Jonathon D. Brown

• University of Washington

In Chap. 10 we examined nonlinear models with normally-distributed errors. Given these conditions, minimizing the residual sum of squares maximizes the likelihood function. Not all variables of interest to scientists are normally distributed, however. Instead of being continuous and unbounded, many variables are discrete (e.g., number of aphids on...

Many phenomena unfold over time. For example, stock prices rise and fall, diseases run their course, and relationships ebb and flow. Occurrences like these create a time series — a sequence of observations identified by the order in which they occur. Owing to properties of inertia and persistence, the observations in a time series tend to change sl...

In Chap. 3 we learned that multiple regression is a powerful tool for modeling the contribution a variable makes to the prediction of a criterion holding other variables constant. Given this ability, it might seem that adding predictors to a regression model is always beneficial, but this is not the case. Part of the problem is collinearity. As dis...

We have covered a variety of statistical models in this book, but all have shared a common feature: The criterion and error term were treated as random variables, but all of the predictors were assumed to be fixed. In this chapter, we will consider models that include a broader mixture of fixed and random variables. For obvious reasons, these model...

When the errors in a regression model are independent and identically distributed, the Gauss-Markov theorem establishes that the ordinary least squares (OLS) estimator is “BLUE” (Best Linear Unbiased Estimator) (see Chap. 2). So far, all of the examples we have encountered in this text have met these assumptions, but in this chapter you will learn...

This is a book about statistical analyses: how to conduct them and how to interpret them. Not all of the analyses involve linear functions and few of them have an exact solution, so it might seem odd to begin by learning to solve a consistent system of linear equations. Yet there are good reasons to start this way. For one thing, linear systems for...

In Chap. 2, we learned how to decompose a rectangular matrix into an orthonormal basis Q and an upper triangular matrix R, and in Chap. 3 we applied the decomposition to a linear regression model. In this chapter you will learn a related decomposition that can create an orthonormal basis from a square, symmetric matrix. The decomposition is known a...

Statistical models commonly assume that the relation between a predictor and a criterion can be described by a straight line. This assumption is often appropriate, but there are times when abandoning it is warranted. Under these circumstances, we have two choices: adapt a linear model to accommodate nonlinear relations (e.g., transform the variable...

In Chap. 9 we learned how to model a nonlinear relation using a cubic spline; in this chapter we will learn how to model a nonlinear relation using nonlinear regression. Methods for performing nonlinear regression have been around for many years, but they were not commonly used before the ready accessibility of high-speed computers. Instead, nonlin...

In Chap. 6 we learned how to detect and manage violations of the Gauss-Markov theorem. In this chapter, we consider a related problem—how to accommodate errors that are not normally distributed. Normally distributed errors are not demanded by the Gauss-Markov theorem, but the errors need to be at least approximately normal if we wish to use the nor...

In Chap. 1 we learned how to solve a system of linear equations. All of the systems were square (i.e., the number of equations equaled the number of unknowns) and each system had an exact solution. Systems like these do not characterize most statistical analyses. Instead, we deal with rectangular systems (more equations than unknowns) for which an...

In Chap. 2 we learned how to use the QR decomposition to solve an overdetermined system of linear equations. Because our emphasis was computational, we focused on learning mathematical operations rather than interpreting the values they produced. Statistical analyses involve more than solving mathematical problems, however, and in this chapter you...

This book demonstrates the importance of computer-generated statistical analyses in behavioral science research, particularly those using the R software environment. Statistical methods are being increasingly developed and refined by computer scientists, with expertise in writing efficient and elegant computer code. Unfortunately, many researchers...

In many areas of science, interest centers on the time it takes for an event to occur. For example, product engineers monitor how long a device lasts before it fails; developmental psychologists study the emergence of language; and educators track how long it takes students to master some task. Historically, issues of this nature were investigated...

In Chap. 4 we learned how to diagonalize a square matrix using the Eigen decomposition. Eigen decomposition has many uses, but it has a limitation: it can only be applied to a square matrix. In this chapter, we will learn how to extend the decomposition to a rectangular matrix using a related method known as a Singular Value Decomposition (SVD). Be...

