Personality and density distributions of behavior, emotions, and situations

Journal of Research in Personality 69 (2017) 225–236

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Personality and density distributions of behavior, emotions, and situations Ashley Bell Jones ⇑, Nicolas A. Brown, David G. Serfass, Ryne A. Sherman Florida Atlantic University, United States

a r t i c l e

i n f o

Article history: Received 16 September 2015 Revised 24 August 2016 Accepted 9 October 2016 Available online 14 October 2016

a b s t r a c t Whole Trait Theory defines personality as a density distribution of one’s momentary behavior, complete with all of its parameters (e.g., mean, SD, skew, kurtosis). Two questions regarding these parameters remain largely unexamined: (1) are individual differences in these parameters stable? And (2) do scores on standard personality tests correspond to these parameters? The current study (N = 209) employed an experience sampling design (Nobs  8300) to examine the stability of density distribution parameters and the relationship between standard personality test scores and density distribution parameters of 10 behaviors/emotions and 8 situation characteristics. Results showed that, (a) individual differences in density distribution parameters are moderately stable and (b) at the bivariate level, personality was associated with numerous distribution parameters for a number of behaviors/emotions, and situations. However, when the appropriate statistical controls were taken into account, these associations diminished. While individual differences in density distribution parameters we moderately stable, standard personality measures rarely correspond to any other parameters of density distributions once the mean of the density distribution is known. Emotionality and eXtraversion appear as exceptions to this general pattern. These results imply that both theory and measurement in personality should be cognizant of within-person variability in behavior. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction Human behavior is both stable and variable across situations. This apparent paradox is resolved by recognizing that behavioral differences between people are quite stable across contexts (i.e., rank-order stability: Funder & Colvin, 1991), while behavioral differences within people are quite common (i.e., situation specificity; Van Heck, Perugini, Caprara, & Fröger, 1994; Dreier, 2011; Fleeson, 2001, 2007). Despite this recognition, personality theories have long-struggled to parsimoniously and simultaneously explain both between- and within-person differences in behavior. For example, trait theories of personality (e.g., Allport, 1937; DeYoung, Quilty, & Peterson, 2007; John, Naumann, & Soto, 2008; Lee & Ashton, 2008; McCrae & Costa, 2008; Zuroff, 1986) have largely emphasized and focused on between-person differences in behavior. For their part, cognitive theories of personality (e.g., Bandura, 1999; Cervone, 2004; Kelly, 1963; Mischel, 1973; Mischel & Shoda, 1995, 2008; Read et al., 2010; Rotter, 1966) have largely emphasized and focused on within-person differences in behavior. The recently developed Whole Trait Theory integrates both trait and cognitive ⇑ Corresponding author at: Department of Psychology, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, United States E-mail address: [email protected] (A.B. Jones). http://dx.doi.org/10.1016/j.jrp.2016.10.006 0092-6566/Ó 2016 Elsevier Inc. All rights reserved.

perspectives on personality in an effort to explain both betweenand within-person differences in behavior. Whole Trait Theory (WTT: Fleeson, 2012; Fleeson & Jayawickreme, 2015) argues that personality itself is the density distribution of an individual’s behavior across situations (see also Fleeson, 2001, 2007). In probability theory, density distributions describe the likelihood that a particular observation will have a particular value. Under conditions of normality, the mean is the first moment, the expected value, and value most likely to be observed from a density distribution. The other parameters of the distribution, variability, skewness, and kurtosis are the second, third, and fourth moments respectively. WTT defines personality as a person’s entire distribution of behaviors, or personality states. ‘‘. . .A person’s trait level refers to his or her distribution of personality states. A distribution is not a single number and Whole Trait Theory argues that individuals’ actual behavior should be described by entire distributions rather than by single numbers” (Fleeson & Jayawickreme, 2015, p. 89). That is, according to WTT, personality corresponds not only to the center of one’s distribution of behavioral enactments, but also to one’s minimum, maximum, variability, skewness, and kurtosis. Such a position poses two problems for personality theory and measurement. The first problem concerns the stability of individual differences in density distribution parameters. Most personality

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psychologists would not consider something to be part of personality unless (a) there are individual differences and (b) those individual differences are relatively stable. Though it is well established that individuals reliably differ in their average levels of behavior (i.e., density distribution means), far less is known about the stability of individual differences in other distribution parameters (e.g., are individual differences in standard deviations reliable?). The best studies examining this question appear in Fleeson’s (2001) seminal article on density distributions. In an experience sampling study, Fleeson found evidence for stability in means (0.91, averaged across all behaviors measured), standard deviations (0.59), skew (0.47), and kurtosis (0.26) in sample of 46 individuals who provide 50 reports on average across 13 days. Similar values were found in a second study of 29 individuals averaging 71 reports across 20–22 days for means (0.97), standard deviations (0.79), skew (0.44), and kurtosis (0.22). While these values suggest that there are individual differences in density distribution parameters are stable, the analysis used by Fleeson (2001) cannot say this definitively because it did not take into account the fact that the mean (or first moment) of a density distribution is often confounded (correlated) with other parameters of the distribution (e.g., standard deviation, skew). That is, people who have very high (or low) means will likely also have low standard deviations because they will repeatedly hit the ceiling (or floor) on most rating scales. Further, the relationship between the first moment of a distribution (i.e., the mean) and later moments (e.g., the SD) is not expected to be linear, but curvilinear (Baird, Le, & Lucas, 2006). Therefore, to evaluate the stability of density distribution parameters beyond the mean, one needs to statistically control for the mean and the mean-squared. To our knowledge, this is the first study to estimate the stability of density distribution parameters while using the proper controls. The second problem posed by Whole Trait Theory pertains to the measurement of personality. Numerous studies have shown that traditional trait personality measures do predict average behavior across both time and situations (Ching et al., 2014; Church et al., 2013; Fleeson, 2001, 2007; Fleeson & Gallagher, 2009; Fleeson & Law, 2015; Funder & Colvin, 1991; Judge, Simon, Hurst, & Kelley, 2014; Sherman, Rauthmann, Brown, Serfass, & Jones, 2015). Thus, personality measures do in fact correspond to the first moment of density distributions of behavior—the mean. Do scores personality measures correspond to any other parameters of density distributions of behavior? The best data available to address this question are reported in a study by Fleeson and Gallagher (2009). Their study combined data sets from 15 experience sampling studies conducted over 8 years and containing nearly 500 subjects and more than 20,000 individual reports. Their analyses indicate that personality scores on the Big Five do in fact correspond to numerous parameters of density distributions of behaviors (e.g., mean, median, mode, maximum, minimum, variability, skew, and kurtosis; see their Table 4). However, as noted previously, such bivariate associations can be misleading because the parameters of a density distribution are often confounded with the distribution’s mean. Appropriately then, Fleeson and Gallagher (2009) controlled for the mean—as well as the squared-mean for some parameters—and found that the associations between personality measures and those additional parameters of the density distribution largely disappeared. The lone exception here was the maximum, for which only the mean was controlled, which still showed strong associations after controlling for the mean. The present study seeks to answer two questions: (1) how stable are parameters of density distributions of behavior, emotion, and situation characteristics? And (2) are trait personality test scores related to the various parameters of density distributions. As such, this study represents a conceptual replication of Fleeson (2001) and Fleeson and Gallagher (2009) in a new sample from a

