coefficient. The estimate of a tetrachoricr, which is calledr _φ, is shown to be equivalent to that obtained from first-order use of the tetrachoricr series. A tabulation is made of corrections needed to maker _φ equivalent numerically to the tetrachoricr. In spite of its greater generality than estimates of tetrachoricr by previous methods, there are limitations, which are pointed out.     

Estimation of a correlation coefficient from an uncertainty measure

In this paper graphs are given for estimating a correlation _XY from a double-entry table. 2H _r , twice the statisticH _r , relative uncertainty (the average of the ratios of the conditional uncertainty of each variable to its uncertainty) was computed. Mean 2H _r 's were computed from 100 samples for each of several sample sizes and numbers of categories. Graphs relating mean 2H _r to , the estimated correlation, for 3–17 categories to each variable and 3 sample sizes—50, 100, and 500—were constructed. 2.5 per cent and 97.5 per cent fiducial limits curves were constructed for establishing confidence limits on _XY and .The research reported in this paper was conducted by personnel of the Aerospace Medical Research Laboratories, Aerospace Medical Division, Air Force Systems Command, Wright-Patterson AFB, Ohio. Further reproduction is authorized to satisfy the needs of the U. S. Government. This paper has been identified by the Aerospace Medical Research Laboratories as AMRL-TR-66-54.     

Temporal stability of behavioural intention as a moderator of intention–health behaviour relationships

Seven prospective studies of health behaviours containing eight prospective datasets testing the moderating role of intention stability on intention–behaviour and past behaviour–behaviour relationships were examined within the context of the Theory of Planned Behaviour. The measure of intention stability was based on lack of change in intentions between the two measurement time points. Across different behaviours, samples and time frames more stable intentions were associated with intentions at time 1 that were stronger predictors of behaviour at time 2. Intention stability did not consistently moderate the past behaviour–behaviour relationship. Across studies the frequency-weighted mean correlation between intentions and behaviour was substantially greater for stable (r ₊?=?0.60) compared to unstable (r ₊?=?0.27) intentions (Z _difference?=?6.65, p?<?0.001). The past behaviour–behaviour correlation was also stronger for stable (r ₊?=?0.50, p?<?0.001) compared to unstable (r₊ ?=?0.34, p?<?0.001) intentions (Z _difference?=?3.12, p?<?0.01). Perceived behavioural control was the variable most strongly related to stable intentions. Implications for understanding the role of health cognitions in the performance of health behaviour are discussed.     

Agentic and Communal Generative Behavior in Four Areas of Adult Life: Implications for Psychological Well-Being

Fifty mothers and 48 fathers of soon-to-be-independent children were interviewed to determine how agentic and communal generative themes would be reflected in parenting, occupation, volunteer work, and leisure activities. Mothers reported more communal themes (F5, 83 = 2.32, p <.05). Correlations between generativity and well-being resulted in a negative relationship for mothers in parenting communal generative acts (r = –.41, p = .007) and total generative acts (r = –.3, p = .05) as assessed by the interview. Negative correlations also emerged between mothers' well-being and communal generative acts from the Generative Behavior Checklist, (r = –.33, p = .02).     

Pattern variants on a square field

A quantitative approach to the psychology of pattern recognition requires knowledge of the number of possible variants of any particular pattern. The general solution for the number [p/m ²] of pattern variants thatp counters can form on a square network ofm ² positions is obtained by elementary group theory. The exact solution is given in terms of the different types (symmetric, asymmetric, etc.) of patterns possible and an approximate formula for the total number of patterns is also developed.The author is indebted to Mr. J. Sandiford for his invaluable assistance on the theoretical aspects of the problem and to Mr. J. L. Griffith for his helpful criticism.     

Note on construction of an item analysis table for the high-low-27-per-cent group method

This paper describes the construction of a new item analysis table for the high-low-27-per-cent group method. The table provides a ready means of translating the observed proportions of success in the two extreme groups (p _H ,p _L ) into measures of item difficulty and item discrimination (p, Δ, andr). The tabled values of both the difficulty index,p, and the discrimination index,r, have been derived from Karl Pearson's tables of the normal bivariate surface.     