This laboratory-based study examined lagged associations between child pain behavior and maternal responses as a function of maternal catastrophizing (CAT). Mothers completed the parent version of the Pain Catastrophizing Scale. Children participated in a validated water ingestion procedure to induce abdominal discomfort with mothers present. Video...

This study examined intra- and inter-personal associations between pain catastrophizing and verbal expression in 70 children with recurrent abdominal pain and their mothers. Participants independently completed the Pain Catastrophizing Scale. Mothers and children then talked about the child’s pain. Speech was categorized using a linguistic analysis...

People seek ideal romantic partners who are similar to themselves. In this research, we tested whether this preference reflects a self-enhancement bias. Study 1 (N = 40) found that people who like themselves a lot (i.e., high self-esteem people) were more likely to describe their ideal romantic partner in terms that matched their self-evaluations t...

In Chaps. 11 and 12, we learned that multiple regression can be used to analyze data with categorical predictors. In the next three chapters, we will extend our coverage to include designs that combine categorical and continuous predictors.

Chapter 1 introduced you to a variety of matrix properties and operations. Among other things, you learned how to use the determinant and inverse of a matrix to solve equations with unknown quantities. In the remainder of this book, you will use these operations to perform a wide variety of statistical analyses.

The suitability of a linear regression model depends on several factors. We briefly covered some of these factors in Chap. 2, and we are now ready for a more detailed discussion. Table 6.1 organizes them into three categories of increasing importance. The first category refers to properties that are desirable but not required; the second refers to...

In Chap. 11, we used multiple regression to analyze data with a single categorical predictor. Yet multiple regression, like analysis of variance, can also be used with designs that combine two or more categorical predictors. In most cases, the categorical variables are crossed to form a factorial design. In this chapter, you will learn how to use m...

In Chap. 2 you learned that ordinary least squares (OLS) estimation minimizes the squared discrepancy between observed values and fitted ones. This procedure is primarily a descriptive tool, as it identifies the weights we use in our sample to best predict y from x. Sample description is not the only function that regression analyses serve, however...

In a linear regression model with multiple predictors, the regression coefficients represent the unique contribution of each variable to the prediction of a criterion holding all other variables constant. Because the coefficients are statistically independent, a one-unit change in x i predicts a b i change in y across all levels of x k . This condi...

In Chap. 13, we discussed analysis of covariance (ANCOVA). With ANCOVA, we enter a continuous predictor into a regression model before adding a categorical one. The presence of the continuous predictor is designed to reduce the error variance, thereby increasing the power of an experimental treatment or grouping variable. ANCOVA is not the only way...

In a linear regression model, the criterion is modeled as a linear combination of the weighted predictors and a disturbance term.$$ y={\beta}_0+{\beta}_1{x}_1+{\beta}_2{x}_2+\dots +{\beta}_k{x}_k+\varepsilon $$ The model gives rise to two, related properties: linearity and additivity.

When scientists find an association between two or more variables, they are rarely content knowing only that the variables are related. Instead, they want to know why they are related; by what causal mechanism does one variable affect another? Unfortunately, the search for causes is fraught with difficulty. As the Scottish philosopher David Hume no...

In this chapter you will learn about matrix algebra. Of all the chapters in the book, this one has the most terms to memorize. Learning matrix algebra is a bit like learning a new language, and the only way to understand the language is to immerse yourself in the terminology until it becomes familiar. I promise that the time you invest will be time...

Multiple regression finds a fitted value for a criterion from a linear combination of the predictors. But suppose we have a collection of variables without a criterion. This state of affairs characterizes our design matrix, X, as none of the predictors is a criterion. Is there a way to create a linear combination of these variables? There is, but i...

In previous chapters, you learned that the errors in a linear regression model are assumed to be independent and normally and identically distributed random variables, with mean 0 and variance σ 2:$$ \varepsilon \sim NID\left(0,{\sigma}^2\right) $$We discussed the normality assumption in Chap. 6, learning ways to determine whether the errors are no...

In previous chapters, you have learned how to calculate regression coefficients and related terms using a single predictor. Yet most phenomena of interest to scientists involve many variables, not just one. Heart disease, for example, is associated with diet, stress, genetics, and exercise, and school performance is associated with aptitude, motiva...

Linear regression normally fits a straight line through a set of observations. Not all relations are characterized by a straight line, however. Suppose we wish to determine how much children enjoy a dessert as a function of the amount of sugar we use in its preparation. Surely children like a sugary treat, but only up to a point. If we put in too m...

The predictors in a linear regression model are usually continuous, not categorical. A categorical variable has clearly defined levels, and the differences between levels are qualitative (either-or) rather than quantitative (more or less). Examples include subject variables (male, female), affiliations (Democrat, Republican, Libertarian), or an exp...

focus . . . on the relation between global self-esteem and evaluations of self in specific domains / argue that self-esteem is rooted in affective processes / high self-esteem (HSE) involves a generic, global liking for oneself that is not dependent on the belief that one possesses specific attributes, but that is nevertheless accompanied by the ge...

People define themselves in terms of their relationship partners and they incorporate their partners into their self-concepts. Consequently, partner enhancement—viewing one’s partner in excessively positive terms—might constitute an indirect form of self-enhancement when feelings of self-worth are threatened. To test this hypothesis, the authors ga...

People evaluate themselves more positively than they evaluate most other people. Although this better than average (BTA) effect was originally thought to represent a motivated bias, several cognitively oriented theorists have questioned whether this is the case. In support of a motivational model, the author reports five studies showing that the BT...

The more people think about their attitude toward some issue, the stronger their attitude becomes. The present research examined whether this strengthening effect also applies to self-evaluative attitudes. In four studies, we had some participants complete a self-evaluation measure before rating their momentary feelings of self-worth (Studies 1, 2,...

Using an item-response theory-based approach (i.e. likelihood ratio test with an iterative procedure), we examined the equivalence of the Rosenberg Self-Esteem Scale (RSES) in a sample of US and Chinese college students. Results from the differential item functioning (DIF) analysis showed that the RSES was not fully equivalent at the item level, as...

In this article, I report three studies showing that global self-esteem influences people's emotional reactions to negative outcomes. Using social outcomes as well as personal ones (Study 1), naturally occurring outcomes as well as experimentally induced ones (Study 2), and implicit self-feelings as well as self-reported ones (Study 3), I show that...

Immigration is a major life event that can create marital distress in couples who migrate together (Min, 2001 ). One instigator of this distress is differences in the rates of acculturation between husbands and wives (Chun and Akutsu, 2003 ; Darvishpour, 2002). Previous qualitative research (Ben-David and Lavee 1994) found that amongst Russian immi...

We dispute Henrich et al.'s analysis of cultural differences at the level of a narrow behavioral-expression for assessing a universalist argument. When Researchers Overlook uNderlying Genotypes (WRONG), they fail to detect universal processes that generate observed differences in expression. We reify this position with our own cross-cultural resear...

Although it is widely assumed that East Asians and Westerners evaluate themselves differently, there is much support for cultural convergences. In this article, I review evidence showing that in both cultures (and to a largely comparable degree), people (a) experience high feelings of self-regard; (b) view themselves and loved ones in highly positi...

Cognitive theories of emotion assert that emotional reactions to events depend on the manner in which events are interpreted and appraised. From this perspective, the same outcome can produce different emotions. For example, a score of 85% on a test can evoke positive feelings if it is considered a success or negative feelings if it is considered a...

It is widely assumed that East Asians evaluate themselves less positively than do Westerners, but this assumption lacks consistent support. In this report, the authors provide evidence that cultural differences in self-evaluations are moderated by two factors: trait importance and self-esteem. American and Chinese college students completed a self-...

Most people hold overly (though not excessively) positive self-views of themselves, their ability to shape environmental events, and their future. These positive illusions are generally (though not always) beneficial, promoting achievement, psychological adjustment, and physical well-being. Social processes conspire to produce these illusions, sugg...

Protective buffering refers to hiding cancer-related thoughts and concerns from one's spouse or partner. In this study, the authors examined the intrapersonal and interpersonal consequences of protective buffering and the motivations for such behavior (desire to shield partner from distress, desire to shield self from distress). Eighty hematopoieti...