different undergraduate population. The 15 samples gathered by Fleeson and Gallagher were drawn from a private university (Wake Forest University) and ranged in size from N = 12 to N = 63. In contrast, our sample is drawn from a public university (Florida Atlantic University) and contains data from N = 209 participants. In addition, this study extends the investigation by Fleeson and Gallagher by (a) including a sixth dimension of personality of Honesty/ Humility and (b) examining—for the first time to our knowledge—how personality may be related to density distributions of situation experiences. 1.1. What about situations? It does not take much to recognize that behavior is at least partially a function of the situation. Although there were some serious efforts to define, taxonomize, and measure situations in the 1970s and 1980s (e.g., Argyle, Furnham, & Graham, 1981; Frederiksen, 1972; Magnusson, 1971, 1981; Pervin, 1978; van Heck, 1984, 1989), a recent surge of research on situations has brought the topic back to the forefront (e.g., Fleeson, 2007; Fournier, Moskowitz, & Zuroff, 2008, 2009; Funder, 2009; Funder, Guillaume, Kumagai, Kawamoto, & Sato, 2012; Rauthmann, 2012, 2015; Rauthmann & Sherman, 2016a, 2016b; Rauthmann, Sherman, & Funder, 2015a, 2015b; Rauthmann et al., 2014; Reis, 2008; Saucier, Bel-Bahar, & Fernandez, 2007; Schmitt et al., 2013; Serfass & Sherman, 2013; Sherman, Nave, & Funder, 2010, 2013; Sherman et al., 2015; Wagerman & Funder, 2009; Yang, Read, & Miller, 2006, 2009). One result from this recent surge is the introduction of the DIAMONDS characteristics of situations (Rauthmann et al., 2014) and its accompanying measurement tools (Rauthmann & Sherman, 2016a, 2016b). The DIAMONDS are Duty (Does something need to be done?), Intellect (Is deep thinking required or desired?), Adversity (Are there external threats?), Mating (Is the situation sexually and/or romantically charged?), pOsitivity (Is the situation enjoyable?), Negativity (Does the situation elicit unpleasant feelings?), Deception (Is someone being untruthful or dishonest?), and Sociality (Are social interaction and relationship formation possible, required, or desired?). The DIAMONDS represent the broadest eight dimensions found in the Riverside Situational Q-sort (RSQ: Wagerman & Funder, 2009), which is the most comprehensive measure of situation characteristics currently available (Rauthmann et al., 2014). Beyond examining the relationships between personality and parameters of density distributions of behavior and emotion, the current study also examines potential relationships between personality and density distributions of the DIAMONDS situation characteristics. Prior theorizing and empirical work suggest that personality ought to be related to the kinds of situations people experience on average (Allport, 1961; Bandura, 1978; Buss, 1987; Emmons, Diener, & Larsen, 1986; Ickes, Snyder, & Garcia, 1997). However, the empirical work in this domain is rather limited. In terms of the DIAMONDS, the only study to examine links between personality and density distributions of situation experience thus far—using the same data analyzed in this study—showed that personality does predict average self-reported situation experiences, though only rather weakly (Sherman et al., 2015). No examination of the association between personality and other distribution parameters has yet been undertaken. 2. Method 2.1. Participants Two hundred-eighteen undergraduate participants with smart phones were solicited from Florida Atlantic University’s subject

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pool in exchange for partial course credit. Data from eight participants were not included in analyses because they completed only the first session of the study. One participant’s personality data was lost due to a computer error; however experience sampling data from this participant are used wherever possible. Thus, most analyses reported here pertain to 209 participants (136 Female, 73 Male, 1 Unknown), though for any given analysis the N may be slightly lower due to missingness. The average age for these participants was 18.61 years (SD = 1.78). The ethnic breakdown for these participants was 18.2% African American, 1.4% Asian, 47.4% Caucasian, 23.0% Hispanic/Latino, 7.6% Other, and 2.4% did not indicate or unknown. Data from this study have been reported elsewhere (Brown & Sherman, 2014; Sherman et al., 2015), but the analyses presented here are new. 2.2. Procedure During an initial laboratory visit, participants received information about the study, provided informed consent, completed a demographic questionnaire and several measures of personality, and participated in a private video interview (see Brown & Sherman, 2014 for more details on the interview). Participants provided research assistants with their phone numbers and were instructed on how to complete mobile surveys. Participants received eight text messages per day for the next seven days at randomly selected (in advance) time points between the hours of 9 am and 11 pm (see Sherman et al., 2015 for text message schedule). The text message contained the link to a survey and a message reading, ‘‘Please complete the survey now.” Participants were instructed that when they received the text, they should follow the link and complete short questionnaires about their situation, behavior, and emotions at the time that they received the text message. Participants were informed that they must complete the survey within an hour of receiving the text, and they must complete at least 75% of the surveys (6 per day or 42 total) to receive full credit for the study. In total, participants completed 9753 reports (82.9%). Survey responses were considered valid if they were started within an hour after any text was sent, finished within an hour after that specific text message was sent, and they were the only survey completed in that interval. Such preprocessing is consistent with similar research using experience sampling methods (McCabe, Mack, & Fleeson, 2012). This left a total of 8318 (70.7%) of completed reports, or 39.61 reports per participant (SD = 9.67, median = 41, min = 1, max = 55). 2.3. Measures 2.3.1. Trait measures 2.3.1.1. Personality. The HEXACO-60 (Ashton & Lee, 2009) is a 60-item measure for assessing the Big 5 personality traits of agreeableness, conscientiousness, extraversion, neuroticism, and openness as well as a sixth personality dimension of honestyhumility. Each item was rated on a five-point scale (1 = disagree strongly, 5 = agree strongly). Additionally, we assessed subjective happiness with the Subjective Happiness Scale (SHS: Lyubomirsky & Lepper, 1999), a 4-item measure of trait happiness. Participants rated themselves on these items using a 1–7 Likerttype rating scale (e.g., ‘‘In general, I consider myself: 1 [not a very happy person], 7 [a very happy person]). The descriptive statistics, including internal consistencies, for all trait and state measures are displayed in Table 1. 2.3.2. State measures 2.3.2.1. Situations. The S8-I (Rauthmann & Sherman, 2016b) contains eight items assessing experience of the DIAMONDS situational characteristics (Rauthmann et al., 2014; Duty, Intellect,

