Anxiety Disorders 17 (2003) 647–665 The effects of anxious responding on mental arithmetic and lexical decision task performance Derek R. Hopkoa,*, Daniel W. McNeilb, C.W. Lejuezc, Mark H. Ashcraftd, Georg H. Eiferte, Jim Rielb a Department of Psychology, The University of Tennessee-Knoxville, Room 301D, Austin Peay Building, Knoxville, TN 37996-0900, USA b West Virginia University, St. Louis, VA, USA c The University of Maryland, College Park, MD, USA d Cleveland State University, Cleveland, OH, USA e Chapman University, Orange, CA, USA Received 17 January 2002; received in revised form 10 April 2002; accepted 23 April 2002 Abstract Anxiety-related responding and skill deficits historically are associated with performance-based problems such as mathematics anxiety, yet the relative contribution of these variables to substandard performance remains poorly understood. Utilizing a 7% carbon dioxide (CO2) gas to induce anxiety, the present study examined the impact of anxious responding on two performance tasks, mental arithmetic and lexical decision. Independent variables included math anxiety group, gender, and gas condition. Dependent variables included task performance and physiological and self-report indices of anxiety. A total of 64 university undergraduate students participated. Physiological and verbal-report measures of anxiety supported the utility of 7% carbon dioxide-enriched air as an anxiety-inducing stimulus. Behavioral disruption on performance tasks, however, did not differ as a function of carbon dioxide inhalation. Performance did differ as a function of math anxiety. High math anxious individuals generally exhibited higher error rates on mathematical tasks, particularly on tasks designed to measure advanced math skill and those requiring working memory resources. These findings are discussed with reference to processing efficiency theory, * Corresponding author. E-mail address: dhopko@utk.edu (D.R. Hopko). 0887-6185/$ – see front matter # 2002 Elsevier Inc. All rights reserved. PII: S 0 8 8 7 - 6 1 8 5 ( 0 2 ) 0 0 2 4 0 - 2 648 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 discordance among anxiety response systems, and the intricacies associated with skill measurement. # 2002 Elsevier Inc. All rights reserved. Keywords: Anxious responding; Mental arithmetic; Lexical decision 1. Introduction Anxiety may be conceptualized according to the physiological, cognitive, and behavioral responses elicited by certain (aversive) environmental stimuli (Lang, 1968). The inverse relation of anxious responding and task performance has been well documented (Eysenck, 1992). For example, individuals with high math anxiety take longer to solve arithmetic problems and commit more errors than individuals with low math anxiety (Ashcraft & Faust, 1994; Faust, Ashcraft, & Fleck, 1996; Hembree, 1990). In spite of this robust finding, and evident among other performance-based anxiety conditions such as test anxiety and social phobia, the issue of whether anxious responding or decreased competence (or skill) is primarily the basis for this observation continues to be debated (Hopko, McNeil, Zvolensky, & Eifert, 2001). Relatedly, our understanding of how anxious responding, skill deficits, and overt performance relate to contextual factors such as task complexity has evolved minimally since pioneering work in this area (Easterbrook, 1959; Yerkes & Dodson, 1908). This lack of clarity limits our theoretical conceptualization of performance-based anxiety and subsequently precludes the development of more effective assessment and treatment strategies designed to minimize the psychosocial impact of these conditions. Accordingly, the need arises to work toward disentangling the relative contributions of anxiety, skill deficits, and task complexity as these variables pertain to performance deficits. Using math anxiety as an exemplar anxiety condition, this issue was addressed in the following experiment. 2. The nature of mathematics anxiety Mathematics anxiety is characterized by feelings of apprehension and tension concerning manipulation of numbers and completion of mathematical problems in various contexts (Richardson & Suinn, 1972). The physiological, cognitive, and behavioral correlates of mathematics anxiety are significant, including physiological reactivity to numeric stimuli (Dew, Galassi, & Galassi, 1984; Faust, 1992) and faulty beliefs and negative attitudes regarding problem-solving abilities (Ashcraft & Kirk, 2001; Richardson & Woolfolk, 1980). On a behavioral level, avoidance of environments and careers that require the utilization of math skills (i.e., global avoidance) and a tendency to sacrifice accuracy for speed when performing numeric tasks (i.e., local avoidance) are typical of math anxious D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 649 individuals (Ashcraft & Faust, 1994; Chipman, Krantz, & Silver, 1992). Math anxiety is included among a spectrum of anxiety conditions referred to as performance-based anxiety disorders (Hopko et al., 2001). These conditions are associated with anxiety elicited in performance contexts and are characterized by escape and/or avoidance of these situations. In the case of math anxiety, anxious responding is elicited in math performance situations and may function independently or concurrently with other factors such as skill deficits and/or motivational differences to negatively impact performance on math-related tasks. 3. Math performance as a function of mathematics anxiety Mathematics anxiety is associated with poorer mathematical performance (i.e., increased response time and error rates), particularly on more complex tasks (Ashcraft & Faust, 1994; Faust et al., 1996). To date, there has been little resolution to the debate of whether performance deficits of high math anxious individuals are more a function of anxious interference or decreased competence (i.e., skill deficits) (Hopko et al., 2001). Much of this controversy may stem from two difficulties. First, achievement scores on math tests are not true indices of math skill, but more accurately a measurement of both anxiety and skill. Indeed, because math stimuli elicit anxiety in math anxious individuals, performance on mathematical exams (i.e., skill level) is confounded by the experience of anxiety. Secondly, manipulations of anxiety have proven difficult, as there continues to be controversy regarding those components of anxiety that are most disruptive in diminishing mathematical performance (Hopko, Ashcraft, Gute, Ruggeiro, & Lewis, 1998; Salame, 1984). This outcome is in part understandable, considering that anxiety symptoms, particularly negative cognitions, can be difficult to control and measure. A solution to these problems may require a more direct manipulation of anxiety. Salame (1984) has outlined two components of test (e.g., math) anxiety, worry and emotionality. The worry component consists of increased self-focused attention, lack of confidence, cognitions regarding failure, and worry about time pressure. The emotionality component involves feelings of apprehension and somatic symptoms associated with autonomic arousal. Instead of continuing to examine performance via the manipulation of worry (Kellogg, Hopko, & Ashcraft, 1999), a more effective procedure might be to directly manipulate the emotionality component. A carbon dioxide (CO2)-based challenge procedure may prove useful in this regard. 4. Carbon dioxide inhalation and anxiety induction Carbon dioxide challenge procedures have effectively been used to produce anxious symptoms that closely resemble naturally occurring panic attacks (Griez & 650 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 van den Hout, 1986; Rapee, Brown, Antony, & Barlow, 1992). The utility of CO2 as an aversive unconditioned stimulus has been well established in that individuals will work to avoid CO2 exposure (Lejuez, O’ Donnell, Wirth, Zvolensky, & Eifert, 1998) and exhibit increased physiological responding and higher selfreported anxiety following CO2 inhalation (Forsyth, Eifert, & Thompson, 1996). Although anxious responding is more pronounced among individuals with panic disorder (Perna, Barbini, Cocchi, & Bertani, 1995; Rapee et al., 1992), CO2 challenge procedures have successfully induced panic in nonclinical samples, without potentiating future panic attacks or panic disorder (Harrington, Schmidt, & Telch, 1996). Studies using the CO2 methodology typically have focused on quantifying the aversive nature of this stimulus (Forsyth et al., 1996), examining anxiety sensitivity as it relates to prediction and control over CO2 inhalation (Lejuez, Eifert, Zvolensky, & Richards, 2000), the efficacy of CO2 as an exposure-based treatment (Griez & van den Hout, 1986), and the utility of pharmacological agents in reducing panic symptoms created by CO2 inhalation (Bertani, Perna, Arancio, & Caldirola, 1997). In the only study that examined the effects of CO2 on cognitive task performance, Sheehy, Kamon, and Kiser (1982) concluded that there were no negative effects of 5% CO2 on reaction time tests, rotor pursuit, and short-term memory for digits and letters. Given the paucity of research in this latter area, CO2 administration may be a useful methodology to examine the relations among skill deficits, anxiety, and performance deficits often characteristic of high math anxious individuals. Accordingly, the following experiment was designed to answer several questions. First, would 7% CO2-enriched air function as an aversive stimulus? Second, would arithmetic and lexical decision task performance be affected as a function of the CO2 challenge? Third, would there be differential effects of CO2 on performance as a function of mathematics anxiety? Fourth, would it be demonstrated that anxiety was the primary component (as opposed to skills deficits) associated with performance deficits of high math anxious individuals? The prediction was made that task performance should be negatively affected in both high and low math anxious subjects as a consequence of CO2 inhalation, particularly on the arithmetic task. Given that anxious responding limits processing resources available in working memory (Eysenck & Calvo, 1992), performance on the lexical task (control condition) was predicted to be less effected, as working memory processing resources generally are unassociated with performance on this task. Second, because anxiety induction would coincide with arithmetic problems, arithmetic performance should be poorest in high math anxious subjects administered CO2 due to the dual anxiety-evoking stimuli. Third, hypothesizing that anxiety is a more likely contributor than skill deficits to performance deficits, low anxious participants who were administered CO2 should exhibit performance deficits similar to high anxious participants not exposed to the stimulus. D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 651 5. Method 5.1. Participants Participants included 64 undergraduate psychology students. Participants were chosen based on their scores on the Revised Math Anxiety Rating Scale (MARS-R; Plake & Parker, 1982), which was administered to 814 students in a preexperimental screening. In the total sample, the mean MARS-R score was 59.0 (S:D: ¼ 17:7). A gender effect was identified (females: N ¼ 418; males; N ¼ 396) whereby females (M ¼ 62:3, S:D: ¼ 18:5) reported more mathematics anxiety than males (M ¼ 55:6, S:D: ¼ 16:1) (tð812Þ ¼ 5:53, P < :001). Math anxiety was not significantly correlated with age (r ¼ :06) and did not differ as a function of ethnicity. To control for pre-existing gender differences in selfreported mathematics anxiety, participants in the top 10% of their same-gender distribution were considered high math anxious, while participants in the bottom 25–35% were categorized as low math anxious. Using these criteria, cutoff scores for the MARS-R (possible range ¼ 24–140) were as follows: males—high anxiety, >77 (M ¼ 88:9, S:D: ¼ 10:9), and low anxiety, >43 and <49 (M ¼ 46:3, S:D: ¼ 2:6); females—high anxiety, >87 (M ¼ 94:2, S:D: ¼ 4:8), and low anxiety, >47 and <53 (M ¼ 49:4, S:D: ¼ 2:0). This method of participant selection previously has been used with samples of anxious individuals (Lejuez et al., 2000; McNeil, Vrana, Melamed, Cuthbert, & Lang, 1993). The rationale behind this approach is to ensure that the high anxious group closely resembles clinically phobic individuals while the low anxious group closely approximates ‘‘normal’’ controls as opposed to individuals who may be prone to underreporting psychological symptoms (McNeil et al., 1993). An equivalent number of males and females (32 of each) participated in the study and were randomly, but equally assigned to either the CO2 condition or control condition. The mean age of participants was 20.5 years (S:D: ¼ 4:5 years). With regard to ethnicity, 59 participants (92%) were Caucasian, 2 were African American (3%), 1 was Asian American (2%), and 2 classified themselves as ‘‘other’’ (3%). A chi-square and t-test revealed no significant differences between anxiety groups as a function of ethnicity or age. Following the medical history, two individuals were excluded from participating due to respiratory problems (i.e., asthma). 5.2. Materials and apparatus 5.2.1. Physiological measurement A Coulbourn Modular Polygraph recorded physiological responding (heart rate and skin conductance). Heart rate was sampled in beats per minute (BPM) and was recorded at a frequency of 100 samples per second. Heart rate followed a standard bilateral placement with electrodes positioned underneath the rib cage. A third electrode was positioned just below the left clavicle and served as a ground. Skin conductance was sampled in microsiemens (ms) and also was 652 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 measured at a rate of 100 samples per second. Electrode placement was on the palmar surface of the first two fingers (middle phalanx) of the nondominant hand. 5.2.2. Physiologic stimulus The physiologic stimulus was 7% CO2-enriched air (7% CO2, 21% O2, 72% NO2) that was administered continuously to half of the participants during the arithmetic and lexical decision tasks (Lejuez, Forsyth, & Eifert, 1999). Although various concentrations and durations of CO2 have been administered, 7% CO2 was chosen based on its safe utilization in several studies (Martinez et al., 1998; Papp et al., 1997) for durations of up to 20 min in humans (Gorman, Papp, Coplan, & Martinez, 1994). 5.2.3. Interview and self-report instruments Participants underwent a semi-structured interview designed to gather a medical/social history and determine eligibility for participation. The Revised Math Anxiety Rating Scale (MARS-R; Plake & Parker, 1982), used in the preliminary screening, is a 24-item version of the Math Anxiety Rating Scale (MARS; Richardson & Suinn, 1972). This instrument measures anxiety in math situations with the composite score comprised of two subscales: Learning Mathematics Anxiety and Mathematics Evaluation Anxiety. Items are answered on a five-point Likert scale, from 0 (no anxiety) to 4 (high anxiety). The MARS-R has a coefficient alpha of .98 and is correlated .97 with the full scale MARS (Plake & Parker, 1982). The Diagnostic Symptoms Questionnaire (DSQ; Rapee et al., 1992) measures physiological and cognitive responses consistent with DSM-III-R panic attack criteria. Sixteen symptoms are rated on an eight-point Likert-type scale (0 ¼ not noticed at all to 7 ¼ very strongly felt). Self-reported anxiety also was assessed periodically throughout the session using a nine-point subjective units of discomfort (SUDS) scale. SUDS ratings were obtained on three dimensions: (a) discomfort, (b) arousal, and (c) aversiveness (i.e., of CO2). SUDS ratings were obtained by asking participants to report ‘‘how much (discomfort, arousal, or aversion) you are currently experiencing,’’ from 0 (absolutely none) to 8 (extreme). 5.2.4. Preexperimental skills tests To control for any pre-existing performance differences in terms of response rate or error rate, all 64 participants completed a basic calculation skills test that included problems similar to the experimental stimuli. This pencil-and-paper production task included 12 problems each in simple addition, simple multiplication, complex addition, and complex multiplication. Problem sets included problems that would not be presented on the computer arithmetic task to prevent practice effects. Participants were instructed to take as much time as needed to complete the task (but were covertly timed). D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 653 Advanced calculation ability was assessed via a quantitative section of the 1996 Scholastic Aptitude Test (SAT-Q). The test consisted of 25 items presented in a multiple-choice format, covering the domains of algebra, geometry, and general numeric problem solving. Participants had 30 min to complete the test. 5.2.5. Arithmetic stimuli A total of 128 problems were administered to each participant, equally divided among four stimulus sets. Arithmetic stimuli were programmed on a 486 microcomputer that recorded response accuracy and response latency. Consistent with previous research (Ashcraft & Faust, 1994; Faust et al., 1996), mean response times were computed for each of the four arithmetic conditions, excluding error trials. Problems remained on the screen until the participant responded, with a 1-s intertrial interval between problems. Problems consisted of two numbers separated by an operation sign, and an answer. Participants were asked to verify whether the answer provided was correct by pressing either a ‘‘true’’ or ‘‘false’’ key. Reaction time (milliseconds) and accuracy were recorded for each trial. Each of the four stimulus sets consisted of 32 verification problems, 16 presented with the correct answer and 16 with an incorrect answer. Order of stimulus sets was counterbalanced across participants. The simple addition problems (e.g., 2 þ 5 ¼ 7) included addends in the range of 2–9 due to evidence that suggests problems including either 0 or 1 as an addend are solved via rules rather than retrieval (Ashcraft, 1982). The simple multiplication problems (e.g., 2  5 ¼ 1) involved multipliers ranging from 2 to 9. The complex addition problems were created by pairing first addends in the range 16–25 with second addends in the range 11–19, with the rule that all problems required a carry. The complex multiplication problems involved a two-digit number multiplied by either a one- or two-digit number (e.g., 15  7 or 13  16). 5.2.6. Lexical decision task In the lexical decision task, participants were exposed to stimuli that consisted of letter strings. Participants were asked to decide whether the letter strings formed a word (i.e., MOTOR) or nonword (e.g., MANTY). A total of 120 stimuli (60 words and 60 nonwords) were presented based on word-frequency categories and stimuli used in previous studies (Allen & Emerson, 1991; Allen, Wallace, & Weber, 1995). Based on norms established by Kucera and Francis (1967), wordfrequency categories were as follows: very high frequency (range ¼ 240–1016 occurrences), medium frequency (range ¼ 151–235 occurrences) and very low frequency (range ¼ 1–5 occurrences). A total of 20 words were presented from each category. 5.3. Procedure Upon arrival at the laboratory, participants were randomly, but equally, assigned to either the CO2 or control condition. Participants were introduced 654 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 to the study, and informed consent was obtained. The medical/social history interview was then completed. Participants were excluded if they endorsed (or had a family history of) circulatory disorders, respiratory disorders, cardiovascular problems, epilepsy, cerebrovascular disease, or pregnancy. Participants then completed the preexperimental skills test and the SAT-Q. 5.3.1. Preexperimental baseline Following completion of the preexperimental tasks, the experimenter attached heart rate and skin conductance apparatus and instructed participants to relax for 5 min to collect initial heart rate and skin conductance data. During this baseline, room lights were dim and the experimenter was absent. 5.3.2. Preexperimental exposure If participants were in the CO2 condition, the experimenter explained and emphasized the safety of this procedure, with participants informed that they might experience some discomfort, ranging from a few physical symptoms to a sensation of anxiety. Participants were informed that they initially would be exposed to CO2 to control for the potential confound of lack of predictability of an aversive stimulus on anxiety-related responding (Lejuez et al., 2000). Participants in the CO2 condition were then administered a 25-s inhalation of CO2-enriched air to expose them to the stimulus. Participants in the control group were informed that they would be inhaling normal room air and underwent an acclimation period of 25 s in which they breathed normal room air. Following this exposure, SUDS ratings were obtained. 5.3.3. Performance tasks Participants next engaged in the two performance tasks, the order of which was counterbalanced. Instructions for each task were presented immediately prior to task initiation. In the arithmetic task, participants were asked to respond as quickly and as accurately as possible to the questions. They were asked to press ‘‘T’’ (for true) if the answer provided was the correct answer, and ‘‘F’’ (for false) if the answer provided was the incorrect answer. Several practice trials were administered. Following these instructions and demonstration, the experimenter proceeded to the adjacent room and simultaneously initiated CO2 administration and the arithmetic task. Following the arithmetic stimuli presentation, the participant was asked for SUDS ratings. 5.3.4. Lexical decision task Participants were asked to identify whether letter strings formed words or nonwords by pressing ‘‘T’’ if the letter string was a word and ‘‘F’’ if the letter string was a nonword. Participants were asked to work as quickly and as accurately as possible. Prior to being presented with experimental stimuli, 10 practice trials were administered. The C-Pap mask was reattached following the practice trials, the experimenter departed from the room, and the lexical task and D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 655 CO2 (if in this condition) were simultaneously initiated. SUDS ratings were obtained following the task. 5.3.5. Postinduction baseline When both tasks were completed, the participant was instructed to relax while heart rate and skin conductance data were collected. Following this 5-min period, the physiological equipment was removed and participants completed the DSQ. They were then debriefed and excused from the experiment. 6. Results 6.1. Preexperimental skills test Error rates and response time were analyzed using a 2 (anxiety group)  2 (gender)  4 (arithmetic condition) mixed factorial design. 6.1.1. Error rates Error rates were determined by dividing the number of incorrect responses by the total number of questions for each arithmetic condition. Collapsed across the three anxiety groups, the main effect of arithmetic condition was significant [Fð3; 180Þ ¼ 12:1, P < :01]. Tukey HSD post hoc analyses revealed that participants made more errors on complex multiplication compared to each of the other arithmetic conditions. All other main effects and interactions were not significant. 6.1.2. Response time Collapsed across the three anxiety groups, the main effect of arithmetic condition was significant [Fð3; 180Þ ¼ 412:09, P < :01]. Post hoc analyses revealed that mean response times for complex problems exceeded those of the simple problems. Response time on complex multiplication was greater than response time on complex addition. All other main effects and interactions were not significant. 6.2. Quantitative section of the Scholastic Aptitude Test Errors and response times were analyzed using a 2 (anxiety group)  2 (gender) ANOVA. For error rate, the main effect of anxiety group was significant [Fð1; 62Þ ¼ 5:78, P < :05]; high math anxious individuals made more errors (M ¼ 13:9, S:D: ¼ 3:8) than low anxious participants (M ¼ 11:2, S:D: ¼ 5:0). For response time, the main effect of anxiety group was significant [Fð1; 62Þ ¼ 4:03, P < :05]; low anxious individuals took longer to complete the SAT (M ¼ 1576 s, S:D: ¼ 199) than high anxious participants (M ¼ 1459 s, S:D: ¼ 258). In both the error rate and response time analyses, the main effect of gender and the interaction of anxiety group and gender were not significant. 656 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 6.3. Computer mental arithmetic task Error rates and response time were analyzed using a 2 (anxiety group)  2 (gender)  2 (gas condition)  4 (arithmetic condition) mixed factorial design. 6.3.1. Error rates The main effect of arithmetic condition was significant [Fð3; 168Þ ¼ 101:94, P < :01]. Collapsed across the two anxiety groups, post hoc analyses revealed that error rates were significantly higher in complex multiplication compared with all other arithmetic conditions. Analyses also revealed a main effect of anxiety group [Fð1; 56Þ ¼ 9:46, P < :01]; high anxious participants had higher overall error rates (M ¼ :10, S:D: ¼ :04) than low anxious participants (M ¼ :07, S:D: ¼ :04). As illustrated in Fig. 1, although the trend was for math anxious individuals to exhibit higher error rates in all four arithmetic conditions, post hoc analyses indicated that error rate was significantly different in only the simple and complex multiplication conditions. All interactions involving anxiety group, gender, gas condition, and arithmetic condition were not significant. 6.3.2. Response times As illustrated in Fig. 2, the main effect of arithmetic condition was significant [Fð3; 168Þ ¼ 163:22, P < :01]. Post hoc analyses revealed that response time Fig. 1. Mean arithmetic task error rates as a function of arithmetic condition and anxiety group. D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 657 Fig. 2. Mean arithmetic task response times as a function of arithmetic condition. Means that do not share a common superscript differ significantly at P < :05. differences among all conditions were significant with the exception of the difference between simple addition and simple multiplication. No other main effects or interactions were significant. 6.4. Lexical decision task Error rates and response time were analyzed using a 2 (anxiety group)  2 (gender)  2 (gas condition)  4 (word type) mixed factorial design. 6.4.1. Error rates Error rates were determined by dividing the number of incorrect responses by the total number of words for each word condition. The main effect of word type was significant [Fð3; 168Þ ¼ 77:76, P < :01]. Collapsed across the total sample, post hoc analyses revealed significantly more errors in the low frequency and nonword conditions compared with both the medium and high frequency conditions. No other main effects or interactions were significant. 6.4.2. Response times The main effect of word type was significant [Fð3; 168Þ ¼ 52:43, P < :01]. Post hoc analyses revealed that response time in the low frequency and nonword 658 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 conditions were longer than response times in the medium and high frequency conditions. No other main effects or interactions were significant. 6.5. Physiological data Physiological data were analyzed using a 2 (anxiety group)  2 (gender)  2 (gas condition)  3 (experimental phase: arithmetic, lexical, and postexperimental) mixed ANOVA. Baseline rates were used as covariates in these analyses. 6.5.1. Heart rate Heart rate was sampled in mean beats/per minute (bpm) and was screened for outliers due to sampling error (e.g., participant movement). As depicted in Fig. 3, the interaction of experimental phase and gas condition was significant [Fð2; 92Þ ¼ 3:36, P < :05]; post hoc comparisons indicated participants who were administered CO2 exhibited higher heart rates than the control participants in both performance conditions. The main effect of gas condition also was significant [Fð1; 46Þ ¼ 11:99, P < :01], but is explained within the context of the interaction. The gender main effect also was significant [Fð1; 46Þ ¼ 5:20, P < :05]; collapsed across the three experimental phases, females had faster heart rates (M ¼ 88:6 bpm) than males (M ¼ 86:5 bpm). No other main effects or interactions were significant. 6.5.2. Skin conductance The main effect of gas condition was significant [Fð1; 46Þ ¼ 7:04, P < :05]. Collapsed across the three experimental phases, compared with the control group (M ¼ 3:5 ms, S:D: ¼ 5:3), those administered CO2 exhibited higher skin Fig. 3. Mean heart rate as a function of gas condition and experimental phase. Means that do not share a common superscript differ significantly at P < :05. D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 659 conductance levels (M ¼ 5:6 ms, S:D: ¼ 6:1). No other main effects or interactions were significant. 6.6. Self-report data Self-report data were analyzed using 2 (anxiety group)  2 (gender)  2 (gas condition) ANOVAs. 6.6.1. Diagnostic Symptoms Questionnaire Only the main effect of gas condition was significant [Fð1; 63Þ ¼ 36:11, P < :01]. Individuals who were administered CO2 reported significantly greater physiological and cognitive symptoms of anxiety/panic (M ¼ 37:2, S:D: ¼ 24:9) than controls (M ¼ 8:5, S:D: ¼ 10:3). 6.6.2. SUDS ratings A significant gas condition  SUDS rating interaction was revealed for the preexperimental exposure [Fð2; 112Þ ¼ 5:41, P < :01], postarithmetic task [Fð2; 112Þ ¼ 19:96, P < :01], and postlexical task analyses [Fð2; 112Þ ¼ 13:77, P < :01]. In all three analyses, post hoc tests indicated that individuals Fig. 4. Mean arousal, discomfort, and aversiveness ratings for the preexperimental exposure as a function of gas condition. Means that do not share a common superscript differ significantly at P < :05. 660 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 who were administered CO2 gave higher arousal, discomfort, and aversiveness ratings. Moreover, in all analyses, for individuals administered CO2, aversiveness ratings were significantly higher than either arousal or discomfort ratings. An example of this relation is presented in Fig. 4 (preexperimental exposure). 7. Discussion The experiment was conducted under the assumption that 7% CO2-enriched air would function as an anxiety-inducing stimulus. Physiological measurement supported this assumption, indicating that individuals who were administered CO2 experienced more autonomic arousal than those in the control condition (increased heart rate and skin conductance), an effect that was observed across both performance tasks. Self-report measures generated consistent findings. As measured by the DSQ, individuals who were administered CO2 reported more physiological and cognitive symptoms of anxiety/panic. Excellent reliability was observed between DSQ and SUDS verbal-report ratings in that individuals who were administered CO2 reported greater arousal, discomfort, and aversiveness. In examining SUDS ratings, perhaps the most significant finding was that individuals who were administered CO2 reported that the experience was more aversive than either arousing or uncomfortable. The major implication of this finding involves the importance of incorporating aversiveness ratings when utilizing the CO2 methodology, as recording only arousal and/or discomfort ratings may result in increased Type II errors. Given the physiological and cognitive reactivity associated with CO2 inhalation, the stimulus was considered to have successfully functioned in an anxiety-eliciting capacity. Accordingly, the question of whether anxious responding affected overt performance became more intriguing. As a preliminary step toward addressing this issue, the preexperimental skills test was used to ensure equivalent basic calculation skill across anxiety groups. Efforts were made to minimize the potential impact of anxiety (i.e., the worry component) by presenting the task in an informal manner (e.g., removal of time pressure). High math anxious individuals did not exhibit performance deficits on this basic calculation skills test, even on complex tasks. In contrast to the preexperimental skills task, the SAT-Q was considered a test of advanced calculation skill. Here the effect of math anxiety became more evident, with high math anxious individuals making more errors. It also was observed, however, that high anxious individuals’ response time was significantly lower than that of low anxious individuals. This finding may be interpreted as support for local avoidance (Ashcraft & Faust, 1994), or the desire to escape from an aversive, anxiety-provoking task. It also is plausible that decreased response times among high anxious individuals are a function of skill deficits on this more complex task. Given that other anxiety measurement (e.g., physiological, verbal report) did not occur during this task, neither explanation can readily be refuted or supported. D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 661 Given the relative equality of anxiety groups on the basic calculation task and the anxiety-eliciting nature of the CO2 stimulus, the computer arithmetic task (with similar arithmetic stimuli) seemed an appropriate forum to study the potential relations among anxiety, skill, and task performance. Differing from the preexperimental tasks, two potential sources of anxiety were introduced to the high math anxious individuals in the experimental phase, arithmetic stimuli and CO2 gas. For the low anxious group, only the latter stimulus was considered functional in eliciting anxious responding. Thus, in addition to the worry component often used in manipulating anxiety (i.e., the inclusion of time pressure, verbal report of math anxiety) an emotionality manipulation also was incorporated (i.e., arousal as elicited by CO2). In addition to the greater potentiality for anxious responding during the experimental phase, the computer arithmetic task, although a test of basic calculation skill, was more demanding in that it required cognitive manipulation (i.e., the utilization of working memory resources) on complex problems. On this task, high math anxious individuals performance deficits became apparent as they exhibited higher overall error rates than individuals with low math anxiety. This finding was most notable in simple and complex multiplication, and approached significance in the complex addition condition. The finding of higher error rates on the simple multiplication problems is provocative, and directly contradicts previous research that has failed to demonstrate such an effect (Ashcraft & Faust, 1994; Faust et al., 1996). Replication is needed to substantiate this finding. In explaining performance deficits on the computer task, because preexperimental basic skill data revealed no differences among anxiety groups, a working memory, or on-line (anxious) interference interpretation (Ashcraft, Kirk, & Hopko, 1998) is preferential over a skill deficit explanation. Specifically, the finding of high anxious individuals’ general tendency to make more errors may be interpreted within the context of processing efficiency theory (Eysenck & Calvo, 1992). According to this theory, to the extent that working memory resources are consumed with task-irrelevant information (e.g., worrisome thoughts), fewer resources are available for task completion, thereby reducing processing efficiency and increasing the probability that errors will occur. Therefore, for individuals with high math anxiety, it is logical that more errors would occur on tasks such as complex multiplication in which responses are more dependent on working memory resources (i.e., these problems require a carry). Further, these tasks would be considerably more taxing on working memory resources when presented without the benefit of a pencil and paper, thus the discrepant findings between administrations. So although it is conceivable that significant anxiety may have been experienced during the preexperimental skills test, environmental circumstances (i.e., untimed task, manual calculation of responses) may have prevented this anxiety from interfering with performance on the arithmetic problems. One may take this analysis a step further and speculate on the anxiety symptoms associated with deficits on the computer task. Among the various 662 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 possibilities, cognitions focused on fear of negative evaluation, perceived lack of ability, or desire to escape may be included. There is no evidence to suggest, however, that physiological arousal plays a critical role. Physiological measurement revealed no support that high anxious individuals exhibited increased heart rate or skin conductance as compared to low anxious individuals. This finding is contradictory to previous research that suggests high anxious individuals experience tachycardia, greater skin conductance responses, constrictions in blood pulse volume, and decreases in peripheral skin temperature when engaged in mathematical tasks (Faust, 1992). On the contrary, the study supports the notion that physiological reactivity and verbal report of math anxiety generally are unrelated (Dew et al., 1984). Further study will be necessary to establish content domains that may be associated with intrusive cognitions of math anxious individuals. Based on the premise that increased anxiety negatively impacts working memory resources and corresponding problem-solving ability, it follows that anxiety induction via the CO2 apparatus would help to demonstrate this effect. In particular, anxiety induction of low anxious individuals would have the expected consequence of decreasing their problem-solving efficiency and equating performance with high anxious participants. Additionally, for high anxious participants exposed to CO2, this group should be particularly affected due to exposure to multiple sources of anxiety. To examine these hypotheses, participants completed two performance tasks, one requiring working memory resources (mental arithmetic), the other not (lexical decision task). In general, using error rate and response time as the dependent variables, there was no evidence to suggest that anxiety induction interfered with performance on either task. Also, despite the finding that high math anxious individuals demonstrated rather robust performance deficits on the arithmetic task, the inclusion of an anxiety-inducing stimulus did not appear to have a synergistic effect. Given the nature of these experimental tasks, it is conceivable that more complicated cognitive tasks (e.g., more difficult working memory tasks) would be more sensitive to the effects of anxiety induction. Because performance deficits were not observed as a consequence of anxiety induction, the stimulus did not appear to mimic the behavioral effects of a ‘‘math anxiety reaction.’’ Therefore, the argument can be made that the CO2 stimulus was inadequate as an anxiety-inducing stimulus. Given the physiological and verbal-report data, this explanation is unlikely. Consequently, experiment results are perhaps most parsimoniously explained as a prototypical example of discordance among anxiety response systems (Hugdahl, 1981), where although a stimulus functions aversively with regard to physiological and verbal-report measures, behavioral disruption is limited. As another explanation, it is feasible that alternative methodologies may be more sensitive to detecting performance deficits as a function of anxiety induction. For example, in addition to the idea of task complexity alluded to earlier, an alternative might be to form groups based on different criteria. Given that the Anxiety Sensitivity Index (ASI; Reiss, Peterson, Gursky, & McNally, 1986) seems to be a reliable predictor of anxious D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 663 responding to CO2 challenge (Asmundson, Norton, Wilson, & Sandler, 1994; Donnell & McNally, 1989), forming groups based on ASI scores may be a viable option. In conclusion, several provocative findings emerged from the present study. The first important finding is the observation that 7% CO2-enriched air elicited physiological and cognitive reactivity, but did not disrupt overt behavior on arithmetic and lexical decision tasks. This result is particularly pertinent given the increasingly popular use of CO2 as an aversive stimulus and the paucity of research that examines the affects of this stimulus from a triple-response system of anxiety and in reference to performance tasks. To follow up, a systematic research effort will be required to directly examine the affects of various durations and concentrations of CO2 as this relates to physiological, self-report, and behavioral indices of anxiety. To this end, a better understanding of anxious responding in more naturalistic environments may be achieved. A second important finding involves advances in understanding the relations among anxiety, skill deficits, and overt performance. In particular, the study demonstrates that performance on a task may be significantly affected by experimental context. Even on a relatively uncomplicated task that required elementary arithmetic skills, two methods of assessment revealed remarkably different findings. Although high and low math anxious individuals were equivalent in basic calculation ability, their ability to cognitively manipulate numeric information differed considerably. This discovery elucidates the importance of clearly defining skills to be measured and the corresponding strategy of measurement. Moreover, accurate measurement of skill, in that it can be equated with overt performance, requires that potential confounds such as anxious responding and motivational differences be controlled (Hopko et al., 2001). The latter was uncontrolled in the present investigation and thus represents a limitation. Related to anxiety measurement and its role in affecting performance, continued emphasis must be placed on operationalization of the construct, with reference to the tripleresponse system of anxiety, worry versus emotionality components, and investigation of worry content. Finally, the third important finding relates to performance deficits exhibited by high math anxious individuals. Given that college admission may be contingent on performance on examinations such as the SAT-Q, increased efforts must be directed toward primary and secondary prevention strategies that both identify individuals at risk for developing math anxiety and provide some method of effective intervention. The relation between anxiety and skill in performance-based anxiety disorders is complex. Experimental isolation of the effects of these variables must continue in that individuals with performance-based anxiety disorders such as math anxiety experience debilitating physiological, cognitive, and overt behavioral dysfunction. Continued investigation should facilitate a more refined theoretical conceptualization of the etiology and maintenance of conditions such as mathematics anxiety and subsequently result in the development of and modification of effective assessment and treatment strategies. 664 D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 References Allen, P. A., & Emerson, P. L. (1991). Holism revisited: evidence for parallel independent word-level and letter-level processors during word recognition. Journal of Experimental Psychology: Human Perception and Performance, 16, 48–64. Allen, P. A., Wallace, & Weber, T. A. (1995). Influence of case type, word frequency, and exposure duration on visual word recognition. Journal of Experimental Psychology: Human Perception and Performance, 21, 914–934. Ashcraft, M. H. (1982). The development of mental arithmetic: a chronometric approach. Developmental Review, 2, 213–236. Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: an exploratory investigation. Cognition and Emotion, 8, 97–125. Ashcraft, M. H., Kirk, E. P., & Hopko, D. R. (1998). On the cognitive consequences of mathematics anxiety. In: C. Donlan (Ed.), The development of mathematical skills (pp. 175–199). London: UCL Press. Ashcraft, M. H., & Kirk, E. P. (2001). The relationships between working memory, math anxiety, and performance. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 157–175. Asmundson, G., Norton, G. R., Wilson, K. G., & Sandler, L. S. (1994). Subjective symptoms and cardiac reactivity to brief hyperventilation in individuals with high anxiety sensitivity. Behaviour Research and Therapy, 32, 237–241. Bertani, A., Perna, G., Arancio, C., & Caldirola, D. (1997). Pharmacologic effect of imipramine, paroxetine, and sertraline on 35% carbon dioxide hypersensitivity in panic patients: a doubleblind, random, placebo-controlled study. Journal of Clinical Psychopharmacology, 17, 97–101. Chipman, S. F., Krantz, D. H., & Silver, R. (1992). Mathematics anxiety and science careers among able college women. Psychological Science, 3, 292–295. Dew, K. M. H., Galassi, J. P., & Galassi, M. D. (1984). Math anxiety: relation with situational test anxiety, performance, physiological arousal, and math avoidance behavior. Journal of Counseling Psychology, 31, 580–583. