Energetic Arousal and Language: Predictions From the Computational Theory of Quantifiers Processing Marcin Zajenkowski, University of Warsaw, Warsaw, Poland Objective: The author examines the relationship between energetic arousal (EA) and the processing of sentences containing natural-language quantifiers. Background: Previous studies and theories have shown that energy may differentially affect various cognitive functions. Recent investigations devoted to quantifiers strongly support the theory that various types of quantifiers involve different cognitive functions in the sentence–picture verification task. Method: In the present study, 201 students were presented with a sentence–picture verification task consisting of simple propositions containing a quantifier that referred to the color of a car on display. Color pictures of cars accompanied the propositions. In addition, the level of participants’ EA was measured before and after the verification task. Results: It was found that EA and performance on proportional quantifiers (e.g., “More than half of the cars are red”) are in an inverted U-shaped relationship. Conclusion: This result may be explained by the fact that proportional sentences engage working memory to a high degree, and previous models of EA–cognition associations have been based on the assumption that tasks that require parallel attentional and memory processes are best performed when energy is moderate. Application: The research described in the present article has several applications, as it shows the optimal human conditions for verbal comprehension. For instance, it may be important in workplace design to control the level of arousal experienced by office staff when work is mostly related to the processing of complex texts. Energy level may be influenced by many factors, such as noise, time of day, or thermal conditions. Keywords: energetic arousal, language, quantifiers, working memory, attention
Address correspondence to Marcin Zajenkowski, Faculty of Psychology, University of Warsaw, Stawki str. 5/7, 00-183 Warsaw, Poland; e-mail: [email protected]. HUMAN FACTORS Vol. 55, No. 5, October 2013, pp. 924–934 DOI:10.1177/0018720812474932 Copyright © 2013, Human Factors and Ergonomics Society.
Introduction
Arousal plays a central role in human performance. It affects work efficiency (Dickman, 2002), driving performance (Matthews et al., 1998), and vigilance, a function required in most human–machine systems that involve human monitoring (Warm, Parasuraman, & Matthews, 2008). Arousal has been linked with performance for several decades. One of the first linkages was expressed in the Yerkes-Dodson law (Yerkes & Dodson, 1908), which states that one should expect an inverted U-shaped relationship between arousal and performance, such that increasing arousal facilitates the performance of a task but only up to a certain point. Arousal that is too high results in performance decrement. Additionally, high arousal should be relatively more beneficial in easy tasks than in difficult ones. Although some data support the YerkesDodson law (see Anderson, 1994), many studies have failed to confirm its assumption (e.g., Matthews, Warm, Reinerman, Langheim, & Saxby, 2010). The main problem with the law is that both arousal and performance are broad, complex constructs. Most recent studies adopt a multidimensional model of arousal, such as Thayer’s (1989) distinction between two subjective states: energetic arousal (EA, or feelings of energy vs. fatigue) and tense arousal (tension vs. calmness). In psychological experiments, the Yerkes-Dodson law has been tested with respect to the former (Humphreys & Revelle, 1984; Matthews et al., 2010). Therefore, the present article focuses on energetic arousal and cognitive performance. Researchers have observed that arousal has different impacts on various cognitive processes during task performance. High energy is usually more beneficial to attention (Helton, Matthews, & Warm 2009; Helton, Shaw, Warm, Matthews, & Hancock, 2008; Humphreys & Revelle, 1984; Matthews et al., 2010), whereas the relationship between energy and other cognitive functions
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(e.g., short-term vs. long-term memory) is ambiguous (e.g., Matthews et al., 2010; Matthews, Deary, & Whiteman, 2009). An integrated framework of arousal and cognition was described by Humphreys and Revelle (1984). The authors proposed a model assuming a number of associations between energy and performance. First, they reviewed data showing the facilitative effect on sustained attention, measured through tests such as letter cancellation, vigilance tasks, or simple arithmetic. They interpreted these results as suggesting that increases in arousal may make information-processing resources more readily available. However, other researchers noted that such may be the case only for resources demanding attentional processes, not automatic ones (Matthews et al., 2010). Second, on the basis of empirical material, Humphreys and Revelle assumed the existence of a negative correlation between cortical arousal and performance on tasks requiring short-term retention of information. Furthermore, the authors hypothesized that tasks that require both attention and short-term memory should show a curvilinear (inverted U-shaped) relationship with energetic arousal as a result of two opposing monotonic processes (positive and negative correlations). In the present study, I aimed to test Humphreys and Revelle’s (1984) framework with respect to the computational theory of natural-language quantifier processing. The latter predicts that different cognitive functions are involved in processing various quantifier types (Szymanik, 2007; Szymanik & Zajenkowski, 2010). The theory may shed new light on the association between arousal and cognition. A quantifier (e.g., “some,” “most,” “fewer than three”) can be defined as a noun phrase that asserts a property from a set and maps it to a truth value (McMillan, Clark, Moore, Devita, & Grossman, 2005). Quantifiers are common in daily speech and are highly familiar. The computational concept of quantifier processing proposed by van Benthem (1986) refers to automata theory, which, in computer science, is the study of abstract machines and the problems they are able to solve. It was suggested that the cognitive difficulty of quantifier processing might be assessed on the basis of the complexity of the
minimal corresponding automata (van Benthem, 1986). Referring to this concept, Szymanik (2007) proposed to distinguish four types of quantifiers that require different automata and potentially various cognitive functions. First, a very simple automaton is necessary to handle Aristotelian quantifiers, such as “all” or “some.” They are recognizable by finite automata with only two states. Intuitively, to test whether the statement “Every car is red” is true, one need not memorize anything; it suffices to check all given cars one by one. If one finds a car that is not red, the statement is false. If one checks the cars and finds none that is red, then the statement is true. The automaton, then, requires only two states: accepting, in which it remains until it finds a nonred item, whereupon it turns to rejecting. Numerical quantifiers are of the form “more than n” or “fewer than n.” The corresponding machines are also finite automata, but in that case, the number of states depends on n. To verify the sentence “More than three cars are red,” one must count all red cars; the maximal number of states necessary for this sentence to be true is three plus at least one, which gives four. Parity quantifiers, such as “an even number of” or “an odd number of,” also can be recognized by two-state finite automata, but in that case, the machines need to loop between the states. For example, consider the statement “An even number of the cars is red.” When one finds a red car, one is in a rejecting state (write false on the hypothetical blackboard); if one finds another red car, one switches to the accepting state (erase false and write true) but switches back to rejecting if one sees another red car, and so on. At every moment, there is only one digit on the blackboard, no matter the size of the set of cars. A two-state finite automaton can realize such an algorithm. The most complex forms of quantifier are proportional quantifiers (“less than half” or “most”), which require a recognition mechanism with unbounded internal memory (van Benthem, 1986). During the computation of these sentences, the sizes of two sets need to be compared; this comparison cannot be simulated by a finite automaton but requires a push-down automaton, which contains a stack, or form of
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storage system. For instance, to verify the sentence “More than half of the cars are red,” one has to count and hold in short-term memory the number of red cars and then compare it with the total number of cars. No such memorization or comparison is necessary when processing other quantifiers. Szymanik and Zajenkowski (2009, 2010) confirmed the model in empirical studies by examining how people process various classes of quantifiers with respect to their computational complexity. The authors concluded that in terms of difficulty (reaction time [RT] and accuracy), the Aristotelian quantifiers are easiest. The difficulty of numerical quantifiers depends on the number, which determines how many states are necessary. The same is true of parity quantifiers: Their difficulty is related to the number of objects that one has to count in the picture. Proportional quantifiers are the hardest to verify and engage working memory to the highest degree. This pattern of results was confirmed in neuroimaging studies, which showed that all quantifiers activated regions of the brain (the right inferior parietal cortex) that are responsible for number knowledge but that only proportional statements engaged brain structures (the prefrontal cortex) specific to working memory (McMillan et al., 2005). Moreover, Szymanik and Zajenkowski (2011) showed that memory load (maintaining arbitrary information in short-term memory) resulted in decreased performance, but, again, only in regard to proportional statements. Finally, Zajenkowski, Styła, and Szymanik (2011) presented data showing that patients with schizophrenia perform proportional quantifiers less accurately than do healthy controls. Many recent results show that schizophrenia is linked to working memory deficits, which may be a cause of the poor score on verbal tasks of individuals with schizophrenia. The computational model of quantifiers has a strong theoretical and empirical background. It appears cognitively plausible, according to behavioral (Szymanik & Zajenkowski, 2009, 2010, 2011), neuroimaging (McMillan et al., 2005), and clinical (Zajenkowski et al., 2011) studies. Therefore, testing the relationship between EA and the processing of different
quantifiers may shed some light on the arousal– performance puzzle. According to Humphreys and Revelle’s (1984) framework, one may expect an inverted U-shaped relationship between EA and performance on proportional sentences. As mentioned earlier, proportional quantifiers engage working memory, and this construct may be seen as the simultaneous storage and transfer of information (Logie, 2011). Other quantifiers require only actual processing of information, mainly object counting and discriminating. These functions engage attention and therefore should be positively related to energy (Humphreys & Revelle, 1984). Method To test the hypotheses derived from Humphreys and Revelle (1984), as well as a computational model (Szymanik, 2007; Szymanik & Zajenkowski, 2010), linear and quadratic relationships between EA and various quantifiers were tested. In the study, performance on three quantifier types was analyzed: proportional, numerical, and parity. Previous investigations showed that Aristotelian quantifiers were very easy to verify in terms of accuracy, and almost all participants solved these sentences correctly. Therefore, they were not included in the present study. Participants
A total of 201 participants took part in the study (107 female and 94 male). Their mean age was 22.40 (SD = 2.71). The sample was composed of undergraduate students from the University of Warsaw. Participants received a small financial reward for taking part in the study (approximately USD$7). There were no differences between men and women in the level of EA and performance. The power analysis showed that with the present sample, an effect size (Cohen’s f2; see Cohen, 1988) for multiple regression of at least .04 may be detected with a power of .80. Materials and Procedure
Participants solved a sentence–picture verification task consisting of 24 simple propositions in Polish, which contained a quantifier that referred to a display of cars on a computer
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Figure 1. An example of a stimulus used in the study.
screen. For each proposition, the pictures contained 15 objects in two colors, as illustrated in Figure 1. They were selected from a single set of 24 pictures. Propositions with “fewer than eight,” “more than seven,” “fewer than half,” and “more than half” were accompanied by a quantity of target items near the criterion for validating or falsifying the proposition (e.g., seven targets in “fewer than half”). Six quantifiers divided into three groups were used in the study. The first group was parity quantifiers (“odd” or “even”), the second group included numerical quantifiers (“fewer than eight” or “more than seven”), and the third was proportional quantifiers (“fewer than half” or “more than half”). Each quantifier appeared four times, twice when it was true and twice when it was false. Hence, within each quantifier group, there were 8 trials, with 24 in total. All the sentences with accompanying pictures were presented randomly. Each quantifier problem resulted in a 15.5-s event. In the event, the proposition and a stimulus
array containing 15 randomly distributed cars were presented for 15 s, followed by a blank screen for 0.50 s. The letters were presented in 20-point Times New Roman. Participants sat in a chair about 90 cm from the computer screen. They were asked to decide if the proposition was true of the presented picture. Participants responded by pressing the button marked P if true and F if false. (The letters refer to the first letters of the Polish words for true and false.) The experiment was performed on a PC running E-Prime Version 2.0. Two performance indices were measured: accuracy (the overall number of correct answers within each quantifier group; maximum = 8) and mean RT (average from overall responses, both correct and incorrect, within each quantifier group). Participants’ level of energy was assessed with a Polish adaptation by Gorynska (Zajenkowski, Goryńska, & Winiewski, 2012) of the UWIST Mood Adjective Check List (Matthews, Jones, & Chamberlain, 1990). This self-report scale includes 10 items measuring EA (with poles
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Figure 2. Mean scores with 95% confidence interval of three types of quantifiers with respect to accuracy (A) and reaction time (B).
energetic–tired) and has high internal consistency (Cronbach’s alpha = .90). In the testing procedure, participants are asked to rate themselves on a scale ranging from 1 (strongly disagree) to 4 (strongly agree). Thus the total score varies between 10 and 40. EA was measured twice: just before the sentence–picture verification task and immediately after it. Results
First, performance on three quantifiers was compared with ANOVA with repeated measures. The Greenhouse-Geisser correction was used when needed. With regard to accuracy, the quantifiers differed significantly, F(2, 400) = 34.03, p < .001; η2 = .15. The comparison among means (with Fisher’s least significant
difference) revealed that proportional quantifiers had a lower score (M = 6.42, SD = 1.38) than parity (M = 7.11, SD = 1.05) and numerical (M = 7.14, SD = 1.10) judgments; the latter two did not differ significantly, p > .05 (see Figure 2A). With regard to RT, the analysis indicated a significant main effect, F(1.7, 340.1) = 222.86, p < .001; η2 = .53. All three conditions differed from one another (p < .05). The time (in milliseconds) needed to verify each quantifier increased as follows: numerical (M = 5,308, SD = 1,281), parity (M = 5,452, SD = 1,288), and proportional (M = 7,014, SD = 1,713; see Figure 2B). The obtained results are consistent with previous data, which showed that proportional quantifiers are the most difficult to process (Szymanik & Zajenkowski, 2010, 2011).
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Table 1: Linear and Quadratic Relationships Between Mean Accuracy of Quantifiers and Energetic Arousal (EA) in a Pretask (Model 1) and Posttask (Model 2) Measurement of EA ΔR2 Model Model 1: Pretask EA as predictor of quantifiers processing EA EA squared Model 2: Posttask EA as predictor of quantifiers processing EA EA squared
Relationship
Numerical
Parity
Proportional
Linear Quadratic
.001 .004
.018 .001
.003 .033*
Linear Quadratic
.006 .001
.011 .010
.013 .071**
Note. In both models, EA as a predictor was entered in the first block, followed by EA squared entered in the second block. Cells show R2 of change and its significance. *p < .05. **p < .001.
Regression analyses were used to test for linear and quadratic effects between EA and verification of the accuracy of quantifier types. The analyses were conducted separately for two measurements of arousal. For each case, hierarchical quadratic regression was applied with specific quantifier as a dependent variable and the centered EA score as a predictor entered in the first block, followed by the squared centered EA score in the second block. The squared term in the regression is usually used to test the quadratic relationship (e.g., Cohen & Cohen, 1983; see also Jankowski, 2012, for recent use). The summary of tested models is shown in Table 1. The analyses revealed that for numerical and parity quantifiers, no significant relationships with EA were obtained before and after the task. With regard to performance on proportional sentences, there were significant quadratic effects in pre- and posttask measurements of energy. In the former case, the model accounted for 3.5% of the variance in accuracy; in the latter, this figure was 8.5%. In both analyses, there was an inverted U-shaped relation (see Figure 3 for the second measurement of EA and accuracy on proportional sentences). Previous findings showed that energy might be associated with RT of the cognitive task
Figure 3. Quadratic relationship between energetic arousal and mean accuracy of proportional quantifiers. The accuracy score for each participant was the sum of correct reactions (dashed line represents mean = 29.66; dotted lines represent range).
(e.g., Dickman, 2002). Hence, similar regression analyses as for accuracy were conducted for mean RTs of three quantifiers (see Table 2). Generally, posttask EA was linearly linked to verification times in the case of all three linguistic conditions. In particular, the relationship was negative, suggesting that participants with high
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Table 2: Linear and Quadratic Relationships Between Mean Reaction Times of Quantifiers and Energetic Arousal (EA) in a Pretask (Model 1) and Posttask (Model 2) Measurement of EA ΔR2 Model Model 1: Pretask EA as predictor of quantifiers processing EA EA squared Model 2: Posttask EA as predictor of quantifiers processing EA EA squared
Relationship
Numerical
Parity
Proportional
Linear Quadratic
.001 .000
.004 .002
.005 .002
Linear Quadratic
.014* .000
.040** .001
.052** .004
Note. In both models, EA as a predictor was entered in the first block, followed by EA squared entered in the second block. Cells show R2 of change and its significance. *p < .1. **p < .05. ***p < .001.
arousal responded more quickly than did lowenergy individuals. To determine the degree to which increases in speed were associated with trade-offs in accuracy, I calculated the correlation between mean RTs and accuracy of each quantifier. The relationship was significant only in the case of proportional sentences (r = .15, p < .05), indicating that faster reactions were linked to poorer performance. Looking at this result together with the findings on EA, I was interested to see how RT and EA predict the accuracy of proportional quantifiers. In a joined model with EA and EA squared, RT (as a third predictor in Model 2 presented in Table 1) did not significantly predict the score of proportional judgments. Given that there were two measurements of EA, and this construct seems to be sensitive to situational factors (see, e.g., Zajenkowski et al., 2012), change between pre- and posttask level of energy was analyzed. Paired-sample t test showed no significant difference, t(200) = .850, p = .396. Moreover, the two measurements were highly correlated, r = .76, p < .001. Discussion In the present study, I analyzed the relationships between EA and cognitive functions involved in verbal comprehension with respect to
natural-language quantifiers. For each type of quantifier, linear and curvilinear relations were tested. The only significant result of accuracy showed that performance on proportional sentences was in an inverted U-shaped relationship with energy, which means that moderate arousal was beneficial for the task, whereas too-low and too-high arousal decreased accuracy. Because this type of quantifier engages working memory to a high degree, the result seems to be consistent with Humphreys and Revelle’s (1984) predictions about a specific relationship between EA and tasks requiring parallel information transfer and short-term memory. The lack of significant results concerning other types of quantifiers may be attributable to their low attentional demands (Matthews et al., 2010). Numerical and parity quantifiers require only simple counting, and previous investigations have indicated that (a) they do not activate brain regions associated with higher-order cognition (McMillan et al., 2005), (b) additional memory load has no impact on their performance (Szymanik & Zajenkowski, 2011), and (c) no difference in their processing has been found between patients with schizophrenia and healthy controls (Zajenkowski et al., 2011). When it comes to RT, the study revealed consistent linear and negative relationships between verification times of all quantifiers and the
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posttask measurement of EA. This finding is in agreement with previous findings (e.g., Dickman, 2002). Moreover, RT of proportional judgments was positively linked to their accuracy but did not predict the score when taken in a model together with EA. It is possible that extreme energy produces impulsive behavior, such that increasing EA corresponds with faster reactions, which in turn results in poorer performance. In light of recent findings, it is reasonable to ask whether more specific aspects of both EA and working memory—a cognitive base of proportional quantifiers—may determine their quadratic association. As regards the previous construct, Dickman (2002) made an interesting distinction that may be important to the present consideration. He proposed to distinguish two aspects of energy: wakefulness and vigor. Only with respect to the latter did the author report an inverted U-shaped relationship with cognition. It is worth mentioning that in the current study, the EA scale contained more adjectives characterizing vigor than wakefulness. On the other hand, working memory is usually described as consisting of storage and executive functions (or attentional control; Engle, Tuholski, Laughlin, & Conway, 1999). Recent works have suggested that only the latter may be crucial and specific to processing proportional quantifiers (Szymanik & Zajenkowski, 2011). It is possible that the executive function involved in the processing of proportional sentences determines its quadratic relationship with energy. This claim can be supported in a number of ways. First, complex tasks were described by Humphreys and Revelle (1984) as requiring memory as well as attentional resources. The authors assumed these processes to be separate, but modern concepts of working memory suggest that concurrent processing and storage are managed by executive functions (e.g., Logie, 2011). Hence, the controlling part of working memory (e.g., dealing with interference between memorizing items and processing other elements) may be crucial for demanding tasks, and therefore, they may require a moderate level of energy. Moreover, Martin and Kerns (2011) showed that different aspects of working memory, namely, memory span and proponent
response inhibition (executive function), might be differentially affected by subjective states. Specifically, they found that positive mood impairs memory but has no effect on cognitive control. However, the authors studied only positive affect, which shares some aspects of EA but is not isomorphic with it (Matthews et al., 2009). Taking into account simpler dimensions within both EA and working memory may shed some light on other findings regarding the relationship between these two constructs. For instance, in a recent article, Matthews and Campbell (2010) tried to establish a dynamic association between stress states and working memory. The authors measured, among other things, a state of task engagement, which integrates energy, motivation, and concentration. In a repeated-measures design study, task engagement was weakly or, on some occasions, not at all correlated with four measurements of operation span task (working memory). These results may be understood in light of the considerations and distinctions noted earlier. First, Matthews and Campbell analyzed only the linear relationship between engagement and task performance, whereas the data presented in this article suggest that it might be important also to test curvilinear effects. Second, task engagement is a very broad construct. Maybe separating the energy and, further, the vigor from other factors of task engagement would result in stronger relations with working memory. Finally, it might be interesting to determine how the aspects of energy contribute to specific functions of the operation span task, such as executive processes and storage. One may wonder whether the obtained results are determined by the specific cognitive functions or by other aspects related to solving proportional sentences. It is worth noting that an inverted U-shaped relationship between energy and cognition was reported mainly in studies in which highly demanding verbal tasks were used. For instance, Revelle, Humphreys, Simon, and Gilliland (1980), as well as Anderson (1994), found an interactive effect between impulsivity, caffeine, and verbal task accuracy, suggesting a curvilinear energy– cognition relationship. The test used in these