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Adversity, Mating, pOsitivity, Negativity, Deception, and Sociality). Each item assesses one situation characteristic on a scale of 1 (extremely uncharacteristic) to 7 (extremely characteristic). 2.3.2.2. Behavior and emotion. Seven seven-point bipolar adjective scales, each with two adjectives serving as anchors, were used to measure momentary behavior: Honesty/Humility (humble, honest—arrogant, dishonest), Emotionality (nervous, emotional—calm, unemotional), Sociability (outgoing, sociable—reserved, quiet), Agreeableness (warm, agreeable—cold, quarrelsome), Conscientiousness (organized, hardworking—disorganized, lazy), Openness/Intellect (intelligent, creative—unintelligent, uncreative), Dominance (dominant, assertive—submissive, unassertive). Note that we used two items for eXtraversion, one tapping its social component and another tapping its dominance component.1 Additionally, three seven-point bipolar adjective scales were used to measure momentary feelings of happiness (happy, positive—sad, negative), self-esteem (feeling good about myself—feeling bad about myself), and authenticity (authentic [true to myself]—inauthentic [not true to myself]). 3. Results We first calculated the distribution parameters – mean, standard deviation, minimum, maximum, skew, and kurtosis – for each person for the DIAMONDS characteristics, behavioral, and affective variables. Descriptive statistics for each of these distribution parameters are displayed in Table 2. 3.1. Stability of density distribution parameters To address our first question—how stable are individual differences in density distribution parameters?—we used the same split-half reliability technique employed by Fleeson (2001), to estimate the reliability of distribution parameters. This entails: (1) randomly splitting each person’s responses to each variable into two equal halves, (2) calculating the distribution parameters for each half, (3) correlating the parameter estimates for the two halves across all participants to obtain a split-half correlation, and (4) applying the Spearman-Brown formula (two times the split-half correlation divided by the split-half correlation plus one) to the split-half correlation to obtain estimates of the reliability of the distribution parameters. Because sampling error is introduced by using random split-halves, we repeated this procedure 100 times and retained the average split-half reliability figures as our best estimates of the reliabilities of the distribution parameters.2 As we noted earlier, density distribution parameters beyond the mean (e.g., sd, skew, etc.) are often confounded by the mean. As a result, the procedure just describe could artificially inflate reliability estimates for those density distribution parameters if the mean (and mean-squared) is not taken into account. To resolve this issue, 1 We recognize that there is some debate as to whether or not momentary selfreported trait enactments should be counted as behavior or something else (e.g., personality states). Indeed, some might define behavior only as objectively observable/measureable cues (e.g., amount of time spent talking, merchandise purchases, number of eye blinks, etc.). For the purposes of the this paper, we use a looser definition of behavior that includes such momentary self-reports (see Furr, 2009 for more discussion). 2 Note that we excluded N = 4 participants (22 observations) in this analysis who had less than 10 total reports (out of the 56 possible) to increase the stability of the parameter estimates. Additionally, we should point out that the intraclass correlation estimated from an unconditional cell means model is often used to estimate the reliability of the mean parameter. However, as no such equivalent is available (to our knowledge) for other density distribution parameters, we employed this method for the mean as well to be consistent and so that the results could be compared across parameters.

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Table 1 Descriptive statistics.

Personality Honesty/Humility Emotionality Extraversion Agreeableness Conscientiousness Openness Subjective Happiness Situations Duty Intellect Adversity Mating Positivity Negativity Deception Sociality

n

M

SD

a

209 209 209 209 209 209 209

3.33 3.27 3.57 3.31 3.59 3.20 5.29

0.55 0.67 0.62 0.63 0.57 0.66 1.20

0.63 0.76 0.79 0.75 0.75 0.74 0.82

8290 8286 8284 8302 8285 8298 8295 8297

4.19 3.33 1.68 2.49 4.42 2.44 1.65 4.04

2.31 2.19 1.35 2.11 2.06 1.84 1.30 2.31

Behavior and Affect Honesty/Humility Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feeling happy Feeling good

n

M

SD

8295 8264 8284 8281 8296 8286 8289 8297 8286 8296

5.68 3.53 4.74 5.40 4.89 5.13 4.45 5.77 5.36 5.40

1.53 1.98 1.97 1.64 1.83 1.62 1.71 1.57 1.75 1.75

Note. Personality scores reflect self-reports at the person level on the HEXACO-60 using a 1–5 scale. Subjective Happiness reflects self-reports on the Subjective Happiness Scale using a 1–7 scale. Situation scores reflect self-reports at the situation level on the S8-I using a 1–7 scale. Behavior and affect reflect self-reports at the situation level on 1–7 bipolar adjective scales.

Table 2 Descriptive statistics for distribution parameters. State-level characteristic

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

Mean

Standard Deviation

Minimum

Maximum

Skew

Kurtosis

M

SD

M

SD

M

SD

M

SD

M

SD

M

SD

5.66 3.51 4.70 5.39 4.85 5.12 4.44 5.76 5.34 5.39 4.19 3.35 1.69 2.53 4.44 2.46 1.68 4.04

1.07 1.17 1.13 1.04 1.05 1.04 1.08 1.11 1.11 1.19 1.16 1.08 0.84 1.21 1.01 1.02 0.82 1.04

1.02 1.55 1.57 1.20 1.46 1.19 1.26 1.00 1.32 1.22 1.96 1.87 0.92 1.62 1.74 1.47 0.88 2.02

0.49 0.50 0.54 0.49 0.49 0.47 0.53 0.53 0.48 0.52 0.58 0.52 0.58 0.76 0.51 0.55 0.59 0.55

2.92 1.27 1.57 2.37 1.71 2.32 1.90 2.99 2.10 2.39 1.30 1.16 1.05 1.15 1.40 1.08 1.05 1.17

1.74 0.76 1.07 1.51 1.16 1.42 1.12 1.84 1.35 1.57 0.96 0.71 0.31 0.66 0.96 0.41 0.30 0.72

6.81 6.55 6.80 6.84 6.80 6.76 6.61 6.87 6.85 6.81 6.92 6.70 4.76 6.13 6.84 6.08 4.55 6.82

0.58 0.99 0.62 0.49 0.55 0.64 0.78 0.51 0.58 0.64 0.33 0.64 2.03 1.38 0.53 1.40 2.17 0.55

1.39 0.30 0.57 1.01 0.64 0.59 0.15 1.55 1.09 1.15 0.11 0.42 2.75 1.45 0.23 1.30 2.55 0.08

1.79 1.24 1.25 1.52 1.20 1.41 1.51 1.83 1.40 1.58 1.02 0.94 2.01 1.72 0.90 1.41 1.97 1.04

4.48 0.78 1.07 2.62 1.06 1.72 2.24 5.03 2.32 2.98 0.21 0.17 1.74 3.91 0.17 2.69 9.53 0.27

9.12 4.94 5.71 6.43 4.98 5.53 6.62 8.87 6.43 7.82 3.53 2.88 12.48 9.28 3.25 6.91 12.44 4.26

Note. N = 209. The M and SD values in the table are computed by first calculating the distribution parameters (e.g., M, SD) for each participant and then summarizing them over all participants. Behavior and affect items (Honesty-Feel Good) were self-reports at the situation level on 1–7 bipolar adjective scales while situation items (DutySociality) used a 1–7 scale unipolar scale.