Depression Following Traumatic Brain Injury: The Validity of the CES-D as a Brief Screening Device

The validity, reliability, and factor structure of the Center for Epidemiological Studies-Depression Scale (CES-D) was examined with 253 patients seen for neuropsychological evaluation following traumatic brain injury (TBI). All patients completed the CES-D; 31 also completed the Beck Depression Inventory (BDI) and 17 completed the Minnesota Multiphasic Personality Inventory-II (MMPI-II). The CES-D demonstrated good concurrent, construct validity, significantly correlating with the BDI (r = .673, p < .0001) and the MMPI-II (Depression Scale T score r = .536, p = .027). The CES-D also demonstrated good internal consistency (coefficient alpha = .8195) and split-half reliability (Spearman–Brown r = .8284). Principal components factor analysis with varimax rotation resulted in a four-factor solution that accounted for 56.01% of the variance. The factor structure differed from the originally reported factor structure, and indicated that somatic difficulties were strongly associated with dysphoric affect in TBI patients. The CES-D is a valid and reliable screening instrument for use with TBI patients.     

Openness relates to COVID-19 vaccination rates across 48 United States but politics trump personality

Does geographic variation in personality across the United States relate to COVID-19 vaccination rates? To answer this question, we combined multiple state-level datasets: (a) Big Five personality averages (i.e., extraversion, agreeableness, conscientiousness, neuroticism, and openness; Rentfrow et al., 2008), (b) COVID-19 full-vaccination rates (CDC, 2021a), (c) health-relevant demographic covariates (population density, per capita gross domestic product, and racial/ethnic data; Webster et al., 2021), and (d) political and religiosity data. Analyses showed openness as the strongest correlate of full-vaccination rates (r = 0.51). Controlling for other traits, demographic covariates, and spatial dependence, openness remained significantly related to full-vaccination rates (r_p = 0.55). Adding political and religiosity data to this model diminished openness effects for full-vaccination rates to non-significance (r_p = 0.26); however, extraversion emerged as a significant correlate of full-vaccination rates (r_p = 0.37). Although politics are paramount, we suspect that states with higher average openness scores are more conducive to novel thinking and behavior—dispositions that may be crucial in motivating people to take newly-developed vaccines based on new technologies to confront a novel coronavirus.     

Health-related Internet habits and health anxiety in university students

Health-related Internet use has grown rapidly, yet little research has considered how health anxious individuals use the Internet for this purpose. Our aim was to examine the relationships between health anxiety and the extent of, reasons for, and consequences of health-related Internet usage in university students (n = 255). Responses on a purpose-made Internet use questionnaire were correlated with health anxiety scores; multiple regression analyses controlling for depression and anxiety were also conducted. Health anxiety positively correlated with (all ps < .01): frequency of health-related searching (r_s = .163), proportion of health-related information sought (r_s = .200), time spent online for health purposes (r_s = .166), and number of searches for both illness (r_s = .453) and wellness (r_s = .208) information. Health anxiety further positively correlated with advantages perceived in health-related Internet use (r_s = .183), heightened tension (r_s = .364) and relief (r_s = .174) post-search, and perceived doctor disadvantages (r_s = .306), yet a greater likelihood to visit a doctor post-search (r_s = .217). Health anxiety also correlated with six measures of possible addiction to using the Internet for health purposes (r_s range = .171 to .366, all ps < .01). Some (including several potentially dysfunctional) aspects of health-related Internet use correlate with health anxiety. Research evaluating the possible role of Internet use in the development and maintenance of health anxiety is warranted.     