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studies consisted of multiple-choice questions similar to those used in the verbal section of Graduate Record Examinations and required participants to deal with verbal analogies, antonyms, and sentence completions. Interestingly, the same task was used in the investigation by Dickman (2002), discussed earlier. It is possible, then, that specific stimuli used in previous studies were responsible for the curvilinear relation between EA and cognition. The tasks were verbal and highly demanding, as were those used in the processing of proportional quantifiers. Moreover, investigations of subjective states and various working memory tasks suggest that verbal and spatial working memory might be differentially affected by positive and negative affect (Martin & Kerns, 2011; Shackman et al., 2006). Of course, this observation does not exclude the potential role of working memory in determining the U-shaped relationship with EA, as it is strongly associated with language behavior. Just and Carpenter (1992) emphasized the special role of working memory in verbal comprehension because it entails processing a sequence of symbols that is produced and perceived over time. Working memory stores the representations that emerge from processing a stream of successive written or spoken words. Finally, it is worth noting that the quadratic relationship between EA and proportional sentence verification was stronger when the mood state was measured after than before the task. This finding is consistent with previous results. For instance, Humphreys and Revelle (1984) noted that in various tasks, the effects of arousal manipulations tended to show up only in the latter stages of an experimental session. Similarly, Matthews and Campbell (2010) found that task engagement was more highly correlated with working memory in posttask measurements. It is possible, then, not only that energy affects performance, as was shown in experimental manipulations (e.g., Revelle et al., 1980) but also that the task has some influence on the level of EA. Matthews et al. (2010) suggested that this influence might be related to selfregulative processes, inasmuch as people may modify their subjective state of energy to the situational demands. The possible alternative
explanation is that posttask energy correlates more strongly with performance because the posttask situation may be more representative of mood during the task than the pretask measurement. However, high correlation between the two measurements of EA suggest that this assumption is less probable. The present study has several limitations. First, only one measure of energetic arousal was used, which limits the conclusions to the theory of Matthews et al. (1990). It would be interesting to examine how other energy-related constructs (e.g., task engagement) are associated with the sentence verification paradigm. Moreover, to capture the specific cognitive functions that may underlie the curvilinear relationship between EA and performance, a variety of tasks should be used. It is also worth noting that the significant results obtained in this study accounted for a small amount of the variance. However, similar effect sizes are usually observed when correlates of mood states are examined. For instance, it was found that correlation coefficients of stress states and working memory varied between .19 and .34 (Matthews & Campbell, 2010), and Pearson’s r of personality traits and momentary measurement of mood did not exceed .30 (Matthews et al., 2009). Matthews et al. (2009) noticed that psychological states may play a mediating role between individuals and situations and therefore should be studied together with other factors, such as demands of the situation or the individual’s dispositions. Therefore, authors of future investigations in the field of EA and language processing should examine, among other things, the contribution of individual differences. One important variable that influences energy in the performance context is personality. Many studies showed that extraversion and activity are significant predictors of energy (e.g., Jankowski & Zajenkowski, 2012; Matthews et al., 2009) and, through that, affect cognition (Humphreys & Revelle, 1984). However, extraversion and EA association is sensitive to many factors, such as time of day (Humphreys & Revelle, 1984) and situational demands (Zajenkowski et al., 2012). Other constructs that should be taken into account are
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general and emotional intelligence, as both might regulate the energy level in a task situation (Matthews & Fellner, 2012; Nęcka, 1997). Finally, it would be interesting to test the influence of EA on quantifier processing with approaches other than computational theory. For instance, Pietroski, Lidz, Hunter, and Halberda (2009) suggested that people may use an approximation mechanism rather than an algorithmic method to assess the truth value of the proportional judgments. The authors proposed an experimental procedure in which the verified picture is presented only for 200 ms. They manipulated the difficulty of the task by decreasing the distance between the two compared sets of objects; for example, a picture with sets of six and nine was easier than one with seven and eight. The research described in the present article has several applications, in that it shows the optimal human conditions for verbal comprehension. For instance, it may be important in workplace design to control the level of arousal experienced by office staff when work is mostly related to the processing of complex texts. The level of arousal may be influenced in many ways. The convincing data show that noise is one of the factors that increase energy (e.g., Helton et al., 2009). One should take this factor into account when designing workplaces close to, for example, rail tracks or highways. Noise also may be a feature of office environments, especially in the form of irrelevant speech (Matthews, Davies, Westerman, & Stammers, 2000). Other factors that are important from the point of view of optimal EA are thermal conditions and time of day. In the case of the former, heat tends to raise autonomic arousal (Matthews et al., 2000), and with respect to the latter, it was found that EA level also varies during the day (Dickman, 2002). All these aspects may be controlled in the planning of working conditions, especially in fields in which language intelligibility is important. The present findings also suggest the best conditions for studying demanding verbal material. Moreover, in the context of working and learning, the increasing role of computers has recently been observed (Calix, Javadpour, & Knapp, 2012). With respect to human–computer interaction, some research suggests that positive affective feedback may influence the level of
arousal and, in turn, the cognitive operations (Partala & Surakka, 2004). Therefore, the current results also may be useful in the development of effective computer interfaces. Acknowledgments I thank Gerald Matthews and William Helton for their insightful comments on my manuscript. This work was supported by Grant No. 2011/01/D/ HS6/01920 funded by the National Science Centre in Poland.
Key Points •• The relationship between energetic arousal and the processing of sentences containing naturallanguage quantifiers was examined. •• Energetic arousal is in an inverted U-shaped relationship with performance on proportional quantifiers. •• This result may be explained by the fact that proportional sentences engage working memory to a high degree.
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Just, M., & Carpenter, P. (1992). A capacity theory of comprehension: Individual differences in working memory. Psychological Review, 99, 122–149. Logie, R. H. (2011). The functional organisation and the capacity limits of working memory. Current Directions in Psychological Science, 20, 240–245. Martin, E. A., & Kerns, J. G. (2011). The influence of positive mood on different aspects of cognitive control. Cognition and Emotion, 25, 265–279. Matthews, G., & Campbell, S. E. (2010). Dynamic relationships between stress states and working memory. Cognition and Emotion, 24, 357–373. Matthews, G., Davies, D. R., Westerman, S. J., & Stammers, R. B. (2000). Human performance: cognition, stress, and individual differences. Philadelphia, PA: Taylor and Francis. Matthews, G., Deary, I., & Whiteman, A. (2009). Personality traits. Cambridge, UK: Cambridge University Press. Matthews, G., Dorn, L., Hoyes, T. W., Davies, D. R., Glendon, A. I., & Taylor, R. G. (1998). Driver stress and performance on a driving simulator. Human Factors, 40, 136–149. Matthews, G., & Fellner, A. N. (2012). The energetics of emotional intelligence. In M. W. Eysenck, M. Fajkowska, & T. Maruszewski (Eds.), Warsaw Lectures on personality, emotion, and cognition (pp. 13–33). Clinton Corners, NY: Eliot Werner. Matthews, G., Jones, D. M., & Chamberlain, A. G. (1990). Refining the measurement of mood: The UWIST mood adjective checklist. British Journal of Psychology, 81, 17–42. Matthews, G., Warm, J. S., Reinerman, L. E., Langheim, L. K., & Saxby, D. J. (2010). Task engagement, attention and executive control. In A. Gruszka, G. Matthews, & B. Szymura (Eds.), Handbook of individual differences in cognition: Attention, memory and executive control (pp. 205–230). New York, NY: Springer. McMillan, C., Clark, R., Moore, P., Devita, C., & Grossman, M. (2005). Neural basis for generalized quantifiers comprehension. Neuropsychologia, 43, 1729–1737. Nęcka, E. (1997). Attention, working memory and arousal: Concepts apt to account for “the process of intelligence.” In G. Matthews (Ed.), Cognitive science perspectives on personality and emotion (pp. 503–554). Amsterdam, Netherlands: Elsevier. Partala, T., & Surakka, V. (2004). The effects of affective interventions in human–computer interaction. Interacting With Computers, 16, 295–309. Pietroski, P., Lidz, J., Hunter, T., & Halberda, J. (2009). The meaning of “most”: Semantics, numerosity, and psychology. Mind and Language, 24, 554–585.