during the computation of the split-half reliabilities just described, we also used linear regressions to statistically control for each half’s mean and mean-squared for each density distribution parameter. The residuals resulting from these regressions were then correlated and the Spearman-Brown formula applied to estimate the split-half reliability of density distribution parameters after controlling for potential mean confounds. This split-half reliability information from these analyses is presented in Table 3, with Rel1 indicating split-half reliabilities computed without controlling for the mean and mean-squared, and Rel2 indicating those reliabilities after proper controls were applied. There are four things of note here. First, the average stability for the mean parameter was very high (0.94), which is consistent with Fleeson’s (2001) results. Second, when the effects of the mean and mean-squared were taken into account, all parameters showed substantial decreases in stability. This was especially true for skew suggesting that it is fairly unstable parameter of density distributions. Still, consistent with WTT’s claim, even after applying proper controls there are reliable individual differences

in these parameters (i.e., individual differences in density distribution parameters are not simply noise). Third, lower-order parameters tended to show higher stability. The average stability was 0.94 for means, 0.65 for standard deviations, 0.54 for minimums, 0.46 for maximums, 0.23 for skew, and 0.47 for kurtosis. This is also consistent with Fleeson’s (2001) finding and implies that reliability is achieved more quickly with means, followed by standard deviations, followed by min and max, with skew and kurtosis bringing up the rear. Overall these findings suggest that, although individual differences in density distribution parameters do show some stability, the estimates provided by Fleeson (2001) may have been overly optimistic because they did not remove the influence of location (mean) on scale (standard deviation) and shape (skew and kurtosis). How large is the influence of density distribution location (mean) on other density distribution parameters? It is possible to judge the size of the relationship between the mean and mean-squared on density distribution parameters by examining the size of the difference between Rel1 and Rel2 in Table 3, with

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A.B. Jones et al. / Journal of Research in Personality 69 (2017) 225–236 Table 3 Reliability information for distribution parameters. State-level characteristic

Mean

Standard Deviation

Minimum

Maximum

Skew

Kurtosis

Rel

Rel1

Rel2

Rel1

Rel2

Rel1

Rel2

Rel1

Rel2

Rel1

Rel2

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.97 0.95 0.94 0.96 0.94 0.96 0.96 0.97 0.96 0.97 0.92 0.91 0.96 0.94 0.91 0.93 0.95 0.88

0.81 0.82 0.86 0.79 0.83 0.82 0.87 0.83 0.80 0.83 0.88 0.84 0.76 0.88 0.87 0.79 0.77 0.88

0.68 0.79 0.82 0.69 0.78 0.77 0.87 0.64 0.68 0.70 0.81 0.77 .05 0.69 0.83 0.53 0.10 0.84

0.75 0.80 0.77 0.73 0.74 0.74 0.70 0.78 0.76 0.79 0.85 0.83 0.84 0.90 0.80 0.77 0.79 0.74

0.47 0.51 0.56 0.51 0.52 0.57 0.56 0.46 0.48 0.49 0.67 0.63 0.27 0.80 0.64 0.51 0.33 0.67

0.86 0.63 0.68 0.72 0.73 0.77 0.72 0.84 0.81 0.83 0.43 0.67 0.68 0.70 0.77 0.70 0.71 0.74

0.70 0.49 0.41 0.51 0.55 0.54 0.62 0.50 0.63 0.65 0.25 0.52 0.07 0.30 0.62 0.37 0.03 0.54

0.71 0.80 0.71 0.78 0.76 0.80 0.59 0.79 0.77 0.77 0.80 0.76 0.47 0.67 0.78 0.73 0.55 0.81

0.40 0.32 0.12 0.43 0.31 0.58 0.16 0.60 0.24 0.41 0.10 0.47 0.30 0.12 0.09 0.10 0.44 0.13

0.63 0.72 0.67 0.74 0.67 0.68 0.70 0.75 0.74 0.67 0.73 0.74 0.53 0.57 0.78 0.67 0.52 0.76

0.43 0.53 0.45 0.58 0.40 0.58 0.65 0.58 0.51 0.43 0.57 0.52 0.35 0.02 0.63 0.26 0.41 0.53

Average

0.94

0.83

0.65

0.78

0.54

0.72

0.46

0.72

0.23

0.68

0.47

Note. N = 205. Rel = split-half reliability estimate for individual differences in density distribution means. Rel1 = split-half reliability estimate for density distribution parameter prior to controlling for distribution mean and mean-squared. Rel2 = split-half reliability estimate for density distribution parameter after controlling for distribution mean and mean-squared. All reliabilities were computed by randomly dividing each person’s responses into equal halves, computing the distribution parameter for each half, and correlating the two halves across all 205 participants. These split-half correlations were then Spearman-Brown upped to the level of the parameter estimates to yield split-half reliability estimates. For Rel2, the scores for each half were first predicted by its’ own mean and mean-squared and the residuals were then used to compute the split-half correlation. This was repeated 100 times to account for random sampling error and the average correlation was taken as the best estimate of the split-half reliability. Table 4 Multiple correlations between density distribution parameter and distribution’s mean + mean-squared. State-level characteristic

Standard Deviation

Minimum

Maximum

Skew

Kurtosis

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.59 0.39 0.42 0.52 0.42 0.43 0.10 0.68 0.56 0.61 0.53 0.46 0.84 0.70 0.43 0.69 0.85 0.44

0.62 0.63 0.58 0.55 0.52 0.48 0.35 0.64 0.60 0.63 0.58 0.63 0.76 0.66 0.56 0.54 0.62 0.49

0.64 0.40 0.64 0.49 0.43 0.64 0.34 0.68 0.73 0.73 0.14 0.38 0.66 0.56 0.45 0.56 0.68 0.42

0.68 0.77 0.79 0.77 0.81 0.69 0.63 0.68 0.82 0.76 0.78 0.85 0.60 0.81 0.85 0.80 0.47 0.75

0.53 0.56 0.59 0.60 0.65 0.49 0.31 0.59 0.64 0.59 0.44 0.51 0.56 0.65 0.69 0.64 0.45 0.48

Average

0.56

0.58

0.55

0.75

0.56

Note. N = 206. Values in table are multiple correlations (R) from regression models predicting each density distribution parameter (columns), using the distribution’s mean and mean-squared as predictors, for each behavior/emotion/situation variable measured (rows). Large values indicate greater association between the distribution parameter and the first moment (mean and mean-squared) of the same distribution, indicating a larger confounding between the distribution parameter and the distribution’s mean.

larger differences indicating a greater influence. However, Table 4 presents the multiple-R between the density distribution parameter and the distribution’s mean and mean-squared for each parameter and each variable. As can be seen, the average association across all parameters is substantial (all Rs > 0.50) indicating that distribution shape and scale parameters are frequently, and often sizably, confounded with distribution location. 3.2. Predicting density distribution parameters from trait measures Having established that density distribution parameters have some stability, we next used least squares regression to predict

the parameters of each behavioral, affective, and situational experience item from HEXACO and happiness scores. We then performed these regressions again while controlling for the mean and mean-squared3 of the distributions (following Baird et al., 2006). All variables were standardized prior to analyses to aid with interpretability. The results of these two methods are displayed side-by-side for each HEXACO variable and happiness, in Tables

3 Under conditions of non-normality, the median may be of more interest and practical importance (Wilcox, 2012). The conclusions for all of the analyses in the manuscript do not substantially change when including the median instead of the mean. Fleeson and Gallagher (2009) reported the same pattern.

