Self-selection biases in correlational studies based on questionnaires

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.The author would like to thank members of the Psychology Department at UWA for references on the illustrative example, namely the effects of sex-stereotyping on achievements in mathematics; thanks are also due to the anonymous reviewers whose comments resulted in material improvements to the paper.     

共同方法变异的影响及其统计控制途径的模型分析

共同方法变异(common method variance, CMV)指两个变量之间变异的重叠是因为使用同类测量工具而导致, 而不是代表潜在构念之间的真实关系。虽然以往研究显示CMV不一定导致研究结果的偏差, 在实际研究中应当加以考量。特别是在使用测量方法的研究中, 如果数据来源越单一, 测量方法越类似, CMV效应使研究结果产生偏差的可能性越大。CMV效应的控制方法包括过程控制法和统计控制法。在统计控制法的选择和使用上, 需要重点考虑该方法是否分离了三大变异(特质变异、方法变异和误差变异), CMV效应是在测量构念层面还是题目层面, CMV效应是加法效应还是乘法效应。控制潜在方法因子途径是统计控制方法中最重要的一类方法, 理解其模型是正确使用这类方法的前提。未来研究应当关注多个研究的CMV效应和侧重评估某个理论研究中CMV所引起的潜在的效度威胁。     

“解释法”样例对小学生学习新运算规则的促进

为证实“解释法”样例设计的促进作用,实验考察了4年级小学生学习“解释”样例与普通样例、“解释”样例和“解释-标记”与普通样例的迁移效果。结果表明：（1）用“解释”样例学习分数加减运算规则的近迁移成绩明显优于普通样例,但远迁移成绩无显著差异;（2）用“解释-标记”样例学习分数乘除法运算规则的远迁移成绩明显优于“解释”样例和普通样例,但近迁移成绩差异不显著,学习“解释”样例的远迁移效果均明显优于普通样例;（3）学习“解释法”设计的比例运算样例,其远、近迁移成绩均明显优于普通样例的迁移成绩,并受被试先备知识的影响。     

Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Gender Differences and Cognition Among Older Adults

The more replicated findings about gender difference in cognitive performance suggest female superiority on visuomotor speed and language ability and male superiority on mechanical and visuospatial tasks. Generally, group strengths found in the early school years become more established at adolescence and remain stable through adulthood. The current study tested whether the patterns established in the early years remained among 30 adult subjects. We also utilized a series of exploratory analyses to determine if observed gender differences were impacted by the covariance present between all cognitive tests. Results suggest that although the patterns established in the early years remain stable through time for males, the established patterns for females are altered with age. Our findings are compelling in supporting a male advantage on visuospatial tasks among older adults. These findings are discussed in terms of common variance between test instruments as a possible source of difference. Our finding that the gender effect tended to increase when common variance was controlled argues that this methodology may enhance the ability to detect domain specific effects.     

A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.     

Testing for independence between pairs of autocorrelated binomial data sequences

A problem arises in analyzing the existence of interdependence between the behavioral sequences of two individuals: tests involving a statistic such as chi-square assume independent observations within each behavioral sequence, a condition which may not exist in actual practice. Using Monte Carlo simulations of binomial data sequences, we found that the use of a chi-square test frequently results in unacceptable Type I error rates when the data sequences are autocorrelated. We compared these results to those from two other methods designed specifically for testing for intersequence independence in the presence of intrasequence autocorrelation. The first method directly tests the intersequence correlation using an approximation of the variance of the intersequence correlation estimated from the sample autocorrelations. The second method uses tables of critical values of the intersequence correlation computed by Nakamuraet al. (J. Am. Stat. Assoc., 1976,71, 214–222). Although these methods were originally designed for normally distributed data, we found that both methods produced much better results than the uncorrected chi-square test when applied to binomial autocorrelated sequences. The superior method appears to be the variance approximation method, which resulted in Type I error rates that were generally less than or equal to 5% when the level of significance was set at .05.