Revelle, W., Humphreys, M. S., Simon, L., & Gilliland, K. (1980). The interactive effect of personality, time of day, and caffeine: A test of the arousal model. Journal of Experimental Psychology: General, 109, l–31. Shackman, A. J., Sarinopoulos, I., Maxwell, J. S., Pizzagalli, D. A., Lavric, A., & Davidson, R. J. (2006). Anxiety selectively disrupts visuospatial working memory. Emotion, 6, 40–61. Szymanik, J. (2007). A comment on a neuroimaging study of natural language quantifier comprehension. Neuropsychologia, 45, 2158–2160. Szymanik, J., & Zajenkowski, M. (2009). Improving methodology of quantifier comprehension experiments. Neuropsychologia, 47, 2682–2683. Szymanik, J., & Zajenkowski, M. (2010). Comprehension of simple quantifiers. Empirical evaluation of a computational model. Cognitive Science, 34, 521–532. Szymanik, J., & Zajenkowski, M. (2011). Contribution of working memory in the parity and proportional judgments. Belgian Journal of Linguistics, 25, 189–206. Thayer, R. E. (1989). The biopsychology of mood and arousal. Oxford, UK: Oxford University Press. van Benthem, J. (1986). Essays in logical semantics. Dordrecht, Netherlands: Reidel. Warm, J. S., Parasuraman, R., & Matthews, G. (2008). Vigilance requires hard mental work and is stressful. Human Factors, 50, 433–441. Yerkes, R. M., & Dodson, J. D. (1908). The relation of strength of stimulus to rapidity of habit-formation. Journal of Comparative Neurology and Psychology, 18, 459–482. Zajenkowski, M., Goryńska, E., & Winiewski, M. (2012). Variability of the relationship between personality and mood. Personality and Individual Differences, 52, 858–861. Zajenkowski, M., Styła, R., & Szymanik, J. (2011). A computational approach to quantifiers as an explanation for some language impairments in schizophrenia. Journal of Communication Disorders, 44, 595–600.
Marcin Zajenkowski received his PhD in psychology from the University of Warsaw in 2009 and is an assistant professor in the Faculty of Psychology at the University. Date received: July 7, 2012 Date accepted: December 20, 2012
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Address correspondence to Marcin Zajenkowski, Faculty of Psychology, University of Warsaw, Stawki str. 5/7, 00-183 Warsaw, Poland; e-mail: [email protected]. HUMAN FACTORS Vol. 55, No. 5, October 2013, pp. 924–934 DOI:10.1177/0018720812474932 Copyright © 2013, Human Factors and Ergonomics Society.
Introduction
Arousal plays a central role in human performance. It affects work efficiency (Dickman, 2002), driving performance (Matthews et al., 1998), and vigilance, a function required in most human–machine systems that involve human monitoring (Warm, Parasuraman, & Matthews, 2008). Arousal has been linked with performance for several decades. One of the first linkages was expressed in the Yerkes-Dodson law (Yerkes & Dodson, 1908), which states that one should expect an inverted U-shaped relationship between arousal and performance, such that increasing arousal facilitates the performance of a task but only up to a certain point. Arousal that is too high results in performance decrement. Additionally, high arousal should be relatively more beneficial in easy tasks than in difficult ones. Although some data support the YerkesDodson law (see Anderson, 1994), many studies have failed to confirm its assumption (e.g., Matthews, Warm, Reinerman, Langheim, & Saxby, 2010). The main problem with the law is that both arousal and performance are broad, complex constructs. Most recent studies adopt a multidimensional model of arousal, such as Thayer’s (1989) distinction between two subjective states: energetic arousal (EA, or feelings of energy vs. fatigue) and tense arousal (tension vs. calmness). In psychological experiments, the Yerkes-Dodson law has been tested with respect to the former (Humphreys & Revelle, 1984; Matthews et al., 2010). Therefore, the present article focuses on energetic arousal and cognitive performance. Researchers have observed that arousal has different impacts on various cognitive processes during task performance. High energy is usually more beneficial to attention (Helton, Matthews, & Warm 2009; Helton, Shaw, Warm, Matthews, & Hancock, 2008; Humphreys & Revelle, 1984; Matthews et al., 2010), whereas the relationship between energy and other cognitive functions
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(e.g., short-term vs. long-term memory) is ambiguous (e.g., Matthews et al., 2010; Matthews, Deary, & Whiteman, 2009). An integrated framework of arousal and cognition was described by Humphreys and Revelle (1984). The authors proposed a model assuming a number of associations between energy and performance. First, they reviewed data showing the facilitative effect on sustained attention, measured through tests such as letter cancellation, vigilance tasks, or simple arithmetic. They interpreted these results as suggesting that increases in arousal may make information-processing resources more readily available. However, other researchers noted that such may be the case only for resources demanding attentional processes, not automatic ones (Matthews et al., 2010). Second, on the basis of empirical material, Humphreys and Revelle assumed the existence of a negative correlation between cortical arousal and performance on tasks requiring short-term retention of information. Furthermore, the authors hypothesized that tasks that require both attention and short-term memory should show a curvilinear (inverted U-shaped) relationship with energetic arousal as a result of two opposing monotonic processes (positive and negative correlations). In the present study, I aimed to test Humphreys and Revelle’s (1984) framework with respect to the computational theory of natural-language quantifier processing. The latter predicts that different cognitive functions are involved in processing various quantifier types (Szymanik, 2007; Szymanik & Zajenkowski, 2010). The theory may shed new light on the association between arousal and cognition. A quantifier (e.g., “some,” “most,” “fewer than three”) can be defined as a noun phrase that asserts a property from a set and maps it to a truth value (McMillan, Clark, Moore, Devita, & Grossman, 2005). Quantifiers are common in daily speech and are highly familiar. The computational concept of quantifier processing proposed by van Benthem (1986) refers to automata theory, which, in computer science, is the study of abstract machines and the problems they are able to solve. It was suggested that the cognitive difficulty of quantifier processing might be assessed on the basis of the complexity of the
minimal corresponding automata (van Benthem, 1986). Referring to this concept, Szymanik (2007) proposed to distinguish four types of quantifiers that require different automata and potentially various cognitive functions. First, a very simple automaton is necessary to handle Aristotelian quantifiers, such as “all” or “some.” They are recognizable by finite automata with only two states. Intuitively, to test whether the statement “Every car is red” is true, one need not memorize anything; it suffices to check all given cars one by one. If one finds a car that is not red, the statement is false. If one checks the cars and finds none that is red, then the statement is true. The automaton, then, requires only two states: accepting, in which it remains until it finds a nonred item, whereupon it turns to rejecting. Numerical quantifiers are of the form “more than n” or “fewer than n.” The corresponding machines are also finite automata, but in that case, the number of states depends on n. To verify the sentence “More than three cars are red,” one must count all red cars; the maximal number of states necessary for this sentence to be true is three plus at least one, which gives four. Parity quantifiers, such as “an even number of” or “an odd number of,” also can be recognized by two-state finite automata, but in that case, the machines need to loop between the states. For example, consider the statement “An even number of the cars is red.” When one finds a red car, one is in a rejecting state (write false on the hypothetical blackboard); if one finds another red car, one switches to the accepting state (erase false and write true) but switches back to rejecting if one sees another red car, and so on. At every moment, there is only one digit on the blackboard, no matter the size of the set of cars. A two-state finite automaton can realize such an algorithm. The most complex forms of quantifier are proportional quantifiers (“less than half” or “most”), which require a recognition mechanism with unbounded internal memory (van Benthem, 1986). During the computation of these sentences, the sizes of two sets need to be compared; this comparison cannot be simulated by a finite automaton but requires a push-down automaton, which contains a stack, or form of