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higher on Honesty-Humility reported experiencing situations that were more positive (0.18) and less adverse ( 0.24), negative ( 0.14), and deceptive ( 0.27) on average across time. The second column of Table 5 (Standard Deviation b) contains two sub-columns. The unbolded sub-column indicates the bivariate standardized slope (correlation) between Honesty-Humility personality scores and the standard deviations of state-level expressions of behavior and emotion, and situation experiences. The bold sub-column indicates the same standardized slopes, but this time while controlling for density distribution means and squared means. As can be seen, people scoring higher on Honestly-Humility reported less variability in their expressions of honest-humble behavior ( 0.20), (b) feelings of authenticity

5–11. The bold columns indicate the analyses in which the mean and squared mean were controlled. Because Tables 5–11 contain a lot of information, we first walk through the results for Table 5 and then summarize the key themes present across all of the Tables. The first column of Table 5 (Mean b) indicates the standardized slope between Honesty-Humility personality scores and mean state-level expressions of behavior, emotion, and situation experiences. As can be seen, people higher on Honesty-Humility reported expressing more honest-humble (0.27), agreeable (0.21), and open (0.15) behavior on average across time. Additionally, people higher on Honesty-Humility reported experiencing more authenticity (0.25), happiness (0.22), and self-esteem (0.20) on average across time. Lastly, people

Table 5 Trait-level honesty-humility associations with distribution parameters of state-level behavior, emotions, and situations. Honesty State-level characteristic

Mean b

Standard Deviation b

Minimum b

Maximum b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.27*** 0.07 0.06 0.21** 0.08 0.15* 0.03 0.25*** 0.22** 0.20** 0.05 0.04 0.24*** 0.12 0.18** 0.14^ 0.27*** 0.04

0.20** 0.02 0.03 0.07 0.01 0.04 0.11 0.20** 0.01 0.10 0.06 0.02 0.19** 0.05 0.04 0.06 0.31*** 0.07

0.21** 0.09 0.01 0.10 0.08 0.09 0.08 0.18** 0.06 0.14* 0.01 0.03 0.08 0.03 0.13^ 0.10 0.07 0.05

0.07 0.11 0.01 0.12^ 0.09 0.04 0.07 0.15* 0.09 0.09 0.03 0.06 0.13^ 0.05 0.04 0.09 0.29*** 0.04

0.04 0.07 0.08 0.05 0.00 0.01 0.11 0.04 0.08 0.02 0.09 0.07 0.02 0.07 0.01 0.07 0.10** 0.14*

0.04 0.10^ 0.06 0.03 0.06 0.03 0.07 0.01 0.07 0.01 0.00 0.01 0.00 0.03 0.04 0.10 0.02 0.07

Skew b 0.03 0.07 0.00 0.06 0.06 0.04 0.06 0.07 0.01 0.01 0.04 0.02 0.02 0.05 0.01 0.02 0.11* 0.08

0.19** 0.06 0.06 0.19** 0.00 0.09 0.01 0.20** 0.19** 0.23** 0.09 0.07 0.28*** 0.19** 0.13^ 0.14* 0.25** 0.09

Kurtosis b 0.17* 0.01 0.02 0.17* 0.01 0.07 0.04 0.17* 0.09 0.16* 0.05 0.00 0.24** 0.17* 0.03 0.11 0.21** 0.01

0.00 0.02 0.02 0.01 0.05 0.01 0.00 0.03 0.02 0.07^ 0.03 0.02 0.10* 0.07* 0.01 0.01 0.06 0.05

0.03 0.05 0.06 0.03 0.03 0.02 0.03 0.06 0.03 0.04 0.06 0.04 0.09^ 0.06 0.03 0.02 0.06 0.05

Note. N = 209. All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. *** p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

Table 6 Trait-level emotionality associations with distribution parameters of state-level behavior, emotions, and situations. Emotionality State-level characteristic

Mean b

Standard Deviation b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.13^ 0.18** 0.09 0.06 0.12^ 0.05 0.04 0.09 0.05 0.03 0.23*** 0.03 0.06 0.09 0.09 0.14* 0.11 0.16*

0.13^ 0.17* 0.13^ 0.18** 0.08 0.15* 0.15* 0.15* 0.18** 0.20** 0.00 0.12^ 0.06 0.08 0.15* 0.28*** 0.01 0.15*

0.14* 0.15* 0.11^ 0.17** 0.10 0.15* 0.15* 0.15** 0.14* 0.16** 0.15* 0.16** 0.03 0.09^ 0.15* 0.18*** 0.01 0.21**

Minimum b 0.12^ 0.03 0.06 0.18* 0.06 0.08 0.08 0.09 0.17* 0.15* 0.03 0.04 0.01 0.05 0.16* 0.03 0.01 0.04

Maximum b 0.16** 0.04 0.08 0.18** 0.10^ 0.10 0.09 0.11* 0.18** 0.15** 0.14* 0.02 0.08^ 0.02 0.14* 0.05 0.10^ 0.14*

0.08 0.25*** 0.07 0.07 0.09 0.04 0.10 0.09 0.06 0.08 0.03 0.07 0.06 0.01 0.04 0.27*** 0.06 0.07

Skew b 0.02 0.18** 0.01 0.03 0.04 0.02 0.08 0.01 0.01 0.03 0.06 0.09 0.05 0.01 0.00 0.18** 0.05 0.04

0.12^ 0.03 0.03 0.07 0.07 0.11 0.03 0.10 0.03 0.07 0.21** 0.03 0.04 0.07 0.02 0.07 0.09 0.09

Kurtosis b 0.06 0.07^ 0.02 0.03 0.01 0.06 0.00 0.03 0.03 0.05 0.06 0.03 0.01 0.00 0.07* 0.04 0.02 0.01

Note. N = 209All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. *** p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

0.04 0.01 0.02 0.00 0.05 0.08 0.03 0.00 0.07 0.03 0.13^ 0.07 0.00 0.08 0.02 0.05 0.04 0.07

0.03 0.01 0.00 0.01 0.03 0.06 0.05 0.00 0.03 0.04 0.06 0.03 0.02 0.05 0.01 0.03 0.01 0.03

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A.B. Jones et al. / Journal of Research in Personality 69 (2017) 225–236 Table 7 Trait-level extraversion associations with distribution parameters of state-level behavior, emotions, and situations. Extraversion State-level characteristic

Mean b

Standard Deviation b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.23*** 0.04 0.37*** 0.35*** 0.32*** 0.29*** 0.26*** 0.23*** 0.33*** 0.34*** 0.06 0.02 0.10 0.12^ 0.16* 0.23*** 0.09 0.11

0.02 0.05 0.00 0.02 0.00 0.07 0.09 0.14^ 0.03 0.09 0.15* 0.13^ 0.05 0.18* 0.09 0.11 0.09 0.14*

0.12* 0.13^ 0.17* 0.11^ 0.08 0.16* 0.12 0.07 0.16* 0.12* 0.14* 0.11^ 0.02 0.14*** 0.15* 0.01 0.01 0.15*

Minimum b 0.16* 0.04 0.22*** 0.15* 0.17* 0.16* 0.10 0.19* 0.21*** 0.22*** 0.06 0.04 0.12^ 0.03 0.11 0.08 0.07 0.02

Maximum b 0.00 0.05 0.02 0.02 0.04 0.02 0.01 0.01 0.01 0.02 0.05 0.01 0.05 0.10^ 0.01 0.02 0.04 0.06

0.17* 0.05 0.12^ 0.20** 0.14* 0.19** 0.22** 0.10 0.14* 0.14* 0.07 0.06 0.12^ 0.12^ 0.21** 0.15* 0.13^ 0.13^

Skew b 0.09 0.08 0.03 0.06 0.02 0.07 0.14* 0.07 0.07 0.03 0.08 0.05 0.09^ 0.08 0.19** 0.06 0.06 0.09