In a provocative article, Heine et al. concluded that self-esteem needs are less important in collectivistic, East Asian countries than in individualistic, Western ones. Their conclusion was based, in part, on evidence that: (i) self-esteem scores are less positively biased in Japan than in Western countries; and that (ii) low self-esteem is less p...

East Asians report lower levels of self-esteem than North Americans and Western Europeans. These differences could mean that self-esteem is a culturally bounded construct, experienced differently in different cultures, or they could mean that self-esteem is a universally relevant construct whose average level is raised or lowered in different cultu...

Although traditionally measured by self-report, researchers have recently begun to measure self-esteem indirectly, using methods thought to tap implicit, unconscious attitudes. These implicit measures rarely show any correspondence with self-report measures of self-esteem, raising questions about what they assess. Using the Implicit Association Tes...

Although people from East Asian countries consistently report lower self-esteem than do those from Western countries, the origins of this difference are unclear. We conducted two studies to illuminate this issue. Study 1 found that Chinese participants appraised themselves less positively than American participants on a cognitive measure of self-ev...

In this article, the authors propose and test an interactionist model of personality functioning. The model maintains that many traits function in a threshold-like manner, such that less situational strength is needed to evoke a trait-relevant response in people who are high on the trait than in those who are low on the trait. Because of these diff...

Expectancies of success are widely thought to influence people's emotional reactions to performance outcomes: The lower one's expectancies, the more delighted one should be following success and the less disappointed one should be following failure. Although this proposition has been accepted almost as a truism, a review of the literature reveals t...

High expectancies of success are widely assumed to have positive effects on performance in achievement situations. However, previous investigations have tended to ignore task difficulty or assume that expectancies affect performance in a linear fashion. In two investigations, we found that (a) expectancies were more closely related to performance a...

Self-enhancement biases are generally weaker or absent in collectivistic cultures than they are in independent ones. The source of this effect has been the topic of debate. Some claim the self-enhancement motive is absent in collectivistic cultures, whereas others claim that collectivistic cultures discourage the motive's expression. The majority o...

Although the self-enhancement motive is commonly held to be a universal human motivation, some theorists have recently argued that it does not operate in Japan. In an attempt to shed light on this issue, the authors conducted an investigation that explored the relation between self-esteem and self-enhancement in Japan and America. In both cultures...

In his commentary, Heine has done a thorough job of reviewing research on self–enhancement biases in Japan. Insofar as he conducted much of the work he reviewed, we assume he has characterized the findings fairly and accurately and see no need to comment further upon them. Instead, we will take this opportunity to discuss the nature of self–enhance...

People who verify a negative self-view expose themselves to criticism and rejection. Because people with low global self-esteem are hurt more by negative feedback than are people with high global self-esteem, the authors predicted that they would be less apt to verify a negative self-view in a more specific domain. Three investigations found suppor...

People who verify a negative self-view expose themselves to criticism and rejection. Because people with low global self-esteem are hurt more by negative feedback than are people with high global self-esteem, the authors predicted that they would be less apt to verify a negative self-view in a more specific domain. Three investigations found suppor...

North Americans view themselves in more positive terms than they view most other people. In the present paper, we report three studies showing that this bias is also found in Japan. For highly valued traits and abilities, Japanese students rated themselves and their best friends in more positive terms than they rated most other students (Study 1 an...

Two experiments investigated how self-esteem guides people's emotional responses to changing evaluative feedback. In both experiments, participants received an initial evaluation (either positive or negative) followed by a second evaluation (either positive or negative). Emotional reactions to the second evaluation were then assessed. High self-est...

This research examined the hypothesis that people with low self-esteem (LSE) are less motivated than people with high self-esteem (HSE) to repair their negative moods. In Study 1, participants completed diaries in response to either a success or a failure in their everyday lives. Participants described what they intended to do next and the reasons...

The affective model of self-esteem development assumes that: (a) self-esteem forms early in life in response to relational and temperamental factors; and (b) once formed, endows high self-esteem people with the ability to promote, protect, and restore feelings of self-worth. In this article, we use the model to examine the relation between self-est...