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storage system. For instance, to verify the sentence “More than half of the cars are red,” one has to count and hold in short-term memory the number of red cars and then compare it with the total number of cars. No such memorization or comparison is necessary when processing other quantifiers. Szymanik and Zajenkowski (2009, 2010) confirmed the model in empirical studies by examining how people process various classes of quantifiers with respect to their computational complexity. The authors concluded that in terms of difficulty (reaction time [RT] and accuracy), the Aristotelian quantifiers are easiest. The difficulty of numerical quantifiers depends on the number, which determines how many states are necessary. The same is true of parity quantifiers: Their difficulty is related to the number of objects that one has to count in the picture. Proportional quantifiers are the hardest to verify and engage working memory to the highest degree. This pattern of results was confirmed in neuroimaging studies, which showed that all quantifiers activated regions of the brain (the right inferior parietal cortex) that are responsible for number knowledge but that only proportional statements engaged brain structures (the prefrontal cortex) specific to working memory (McMillan et al., 2005). Moreover, Szymanik and Zajenkowski (2011) showed that memory load (maintaining arbitrary information in short-term memory) resulted in decreased performance, but, again, only in regard to proportional statements. Finally, Zajenkowski, Styła, and Szymanik (2011) presented data showing that patients with schizophrenia perform proportional quantifiers less accurately than do healthy controls. Many recent results show that schizophrenia is linked to working memory deficits, which may be a cause of the poor score on verbal tasks of individuals with schizophrenia. The computational model of quantifiers has a strong theoretical and empirical background. It appears cognitively plausible, according to behavioral (Szymanik & Zajenkowski, 2009, 2010, 2011), neuroimaging (McMillan et al., 2005), and clinical (Zajenkowski et al., 2011) studies. Therefore, testing the relationship between EA and the processing of different
quantifiers may shed some light on the arousal– performance puzzle. According to Humphreys and Revelle’s (1984) framework, one may expect an inverted U-shaped relationship between EA and performance on proportional sentences. As mentioned earlier, proportional quantifiers engage working memory, and this construct may be seen as the simultaneous storage and transfer of information (Logie, 2011). Other quantifiers require only actual processing of information, mainly object counting and discriminating. These functions engage attention and therefore should be positively related to energy (Humphreys & Revelle, 1984). Method To test the hypotheses derived from Humphreys and Revelle (1984), as well as a computational model (Szymanik, 2007; Szymanik & Zajenkowski, 2010), linear and quadratic relationships between EA and various quantifiers were tested. In the study, performance on three quantifier types was analyzed: proportional, numerical, and parity. Previous investigations showed that Aristotelian quantifiers were very easy to verify in terms of accuracy, and almost all participants solved these sentences correctly. Therefore, they were not included in the present study. Participants
A total of 201 participants took part in the study (107 female and 94 male). Their mean age was 22.40 (SD = 2.71). The sample was composed of undergraduate students from the University of Warsaw. Participants received a small financial reward for taking part in the study (approximately USD$7). There were no differences between men and women in the level of EA and performance. The power analysis showed that with the present sample, an effect size (Cohen’s f2; see Cohen, 1988) for multiple regression of at least .04 may be detected with a power of .80. Materials and Procedure
Participants solved a sentence–picture verification task consisting of 24 simple propositions in Polish, which contained a quantifier that referred to a display of cars on a computer
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Figure 1. An example of a stimulus used in the study.
screen. For each proposition, the pictures contained 15 objects in two colors, as illustrated in Figure 1. They were selected from a single set of 24 pictures. Propositions with “fewer than eight,” “more than seven,” “fewer than half,” and “more than half” were accompanied by a quantity of target items near the criterion for validating or falsifying the proposition (e.g., seven targets in “fewer than half”). Six quantifiers divided into three groups were used in the study. The first group was parity quantifiers (“odd” or “even”), the second group included numerical quantifiers (“fewer than eight” or “more than seven”), and the third was proportional quantifiers (“fewer than half” or “more than half”). Each quantifier appeared four times, twice when it was true and twice when it was false. Hence, within each quantifier group, there were 8 trials, with 24 in total. All the sentences with accompanying pictures were presented randomly. Each quantifier problem resulted in a 15.5-s event. In the event, the proposition and a stimulus
array containing 15 randomly distributed cars were presented for 15 s, followed by a blank screen for 0.50 s. The letters were presented in 20-point Times New Roman. Participants sat in a chair about 90 cm from the computer screen. They were asked to decide if the proposition was true of the presented picture. Participants responded by pressing the button marked P if true and F if false. (The letters refer to the first letters of the Polish words for true and false.) The experiment was performed on a PC running E-Prime Version 2.0. Two performance indices were measured: accuracy (the overall number of correct answers within each quantifier group; maximum = 8) and mean RT (average from overall responses, both correct and incorrect, within each quantifier group). Participants’ level of energy was assessed with a Polish adaptation by Gorynska (Zajenkowski, Goryńska, & Winiewski, 2012) of the UWIST Mood Adjective Check List (Matthews, Jones, & Chamberlain, 1990). This self-report scale includes 10 items measuring EA (with poles
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Figure 2. Mean scores with 95% confidence interval of three types of quantifiers with respect to accuracy (A) and reaction time (B).
energetic–tired) and has high internal consistency (Cronbach’s alpha = .90). In the testing procedure, participants are asked to rate themselves on a scale ranging from 1 (strongly disagree) to 4 (strongly agree). Thus the total score varies between 10 and 40. EA was measured twice: just before the sentence–picture verification task and immediately after it. Results
First, performance on three quantifiers was compared with ANOVA with repeated measures. The Greenhouse-Geisser correction was used when needed. With regard to accuracy, the quantifiers differed significantly, F(2, 400) = 34.03, p < .001; η2 = .15. The comparison among means (with Fisher’s least significant
difference) revealed that proportional quantifiers had a lower score (M = 6.42, SD = 1.38) than parity (M = 7.11, SD = 1.05) and numerical (M = 7.14, SD = 1.10) judgments; the latter two did not differ significantly, p > .05 (see Figure 2A). With regard to RT, the analysis indicated a significant main effect, F(1.7, 340.1) = 222.86, p < .001; η2 = .53. All three conditions differed from one another (p < .05). The time (in milliseconds) needed to verify each quantifier increased as follows: numerical (M = 5,308, SD = 1,281), parity (M = 5,452, SD = 1,288), and proportional (M = 7,014, SD = 1,713; see Figure 2B). The obtained results are consistent with previous data, which showed that proportional quantifiers are the most difficult to process (Szymanik & Zajenkowski, 2010, 2011).
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Table 1: Linear and Quadratic Relationships Between Mean Accuracy of Quantifiers and Energetic Arousal (EA) in a Pretask (Model 1) and Posttask (Model 2) Measurement of EA ΔR2 Model Model 1: Pretask EA as predictor of quantifiers processing EA EA squared Model 2: Posttask EA as predictor of quantifiers processing EA EA squared
Relationship
Numerical
Parity
Proportional
Linear Quadratic
.001 .004
.018 .001
.003 .033*
Linear Quadratic
.006 .001
.011 .010
.013 .071**
Note. In both models, EA as a predictor was entered in the first block, followed by EA squared entered in the second block. Cells show R2 of change and its significance. *p < .05. **p < .001.
Regression analyses were used to test for linear and quadratic effects between EA and verification of the accuracy of quantifier types. The analyses were conducted separately for two measurements of arousal. For each case, hierarchical quadratic regression was applied with specific quantifier as a dependent variable and the centered EA score as a predictor entered in the first block, followed by the squared centered EA score in the second block. The squared term in the regression is usually used to test the quadratic relationship (e.g., Cohen & Cohen, 1983; see also Jankowski, 2012, for recent use). The summary of tested models is shown in Table 1. The analyses revealed that for numerical and parity quantifiers, no significant relationships with EA were obtained before and after the task. With regard to performance on proportional sentences, there were significant quadratic effects in pre- and posttask measurements of energy. In the former case, the model accounted for 3.5% of the variance in accuracy; in the latter, this figure was 8.5%. In both analyses, there was an inverted U-shaped relation (see Figure 3 for the second measurement of EA and accuracy on proportional sentences). Previous findings showed that energy might be associated with RT of the cognitive task
Figure 3. Quadratic relationship between energetic arousal and mean accuracy of proportional quantifiers. The accuracy score for each participant was the sum of correct reactions (dashed line represents mean = 29.66; dotted lines represent range).
(e.g., Dickman, 2002). Hence, similar regression analyses as for accuracy were conducted for mean RTs of three quantifiers (see Table 2). Generally, posttask EA was linearly linked to verification times in the case of all three linguistic conditions. In particular, the relationship was negative, suggesting that participants with high
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Table 2: Linear and Quadratic Relationships Between Mean Reaction Times of Quantifiers and Energetic Arousal (EA) in a Pretask (Model 1) and Posttask (Model 2) Measurement of EA ΔR2 Model Model 1: Pretask EA as predictor of quantifiers processing EA EA squared Model 2: Posttask EA as predictor of quantifiers processing EA EA squared
Relationship
Numerical
Parity
Proportional
Linear Quadratic
.001 .000
.004 .002
.005 .002
Linear Quadratic
.014* .000
.040** .001
.052** .004
Note. In both models, EA as a predictor was entered in the first block, followed by EA squared entered in the second block. Cells show R2 of change and its significance. *p < .1. **p < .05. ***p < .001.
arousal responded more quickly than did lowenergy individuals. To determine the degree to which increases in speed were associated with trade-offs in accuracy, I calculated the correlation between mean RTs and accuracy of each quantifier. The relationship was significant only in the case of proportional sentences (r = .15, p < .05), indicating that faster reactions were linked to poorer performance. Looking at this result together with the findings on EA, I was interested to see how RT and EA predict the accuracy of proportional quantifiers. In a joined model with EA and EA squared, RT (as a third predictor in Model 2 presented in Table 1) did not significantly predict the score of proportional judgments. Given that there were two measurements of EA, and this construct seems to be sensitive to situational factors (see, e.g., Zajenkowski et al., 2012), change between pre- and posttask level of energy was analyzed. Paired-sample t test showed no significant difference, t(200) = .850, p = .396. Moreover, the two measurements were highly correlated, r = .76, p < .001. Discussion In the present study, I analyzed the relationships between EA and cognitive functions involved in verbal comprehension with respect to
natural-language quantifiers. For each type of quantifier, linear and curvilinear relations were tested. The only significant result of accuracy showed that performance on proportional sentences was in an inverted U-shaped relationship with energy, which means that moderate arousal was beneficial for the task, whereas too-low and too-high arousal decreased accuracy. Because this type of quantifier engages working memory to a high degree, the result seems to be consistent with Humphreys and Revelle’s (1984) predictions about a specific relationship between EA and tasks requiring parallel information transfer and short-term memory. The lack of significant results concerning other types of quantifiers may be attributable to their low attentional demands (Matthews et al., 2010). Numerical and parity quantifiers require only simple counting, and previous investigations have indicated that (a) they do not activate brain regions associated with higher-order cognition (McMillan et al., 2005), (b) additional memory load has no impact on their performance (Szymanik & Zajenkowski, 2011), and (c) no difference in their processing has been found between patients with schizophrenia and healthy controls (Zajenkowski et al., 2011). When it comes to RT, the study revealed consistent linear and negative relationships between verification times of all quantifiers and the
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posttask measurement of EA. This finding is in agreement with previous findings (e.g., Dickman, 2002). Moreover, RT of proportional judgments was positively linked to their accuracy but did not predict the score when taken in a model together with EA. It is possible that extreme energy produces impulsive behavior, such that increasing EA corresponds with faster reactions, which in turn results in poorer performance. In light of recent findings, it is reasonable to ask whether more specific aspects of both EA and working memory—a cognitive base of proportional quantifiers—may determine their quadratic association. As regards the previous construct, Dickman (2002) made an interesting distinction that may be important to the present consideration. He proposed to distinguish two aspects of energy: wakefulness and vigor. Only with respect to the latter did the author report an inverted U-shaped relationship with cognition. It is worth mentioning that in the current study, the EA scale contained more adjectives characterizing vigor than wakefulness. On the other hand, working memory is usually described as consisting of storage and executive functions (or attentional control; Engle, Tuholski, Laughlin, & Conway, 1999). Recent works have suggested that only the latter may be crucial and specific to processing proportional quantifiers (Szymanik & Zajenkowski, 2011). It is possible that the executive function involved in the processing of proportional sentences determines its quadratic relationship with energy. This claim can be supported in a number of ways. First, complex tasks were described by Humphreys and Revelle (1984) as requiring memory as well as attentional resources. The authors assumed these processes to be separate, but modern concepts of working memory suggest that concurrent processing and storage are managed by executive functions (e.g., Logie, 2011). Hence, the controlling part of working memory (e.g., dealing with interference between memorizing items and processing other elements) may be crucial for demanding tasks, and therefore, they may require a moderate level of energy. Moreover, Martin and Kerns (2011) showed that different aspects of working memory, namely, memory span and proponent
response inhibition (executive function), might be differentially affected by subjective states. Specifically, they found that positive mood impairs memory but has no effect on cognitive control. However, the authors studied only positive affect, which shares some aspects of EA but is not isomorphic with it (Matthews et al., 2009). Taking into account simpler dimensions within both EA and working memory may shed some light on other findings regarding the relationship between these two constructs. For instance, in a recent article, Matthews and Campbell (2010) tried to establish a dynamic association between stress states and working memory. The authors measured, among other things, a state of task engagement, which integrates energy, motivation, and concentration. In a repeated-measures design study, task engagement was weakly or, on some occasions, not at all correlated with four measurements of operation span task (working memory). These results may be understood in light of the considerations and distinctions noted earlier. First, Matthews and Campbell analyzed only the linear relationship between engagement and task performance, whereas the data presented in this article suggest that it might be important also to test curvilinear effects. Second, task engagement is a very broad construct. Maybe separating the energy and, further, the vigor from other factors of task engagement would result in stronger relations with working memory. Finally, it might be interesting to determine how the aspects of energy contribute to specific functions of the operation span task, such as executive processes and storage. One may wonder whether the obtained results are determined by the specific cognitive functions or by other aspects related to solving proportional sentences. It is worth noting that an inverted U-shaped relationship between energy and cognition was reported mainly in studies in which highly demanding verbal tasks were used. For instance, Revelle, Humphreys, Simon, and Gilliland (1980), as well as Anderson (1994), found an interactive effect between impulsivity, caffeine, and verbal task accuracy, suggesting a curvilinear energy– cognition relationship. The test used in these
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studies consisted of multiple-choice questions similar to those used in the verbal section of Graduate Record Examinations and required participants to deal with verbal analogies, antonyms, and sentence completions. Interestingly, the same task was used in the investigation by Dickman (2002), discussed earlier. It is possible, then, that specific stimuli used in previous studies were responsible for the curvilinear relation between EA and cognition. The tasks were verbal and highly demanding, as were those used in the processing of proportional quantifiers. Moreover, investigations of subjective states and various working memory tasks suggest that verbal and spatial working memory might be differentially affected by positive and negative affect (Martin & Kerns, 2011; Shackman et al., 2006). Of course, this observation does not exclude the potential role of working memory in determining the U-shaped relationship with EA, as it is strongly associated with language behavior. Just and Carpenter (1992) emphasized the special role of working memory in verbal comprehension because it entails processing a sequence of symbols that is produced and perceived over time. Working memory stores the representations that emerge from processing a stream of successive written or spoken words. Finally, it is worth noting that the quadratic relationship between EA and proportional sentence verification was stronger when the mood state was measured after than before the task. This finding is consistent with previous results. For instance, Humphreys and Revelle (1984) noted that in various tasks, the effects of arousal manipulations tended to show up only in the latter stages of an experimental session. Similarly, Matthews and Campbell (2010) found that task engagement was more highly correlated with working memory in posttask measurements. It is possible, then, not only that energy affects performance, as was shown in experimental manipulations (e.g., Revelle et al., 1980) but also that the task has some influence on the level of EA. Matthews et al. (2010) suggested that this influence might be related to selfregulative processes, inasmuch as people may modify their subjective state of energy to the situational demands. The possible alternative
explanation is that posttask energy correlates more strongly with performance because the posttask situation may be more representative of mood during the task than the pretask measurement. However, high correlation between the two measurements of EA suggest that this assumption is less probable. The present study has several limitations. First, only one measure of energetic arousal was used, which limits the conclusions to the theory of Matthews et al. (1990). It would be interesting to examine how other energy-related constructs (e.g., task engagement) are associated with the sentence verification paradigm. Moreover, to capture the specific cognitive functions that may underlie the curvilinear relationship between EA and performance, a variety of tasks should be used. It is also worth noting that the significant results obtained in this study accounted for a small amount of the variance. However, similar effect sizes are usually observed when correlates of mood states are examined. For instance, it was found that correlation coefficients of stress states and working memory varied between .19 and .34 (Matthews & Campbell, 2010), and Pearson’s r of personality traits and momentary measurement of mood did not exceed .30 (Matthews et al., 2009). Matthews et al. (2009) noticed that psychological states may play a mediating role between individuals and situations and therefore should be studied together with other factors, such as demands of the situation or the individual’s dispositions. Therefore, authors of future investigations in the field of EA and language processing should examine, among other things, the contribution of individual differences. One important variable that influences energy in the performance context is personality. Many studies showed that extraversion and activity are significant predictors of energy (e.g., Jankowski & Zajenkowski, 2012; Matthews et al., 2009) and, through that, affect cognition (Humphreys & Revelle, 1984). However, extraversion and EA association is sensitive to many factors, such as time of day (Humphreys & Revelle, 1984) and situational demands (Zajenkowski et al., 2012). Other constructs that should be taken into account are
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general and emotional intelligence, as both might regulate the energy level in a task situation (Matthews & Fellner, 2012; Nęcka, 1997). Finally, it would be interesting to test the influence of EA on quantifier processing with approaches other than computational theory. For instance, Pietroski, Lidz, Hunter, and Halberda (2009) suggested that people may use an approximation mechanism rather than an algorithmic method to assess the truth value of the proportional judgments. The authors proposed an experimental procedure in which the verified picture is presented only for 200 ms. They manipulated the difficulty of the task by decreasing the distance between the two compared sets of objects; for example, a picture with sets of six and nine was easier than one with seven and eight. The research described in the present article has several applications, in that it shows the optimal human conditions for verbal comprehension. For instance, it may be important in workplace design to control the level of arousal experienced by office staff when work is mostly related to the processing of complex texts. The level of arousal may be influenced in many ways. The convincing data show that noise is one of the factors that increase energy (e.g., Helton et al., 2009). One should take this factor into account when designing workplaces close to, for example, rail tracks or highways. Noise also may be a feature of office environments, especially in the form of irrelevant speech (Matthews, Davies, Westerman, & Stammers, 2000). Other factors that are important from the point of view of optimal EA are thermal conditions and time of day. In the case of the former, heat tends to raise autonomic arousal (Matthews et al., 2000), and with respect to the latter, it was found that EA level also varies during the day (Dickman, 2002). All these aspects may be controlled in the planning of working conditions, especially in fields in which language intelligibility is important. The present findings also suggest the best conditions for studying demanding verbal material. Moreover, in the context of working and learning, the increasing role of computers has recently been observed (Calix, Javadpour, & Knapp, 2012). With respect to human–computer interaction, some research suggests that positive affective feedback may influence the level of
arousal and, in turn, the cognitive operations (Partala & Surakka, 2004). Therefore, the current results also may be useful in the development of effective computer interfaces. Acknowledgments I thank Gerald Matthews and William Helton for their insightful comments on my manuscript. This work was supported by Grant No. 2011/01/D/ HS6/01920 funded by the National Science Centre in Poland.
Key Points •• The relationship between energetic arousal and the processing of sentences containing naturallanguage quantifiers was examined. •• Energetic arousal is in an inverted U-shaped relationship with performance on proportional quantifiers. •• This result may be explained by the fact that proportional sentences engage working memory to a high degree.
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Marcin Zajenkowski received his PhD in psychology from the University of Warsaw in 2009 and is an assistant professor in the Faculty of Psychology at the University. Date received: July 7, 2012 Date accepted: December 20, 2012
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