0.11 0.03 0.24*** 0.27*** 0.25*** 0.19** 0.08 0.18* 0.28*** 0.29*** 0.05 0.02 0.02 0.06 0.07 0.13^ 0.03 0.04

Kurtosis b 0.05 0.02 0.10* 0.00 0.00 0.03 0.09 0.01 0.01 0.00 0.00 0.00 0.01 0.03 0.04 0.03 0.01 0.03

0.04 0.08 0.12^ 0.12 0.14* 0.06 0.04 0.17* 0.18* 0.18** 0.04 0.10 0.01 0.04 0.05 0.04 0.02 0.05

0.07 0.00 0.11^ 0.05 0.01 0.06 0.02 0.01 0.03 0.03 0.04 0.05 0.01 0.01 0.07 0.05 0.01 0.05

Note. N = 209All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. *** p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

Table 8 Trait-level agreeableness associations with distribution parameters of state-level behavior, emotions, and situations. Agreeableness State-level characteristic

Mean b

Standard Deviation b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.20*** 0.11 0.10 0.29*** 0.08 0.17* 0.10 0.16* 0.28*** 0.21** 0.01 0.01 0.18** 0.03 0.29*** 0.18** 0.17* 0.14^

0.12^ 0.01 0.06 0.07 0.00 0.01 0.15* 0.16* 0.06 0.07 0.08 0.01 0.13^ 0.14* 0.04 0.09 0.17* 0.09

Minimum b 0.04 0.02 0.10 0.01 0.01 0.04 0.14* 0.08 0.04 0.01 0.14* 0.07 0.04 0.12* 0.13^ 0.02 0.04 0.12^

0.15* 0.15* 0.07 0.13^ 0.13^ 0.06 0.13^ 0.19** 0.15* 0.10 0.03 0.10 0.13^ 0.08 0.09 0.12^ 0.04 0.10

Maximum b 0.05 0.12* 0.02 0.01 0.10^ 0.01 0.10 0.10^ 0.00 0.02 0.07 0.16** 0.03 0.09^ 0.07 0.07 0.01 0.16**

0.10 0.10 0.04 0.13^ 0.02 0.08 0.08 0.05 0.10 0.10 0.04 0.01 0.09 0.09 0.12^ 0.06 0.18* 0.09

Skew b 0.00 0.05 0.00 0.00 0.01 0.01 0.12^ 0.02 0.04 0.02 0.04 0.03 0.01 0.06 0.05 0.04 0.07 0.05

0.15* 0.07 0.11 0.27*** 0.01 0.17* 0.09 0.07 0.26*** 0.18* 0.02 0.02 0.20** 0.06 0.20** 0.18* 0.10 0.12^

Kurtosis b 0.01 0.00 0.01 0.04 0.05 0.03 0.05 0.03 0.01 0.01 0.03 0.04 0.02 0.04 0.04 0.01 0.05 0.02

0.16* 0.02 0.12^ 0.17* 0.04 0.08 0.04 0.05 0.17* 0.14^ 0.07 0.12^ 0.17* 0.05 0.03 0.12^ 0.05 0.04

0.07 0.04 0.04 0.04 0.06 0.01 0.04 0.01 0.02 0.03 0.04 0.03 0.04 0.04 0.03 0.01 0.08 0.02

Note. N = 209All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. *** p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

( 0.20), and (c) experiences of adverse ( 0.19) and deceptive ( 0.31) situation characteristics. However, because standard deviations of density distributions are confounded with the mean and the squared mean of the density distribution (e.g., someone with a mean near the scale maximum is very likely to have less variability than someone nearer the middle; see Baird et al., 2006) these associations could be entirely driven by the mean alone, and therefore misleading. As shown in the bold sub-column, when properly controlling for the mean and the squared mean of the density distribution, the associations between HonestyHumility scores and the standard deviations of behavioral, emotional, and situational density distributions practically

disappear. In terms of this specific result (Honestly-Humility and standard deviations), this means that correspondence between personality scores on Honesty-Humility and variability in behavioral, emotional, and situational experiences is spurious. The associations tell us nothing more than what we already know from the association of Honesty-Humility with the mean of the density distribution. The analytic procedure and logic of the foregoing paragraph can be applied to each additional distribution parameter (min, max, skew, kurtosis) shown in Table 5. As can be seen, the pattern of results is quite similar for each distribution parameter: HonestyHumility is related to those behaviors, emotions, and situations

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Table 9 Trait-level conscientiousness associations with distribution parameters of state-level behavior, emotions, and situations. Conscientiousness State-level characteristic

Mean b

Standard Deviation b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.21** 0.12^ 0.15* 0.20** 0.33*** 0.25*** 0.21** 0.20** 0.20** 0.19*** 0.11 0.10 0.18* 0.02 0.08 0.17* 0.18* 0.00

0.10 0.01 0.08 0.06 0.02 0.03 0.15* 0.16* 0.01 0.09 0.10 0.19** 0.12^ 0.05 0.03 0.07 0.15* 0.14*

Minimum b 0.03 0.11^ 0.18** 0.09 0.11^ 0.04 0.18* 0.00 0.12* 0.06 0.15* 0.18** 0.00 0.10^ 0.08 0.08 0.03 0.16*

0.09 0.02 0.01 0.06 0.06 0.10 0.04 0.13^ 0.03 0.13^ 0.03 0.04 0.10 0.03 0.03 0.07 0.13^ 0.00

Maximum b 0.06 0.05 0.13* 0.09 0.10 0.02 0.12^ 0.03 0.11* 0.01 0.03 0.07 0.03 0.05 0.09 0.06 0.06 0.01

0.12^ 0.03 0.11 0.18** 0.17* 0.09 0.14* 0.13^ 0.14* 0.11 0.17** 0.11 0.09 0.07 0.06 0.07 0.13^ 0.07

Skew b 0.05 0.07 0.12* 0.14* 0.05 0.02 0.07 0.10^ 0.11* 0.07 0.16* 0.08 0.01 0.11^ 0.06 0.06 0.02 0.08

0.19** 0.17* 0.15* 0.21** 0.21** 0.14* 0.15* 0.20** 0.22** 0.21** 0.02 0.04 0.19** 0.11 0.04 0.16* 0.17* 0.08

Kurtosis b 0.02 0.08* 0.00 0.05 0.04 0.02 0.01 0.04 0.03 0.04 0.06 0.06 0.08* 0.07^ 0.02 0.01 0.06 0.07

0.18* 0.09 0.10 0.18* 0.08 0.06 0.03 0.19** 0.17* 0.15* 0.08 0.12^ 0.14^ 0.07 0.08 0.11 0.14^ 0.07

0.05 0.05 0.04 0.03 0.08 0.02 0.08 0.05 0.03 0.02 0.09 0.10^ 0.05 0.02 0.02 0.02 0.06 0.09

Note. N = 209All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. *** p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

that seem (post hoc) most sensible (e.g., honest/humble and agreeable behavior, adverse and deceptive situations) at the bivariate level, but these associations diminish when the mean and squared mean of the distribution are controlled. Across all seven of the Tables 5–11, the pattern just described for Honesty-Humility generally holds. At the bivariate level, personality is associated with numerous distribution parameters from theoretically sensible behaviors, emotions, and situations. However, when the mean and squared mean of the distribution are included in the analysis, these effects largely diminish. For example, people who scored higher in Agreeableness had higher minimum (0.13) and maximum (0.13) expressions of agreeable behavior, were more likely to have left skewed distributions ( 0.27; i.e., their low end of the scale was farther from their center), and more kurtosis (0.17). However, when the mean and mean-squared were included in the analysis, these effects became 0.01, 0.00, 0.04, and 0.04 respectively. Two personality characteristics were exceptions to this general pattern: Emotionality and eXtraversion. For Emotionality (Table 6), it can be seen that, even when controlling for the mean and the squared mean of the density distributions, standard deviations and minimums still showed substantial associations with Emotionality. Interestingly, this pattern was not just true for those behaviors, emotions, and situation characteristics that are (post hoc) most plausibly related to Emotionality, but for nearly every behavior, emotion, and situation characteristic. Additionally, Table 6 shows that people who scored high on Emotionality were more likely to have higher maximums in their density distributions for emotionality behavior and situational Negativity even when the appropriate controls were taken into account. Overall, we believe that this pattern of relationships is not too surprising. Indeed, at the outset of the study we expected that if any of the personality characteristics would show unique relationships with size and shape of density distributions it would be Emotionality. The term Emotionality itself refers to the fact that people who score higher should be more reactive to their situations (i.e., more variable in behavior, emotions, and situational experiences). Thus we feel fairly confident in the replicability of this pattern.

The results for eXtraversion, however, were a bit more surprising to us. As can be seen in Table 7, the bivariate relationships between eXtraversion and the standard deviation for each of the behaviors, emotions, and situation characteristics were quite small, with the possible exceptions of Mating (0.18) and Sociality (0.14). However, when the mean and the squared mean from the density distributions were statistically controlled, the size of the relationships between the standard deviations and eXtraversion often increased, and sometimes changed directions entirely. We did not anticipate this pattern of results. As such, we have less confidence in the replicability of this finding and can only speculate (see next section) as to why this may have occurred. 4. Discussion This study had two aims. The first was to estimate the stability of density distribution parameters. Using a large and diverse sample of undergraduate students we measured a host of behavior, emotion, and situation characteristics in an experience sampling design. The results showed that while stability of density distribution means is quite high, the stability of other density distribution parameters is substantially lower, especially when the proper statistical controls are applied. Thus, although individuals may actually differ in the size and shape of their density distributions of behavior, emotion, and situation experiences, reliably detecting these individual differences will require a large number of repeated measures. The present study measured participants (on average) 40 times over the course of 1 week. Yet, the average stability of individual differences in standard deviations across behaviors, emotions, and situation characteristics was 0.65.4 The second aim of this study was to examine the relationships between personality and density distribution parameters for a number of behaviors, emotions, and situation characteristics. Specifically, we wondered if scores on personality measures could 4 Astute readers may note that two situation dimensions (Adversity and Deception) showed particularly low stabilities ( 0.05 and 0.10; see Table 3). If they are removed, the average stability is 0.74, which is perhaps a bit more optimistic.

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A.B. Jones et al. / Journal of Research in Personality 69 (2017) 225–236 Table 10 Trait-level openness associations with distribution parameters of state-level behavior, emotions, and situations. Openness State-level characteristic

Mean b

Standard Deviation b

Minimum b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.12^ 0.06 0.03 0.06 0.09 0.18** 0.11 0.12^ 0.08 0.07 0.01 0.06 0.01 0.05 0.12^ 0.00 0.01 0.03

0.14* 0.02 0.01 0.06 0.12^ 0.11 0.12^ 0.13^ 0.12^ 0.15* 0.07 0.04 0.03 0.07 0.05 0.01 0.07 0.14*

0.19** 0.02 0.01 0.04 0.12^ 0.14* 0.08 0.12^ 0.06 0.13^ 0.04 0.03 0.01 0.10 0.10 0.03 0.01 0.09

0.05 0.02 0.05 0.01 0.06 0.05 0.11 0.03 0.04 0.08 0.07 0.06 0.05 0.08 0.04 0.03 0.06 0.12^

Maximum b 0.10^ 0.01 0.03 0.01 0.05 0.04 0.04 0.03 0.02 0.07 0.03 0.02 0.00 0.07 0.06 0.01 0.02 0.09

0.03 0.00 0.04 0.05 0.02 0.00 0.10 0.06 0.08 0.03 0.04 0.01 0.05 0.05 0.01 0.06 0.12^ 0.14*

Skew b 0.01 0.01 0.01 0.06 0.01 0.05 0.14* 0.04 0.07 0.01 0.04 0.00 0.06 0.06 0.04 0.08 0.11* 0.12^

0.10 0.01 0.08 0.09 0.06 0.15* 0.12^ 0.16* 0.13^ 0.11 0.03 0.00 0.06 0.04 0.09 0.02 0.06 0.01

Kurtosis b 0.00 0.02 0.03 0.03 0.03 0.01 0.05 0.06 0.02 0.02 0.00 0.02 0.02 0.00 0.01 0.02 0.02 0.02

0.08 0.03 0.10 0.10 0.05 0.13^ 0.11 0.19** 0.12^ 0.14** 0.07 0.03 0.05 0.02 0.00 0.01 0.04 0.02

0.00 0.01 0.04 0.03 0.04 0.04 0.09 0.10^ 0.03 0.06 0.05 0.03 0.00 0.00 0.07 0.03 0.01 0.00

Note. N = 209All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

***

Table 11 Trait-level subjective happiness associations with distribution parameters of state-level behavior, emotions, and situations. Subjective happiness State-level characteristic

Mean b

Standard Deviation b

Minimum b

Honesty Emotionality Sociability Agreeableness Conscientiousness Openness Dominance Authenticity Feel Happy Feel Good Duty Intellect Adversity Mating pOsitivity Negativity Deception Sociality

0.28*** 0.03 0.29*** 0.42*** 0.32*** 0.35*** 0.16* 0.25*** 0.39*** 0.38*** 0.07 0.05 0.11 0.12^ 0.27*** 0.27*** 0.11 0.15*

0.12^ 0.04 0.01 0.05 0.00 0.00 0.08 0.18 0.05 0.13^ 0.08 0.06 0.14^ 0.13^ 0.05 0.18** 0.19** 0.10

0.22** 0.00 0.18** 0.17* 0.14* 0.22** 0.08 0.23*** 0.23*** 0.22** 0.03 0.04 0.06 0.05 0.18** 0.05 0.03 0.04

0.04 0.14* 0.14* 0.11^ 0.05 0.05 0.10 0.02 0.17** 0.11^ 0.10^ 0.08 0.02 0.09^ 0.14* 0.01 0.02 0.13*

Maximum b 0.04 0.08 0.02 0.05 0.02 0.09 0.03 0.05 0.03 0.06 0.03 0.03 0.06 0.02 0.03 0.02 0.01 0.04

0.19** 0.02 0.09 0.21** 0.14* 0.23*** 0.17* 0.12^ 0.16* 0.15* 0.10 0.11 0.15* 0.12^ 0.24*** 0.17* 0.19** 0.16*

Skew b 0.09 0.05 0.03 0.05 0.01 0.07 0.11^ 0.07 0.07 0.03 0.11^ 0.14* 0.06 0.08 0.20** 0.01 0.06 0.13*