Self-esteem has been linked to a diverse array of positive and negative affective states. The present research explored the nature of these relationships. Study 1 found that self-esteem (as measured by the Rosenberg Self-Esteem Scale) is more closely associated with self-relevant emotional states than with emotional states that do not directly impl...

Examines the manner in which expectancies of success affect task performance and people's emotional reactions to their performance outcomes. The issue under consideration is the following: Are people better served by undertaking achievement-related tasks with high expectancies of success or are they better off being more modest and realistic? Four...

A critical question in self-esteem research is whether people's reactions to success and failure are guided by their global self-esteem level or by their more specific beliefs about their abilities and attributes. To address this issue, the authors led participants to experience success or failure on an alleged test and then assessed their cognitiv...

A critical question in self-esteem research is whether people's reactions to success and failure are guided by their global self-esteem level or by their more specific beliefs about their abilities and attributes. To address this issue, the authors led participants to experience success or failure on an alleged test and then assessed their cognitiv...

Review of Self-Esteem: Research, Theory, and Practice by Chris Mruk (see record 1995-97096-000 ). On the scholarly side, Mruk provides a reasonably comprehensive and readable history of the nature and origins of self-esteem. Many previously unknown references from various fields in the social sciences and the popular press are included. As a refere...

Accurate self-knowledge is widely assumed to be necessary, sought after, and characteristic of most people. In this article, the authors examine the logical and evidentiary basis of these assumptions and reach the opposite conclusions.

Low self-esteem people are assumed to have more severe emotional reactions to failure than are high self-esteem people, but this assumption has not received consistent empirical support. In this article the authors report 2 investigations that found that self-esteem differences of this sort emerge for emotions that directly implicate the self (e.g....

Low self-esteem people are assumed to have more severe emotional reactions to failure than are high self-esteem people, but this assumption has not received consistent empirical support. In this article the authors report 2 investigations that found that self-esteem differences of this sort emerge for emotions that directly implicate the self (e.g....

Comments on the argument by J. Schedler et al (see record 1994-09623-001 ) that standard mental health scales appear unable to distinguish between genuine mental health and the illusion of mental health created by psychological defenses. It is asserted that Schedler et al go beyond appropriate empirical and conceptual boundaries by extending their...

S. E. Taylor and J. D. Brown (see record 1992-16903-001 ) published an article that challenged the notion that accurate perceptions of self and the world are essential for mental health. The authors argued instead that people's perceptions in these domains are positively biased and that these positive illusions promote psychological well-being. In...

Three studies found that self-esteem moderates the relation between mood and self-evaluation. In Study 1, a standard mood-induction procedure was used to induce positive, negative, or neutral moods in low self-esteem (LSE) Ss and high self-esteem Ss. Afterward, Ss evaluated their specific qualities and characteristics (e.g., How smart are you? How...

[argue] that all individuals experience a powerful need to enhance their feelings of personal worth, but that these needs are supplemented by a collateral need to maintain self-consistency / people with high self-esteem experience little or no conflict in satisfying these dual imperatives / for [low self-esteem] individuals, self-enhancement needs...

Four studies examined how the characteristics of others affect people's self-appraisals. Ss viewed photographs of physically attractive or unattractive targets, then rated their own attractiveness. Study 1 found evidence for a contrast effect: Ss' self-appraisals were more favorable after viewing an unattractive same-sex target than after viewing a...

Four studies examined how the characteristics of others affect people's self-appraisals. Ss viewed photographs of physically attractive or unattractive targets, then rated their own attractiveness. Study 1 found evidence for a contrast effect: Ss' self-appraisals were more favorable after viewing an unattractive same-sex target than after viewing a...

People regard themselves in more favorable terms than they regard others. Two experiments examined how this bias is influenced by threats to self-esteem (i.e., failure) and the private vs public nature of the context in which judgments of self and others are made. Private failure led subjects to exaggerate their superiority over others; public fail...

Asymmetrical attributions for success and failure are an established empirical fact, but the origins of this asymmetry are still the source of some debate. The present research examined whether physiological arousal plays a role in the generation of self-serving attributional judgments. Subjects received false feedback on an achievement-related tas...

Previous research suggests that physical fitness moderates the adverse effects of stressful life events. However, a reliance on self-reports of fitness and health may limit the validity of prior investigations. The present research tested the stress-buffering effect of fitness with subjective and objective indicators of exercise, fitness, and physi...

Two studies examined how situational variables and personal factors affect peoples' immediate representations of self and how, once activated, these representations guide behavior. In Study 1, Ss with high self-esteem (HSE) and Ss with low self-esteem (LSE) first experienced success or failure at an alleged test of their intellectual ability. Subse...

Examined 228 undergraduates' interest in evaluating their abilities after controlling for their anticipations of success. In 4 studies, the search for ability-relevant feedback was most evident when Ss had reason to believe that they would gain positive, rather than negative, information about the self. However, even those led to believe that feedb...

Previous research regarding the effects of positive life events on physical health has been inconclusive. We tested the hypothesis that positive life events have a detrimental effect on health only among people with negative self-views. This prediction derives from an identity disruption model of stress, which holds that an accumulation of life eve...

Previous research regarding the effects of positive life events on physical health has been inconclusive. We tested the hypothesis that positive life events have a detrimental effect on health only among people with negative self-views. This prediction derives from an identity disruption model of stress, which holds that an accumulation of life eve...

In two studies we examined the informational value of ability and effort cues as guides to achievement-related judgments about others. Using a response time methodology, we first presented subjects with information concerning how much ability a failing student had, how hard the student tried, or both. Subsequently, subjects reported interpersonal e...

In two studies we examined the informational value of ability and effort cues as guides to achievement-related judgments about others. Using a response time methodology, we first presented subjects with information concerning how much ability a failing student had, how hard the student tried, or both. Subsequently, subjects reported interpersonal e...

This study assessed the relationship of stressful life circumstances to illness symptoms and depressed mood among adolescent girls (in the 7th through the 11th grades). At two times, respondents indicated whether each of 20 commonly experienced circumstances had occurred to them and whether they rated its occurrence as positive or negative. Additio...

Two studies explored the relation between self-esteem and self-enhancement biases. It was proposed that people with high self-esteem engage in forms of self-enhancement in which the self is directly linked to positive identities and outcomes, whereas people with low self-esteem engage in forms of self-enhancement in which the self is indirectly lin...

Previous research concerned with whether self-directed attention increases self-attributions has produced inconclusive findings. The present research sought to clarify the issue by proposing that the effects of self-directed attention on causal judgments depend upon the match between the valence of the to-be-explained outcome and the attributer's s...

This research examined favouritism in group product evaluations as a function of personal involvement. After being divided into groups on an arbitrary basis, subjects worked at a group brainstorming task. Some subjects then assessed the merits of their own group's product relative to that of an outgroup's product, whereas other subjects assessed th...

Although perceptions of control occupied a central role in the development of learned helplessness theory, recent helplessness research has not considered controllability judgments when relating attributions to depression. Supporting the importance of this construct, the research discussed in this article found evidence that judgments of control in...

Many prominent theorists have argued that accurate perceptions of the self, the world, and the future are essential for mental health. Yet considerable research evidence suggests that overly positive self-evaluations, exaggerated perceptions of control or mastery, and unrealistic optimism are characteristic of normal human thought. Moreover, these...

The hypothesis that physical exercise provides benefits to individuals under periods of life stress has rarely been subject to empirical verification. This article presents the results of a longitudinal study of stress and well-being in adolescence in which the ability of exercise to buffer stress-induced deteriorations in physical health was exami...

Although perceptions of control occupied a central role in the development of learned helplessness theory, recent helplessness research has not considered controllability judgments when relating attributions to depression. Supporting the importance of this construct, the research discussed in this article found evidence that judgments of control in...

The hypothesis that physical exercise provides benefits to individuals under periods of life stress has rarely been subject to empirical verification. This article presents the results of a longitudinal study of stress and well-being in adolescence in which the ability of exercise to buffer stress-induced deteriorations in physical health was exami...

Three investigations are reported that examined the relation between self-appraisals and appraisals of others. In Experiment 1, subjects rated a series of valenced trait adjectives according to how well the traits described the self and others. Individuals displayed a pronounced “self-other bias,” such that positive attributes were rated as more de...