Motivation for physical activity in young adults with physical disabilities during a rehabilitation stay: a longitudinal test of self‐determination theory

We tested a self‐determination theory (SDT) process model during a 3 week physical activity rehabilitation stay among young adults with a physical disability (N = 44, M_age = 24.7, SD = 5.1). As hypothesized, perceived autonomy support positively predicted needs satisfaction at the end of the stay (r = .38, p < .01). Further, needs satisfaction was positively linked to changes in autonomous motivation for physical activity (r = .47, p < .01). Both changes in autonomous motivation and self‐efficacy were associated with physical activity increases over the stay (r = .57, p < .01 and r = .47, p < .01, respectively). Bootstrapping results supported the SDT process model, indicating a support for a development toward more self‐determined motivation in rehabilitation.     

A statistical test for means of samples from skew populations

This paper presents a test for determining significance of differences between means of samples which are drawn from positively skewed populations, more specifically, those having a Pearson Type III distribution function. The quantity 2npx _g /x _p (wherep equals the mean squared divided by the variance andn is the number of cases in the sample), which distributes itself as Chi Square for 2np degrees of freedom, may be referred to the tables of Chi Square for testing hypotheses about the value of the true mean. For two independent samples, the larger mean divided by the smaller mean, which distributes itself asF for 2n ₁ p ₁ and 2n ₂ p ₂ degrees of freedom, may be referred to theF distribution tables for testing significance of difference between means. The test assumes that the range of possible scores is from zero to infinity. When a lower theoretical score limit (c) exists which is not zero, the quantity (Mean —c) should be used instead of the mean in all calculations.     

Locus of control and persistence in structured and unstructured preschool classrooms

The effect of locus of control and classroom structure on persistence and attention in preschool children was examined. Teachers' ratings of persistence were obtained for 16 children from a relatively structured classroom and for 18 children from a relatively unstructured classroom. Locus of control was measured by administering the Preschool and Primary Nowicki-Strickland Internal-External Scale (Nowicki & Duke, 1974). As predicted, teachers from the structured classrooms rated externally controlled children as more persistent (r=.55, p<.05), while teachers from the unstructured classroom rated internally controlled children as more persistent (r= -.35, p<.10). Practical implications of this line of research for making classroom placement decisions are discussed.     

Demographic characteristics,social competence,and behavior problems in children with gender identity disorder: a cross-national,cross-clinic comparative analysis

This study examined demographic characteristics, social competence, and behavior problems in clinic-referred children with gender identity problems in Toronto, Canada (N = 358), and Utrecht, The Netherlands (N = 130). The Toronto sample was, on average, about a year younger than the Utrecht sample at referral, had a higher percentage of boys, had a higher mean IQ, and was less likely to be living with both parents. On the Child Behavior Checklist (CBCL), both groups showed, on average, clinical range scores in both social competence and behavior problems. A CBCL-derived measure of poor peer relations showed that boys in both clinics had worse ratings than did the girls. A multiple regression analysis showed that poor peer relations were the strongest predictor of behavior problems in both samples. This study—the first cross-national, cross-clinic comparative analysis of children with gender identity disorder—found far more similarities than differences in both social competence and behavior problems. The most salient demographic difference was age at referral. Cross-national differences in factors that might influence referral patterns are discussed.     

Visual scanning patterns and executive function in relation to facial emotion recognition in aging

ABSTRACT

Objective: The ability to perceive facial emotion varies with age. Relative to younger adults (YA), older adults (OA) are less accurate at identifying fear, anger, and sadness, and more accurate at identifying disgust. Because different emotions are conveyed by different parts of the face, changes in visual scanning patterns may account for age-related variability. We investigated the relation between scanning patterns and recognition of facial emotions. Additionally, as frontal-lobe changes with age may affect scanning patterns and emotion recognition, we examined correlations between scanning parameters and performance on executive function tests. Methods: We recorded eye movements from 16 OA (mean age 68.9) and 16 YA (mean age 19.2) while they categorized facial expressions and non-face control images (landscapes), and administered standard tests of executive function. Results: OA were less accurate than YA at identifying fear (p < .05, r = .44) and more accurate at identifying disgust (p < .05, r = .39). OA fixated less than YA on the top half of the face for disgust, fearful, happy, neutral, and sad faces (p values < .05, r values ≥ .38), whereas there was no group difference for landscapes. For OA, executive function was correlated with recognition of sad expressions and with scanning patterns for fearful, sad, and surprised expressions. Conclusion: We report significant age-related differences in visual scanning that are specific to faces. The observed relation between scanning patterns and executive function supports the hypothesis that frontal-lobe changes with age may underlie some changes in emotion recognition.     

Concerning the integration of sciences: Kinds and stages

The detailed analysis allows to discern seven kinds of integration, namely: I₁ consisting in the synthesis of scientific disciplines from their elements, including disciplinary unification I₁; I₂ inclusion of a science in (reduction to) another, more general; I₃ — links between different sciences, especially establishing of common elements; I₄ — interdisciplines bridging various sciences; I₅ — combination of two (or more) disciplines into a new (complex) science; I₆ — a general approach to several domains or multidisciplinary unification; I₇ — transdisciplinary sciences about relations of the same type in various traditional domains. These kinds of integration are interwoven with processes of differentiation, viz. D₁ — internal differentiation of the sciences resulting of I₁; D₂ — interdisciplinary differentiation concomitant I₄, and D₃ — specialization of I₇ sciences in several sections. As a result integration and differentiation are combined in the pairs I₁ — D₁, I₇ — D₃, and D₂ — I₄. The processes of integration (and differentiation) may be presented schematically in the following (not strictly isolated one of another) sequence: in the 17th century started I₁ followed by D₁, and in the last decades by I₁ during the 18th and the 19th c. cases of I₂ and I₃ appear; I₄ (together with D₂) is unfolding since the late 19th century. Finally, I₇ (and D₃), as well as I₅ and I₆ pertain to the latter half of our century. Representative are for one thing I₁, I₄, and I₇ outlining the main stages of integration and at the same time connected with respective kinds of differentiation.     

Designer testing: using subjects'' personal vocabulary to produce individualised tests

The principle of designer tests is that of using a subject's own semantics rather than lists of words that may or may not be relevant or even understandable for the subject. The Personalised Emotional Index (PEI) is a prototype designer test, in this case a mood test, that uses words that the subject chooses from a list of suggestions within mood categories. Each person's test is custom made from familiar and understandable words from his/her own vocabulary. Such a test has much face validity, can be succinct and has comprehensibility for the subject. The results obtained when using this test at the same time as the Profile of Mood States Bipolar Version (POMS-BI) were very similar (e.g. in a regression analysis, the ‘elated-depressed' variable predicted present overall mood on both tests (POMS: t=5.25, p<0.000, PEI: t=5.84, p<0.000) with a high correlation for total scores (r=0.82, p<0.000). The PEI results were correlated within the two week interval (r's about −0.74; p<0.000) and reasonably but not highly correlated on retesting some months after the first testing (r's about −0.25; p<0.000). It was successfully used to differentiate mood variables from a group consisting of caregivers of people with schizophrenia (n=30, producing 399 days of data) and a group of unselected controls (n=62, producing 1080 days of data). The test appears to have validity, reliability, comparability, and utility.     

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.     

Decision policies minimizing risk in a multistage betting game

Considered in this paper is a decision task which has been employed to study multistage betting behavior. When the task commences, a decision maker (DM) is provided with some capital x (x > 0) which he is required to allocate over m (m > 1) mutually exclusive and collectively exhaustive alternatives, each of which occurs with probability p_i (p_i > 0, i = 1,…, m; Σ_i=1^mp_i = 1). If the amount y_i is allocated to alternative i (y_i ≥ 0, Σ_i=1^my_i = x) and alternative i obtains, DM's capital for the next stage of the game becomes y_ir_i, where r_i (r_i > 0) is the return per unit allocated to alternative i. The task consists of N stages.Defining risk in terms of the mean and variance of DM's bets, and assuming that the minimization of risk is DM's objective, decision policies satisfying this objective are derived in closed form and their testable properties are briefly discussed.