0.16* 0.06 0.19** 0.35*** 0.19** 0.18** 0.02 0.17* 0.33*** 0.38 0.15* 0.11 0.14^ 0.00 0.13^ 0.24*** 0.15^ 0.01

Kurtosis b 0.05 0.07 0.10* 0.02 0.04 0.07 0.12* 0.04 0.04 0.04 0.06 0.05 0.05 0.07* 0.07^ 0.02 0.01 0.11*

0.11 0.01 0.12^ 0.19** 0.07 0.10 0.03 0.16* 0.19** 0.22** 0.05 0.05 0.07 0.00 0.06 0.12^ 0.11 0.04

0.03 0.11^ 0.09 0.04 0.05 0.02 0.04 0.02 0.07 0.03 0.06 0.06 0.01 0.04 0.08 0.08 0.03 0.06

Note. N = 209All coefficients are standardized regression coefficients. Bold scores indicate calculations while controlling for mean and squared mean. *** p < 0.001. ** p < 0.01. * p < 0.05. ^ p < 0.10.

predict parameters of density distributions beyond the mean (i.e., standard deviation, minimum, maximum, skew, and kurtosis). In general, across the six HEXACO personality characteristics and Subjective Happiness, we found that personality scores are related to many of these distribution parameters at the bivariate level. However, when the appropriate statistical controls are applied, these associations largely dissipated. That is, scores on personality measures only seem to be able to predict the mean (or location) of density distributions of behavior, emotion, and situation characteristics. This pattern of results is quite consistent with those found by Fleeson and Gallagher (2009). Two exceptions, one expected and one unexpected, to this general pattern were found. Emotionality predicted both standard

deviations and minimums of density distributions for numerous behaviors, emotions, and situation characteristics. Although Fleeson and Gallagher did not report such a result, we did anticipate this possibility ourselves given the fact that Emotionality is supposed to measure volatility in emotion and behavior. The second exception to the general pattern—eXtraversion uniquely predicting standard deviations in density distributions for numerous behaviors, emotions, and situation characteristics—was not anticipated prior to conducting this study. As such, we feel substantially less confident in the replicability of this result. However, we do consider two speculative explanations for this result. The first is that, like Emotionality, eXtraversion is more emotionally based (i.e., it is closely linked with positive affect). Thus, people who

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are extraverted may experience more variability in their behavior, emotions, and situation experiences because they are more emotional in general. However, in direct contradiction to this speculation is the fact that a similar pattern of results was not seen for Subjective Happiness. A second possibility, and one that we believe is worth further attention, is the link between eXtraversion and social skill (e.g., self-monitoring; Snyder, 1974). It is possible that extraverts experience more variability in their behavior, emotions, and situation experiences because they are more socially skilled and better at adapting their behavior, emotions, and perceptions of situations as the situations themselves change. Despite the possible appeal of this explanation, more research should examine the links, and potential mediating factors, between extraversion and variability in density distributions. 4.1. Implications for whole trait theory and personality assessment Previous research has overwhelmingly demonstrated that personality measures correspond closely to the central tendency parameter of density distributions. In other words, personality measures predict how people will behave on average across time and situations. As just discussed, the results of this study, demonstrate that, in general, personality measures do not correspond to any other parameters of density distributions once the location (mean) of the density distribution is taken into account (see previous paragraph for two exceptions). This means that scores on personality tests reflect one’s central tendency, expected, or typical behavior, and not much else. However, as shown in Table 3, parameters of density distributions, beyond the mean, show only moderate levels of reliability even after 40 measurements. Still, the reliabilities of individual differences in these parameters were not zero. Thus, consistent with Whole Trait Theory (Fleeson & Jayawickreme, 2015), individuals do reliably differ in their standing on density distribution parameters. However, reliably measuring these individual differences will be challenging and require many repeated assessments to obtain stable estimates. The lack of association between the various parameters of density distributions (beyond means) and traditional personality test scores suggests that personality psychologists may reconsider traditional personality measurement techniques. As the data here show, while these techniques are quite adept at measuring how one might most probabilistically behave in a given situation, they have little ability to assess variability in one’s behavior across situations. This being the case, two important steps remain. First, it is incumbent upon personality researchers to determine if individual differences in density distribution parameters have any practical value. It is well-known that individual differences in density distribution means (i.e., personality trait scores) predict important social outcomes. Can the same be said for individual differences in density distribution size (standard deviation) and shapes (skew and kurtosis)? This should be high priority for future research using the density distribution approach. Second, if it is determined that density distribution size and shape can predict important outcomes (beyond the mean), personality researchers should consider developing self-report tools that can quickly and efficiently capture individual differences in density distribution shape and size. As noted here, reliably measuring individual differences in density distribution parameters beyond the mean will be quite challenging using current experience sampling method techniques. This is especially true from an applied standpoint. For example, potential employers will be unlikely to ask their applicants to complete an experience sampling study as part of the application process. Thus, if individual differences in density distribution parameters (beyond the mean) can predict important outcomes, it may be quite valuable to both research and practice in

personality science to develop tools for rapidly and reliably assessing such individual differences.

4.2. Limitations The experience sampling design of this study provided us with the ability to assess a large number of behaviors, emotions, and situation characteristics over a relatively extended period of time (1 week). However, in order to reduce participant fatigue, we limited the number of items used for each state-level construct to only one item per dimension. As such, it may be a bit premature to conclude that, for example, person-level Honesty/Humility does not uniquely predict density distribution parameters (beyond the mean) in the behaviors that makeup the Honesty/Humility dimension, because only a single behavioral item was employed in this study. Further, it is possible that the nature of the experience sampling design (i.e., repeatedly asking participants the same questions) prompted participants to contemplate, or even emphasize, how their responses differ between time points (cf. Baird & Lucas, 2011). This may lead to greater variability in responses to these items, thus distorting the true variability in behavior, emotions, and situation experiences. However, recent empirical evidence from an in-lab experience sampling study suggests that this is less of an issue than previously thought (Fleeson & Law, 2015).

5. Conclusions The everyday behavior, emotions, and situations experienced by a given person—when considered in aggregate across time—form density distributions, complete with all of their typical parameters (e.g., mean, standard deviation, skew). This study asked (1) whether individual differences in these parameters are stable and (2) whether typical personality measures could predict individual differences in these parameters. The results indicate that the stability of individual differences is only moderate for parameters related to size (standard deviation) and shape (skew and kurtosis), even after 40 measurements, when one appropriately controls for the location (mean) of the distribution. Additionally, personality measures have little association with individual differences in density distribution parameters beyond the mean (e.g., standard deviation, min, max) when these parameters are properly disentangled from their association with the mean. The major exception to this rule is Emotionality, which does seem to predict individual differences in both location and spread parameters of density distributions. Despite relatively moderate stabilities in density distribution parameters beyond the mean, this study provides evidence for these parameters as individual differences in personality, consistent with Whole Trait Theory (Fleeson & Jayawickreme, 2015). A high priority for future research should be determining whether individual differences in density distribution parameters predict important social outcomes (e.g., longevity, career success, relationship satisfaction, etc.) and possibly developing tools for more efficiently and reliably measuring individual differences in density distribution parameters.

Author notes All statistical analyses were conducted using R (R Core Development Team, 2014). Supplemental materials, including data and analytic scripts for reproducing the results presented herein will be available at psy2.fau.edu/shermanr/variabilityRscript.r.

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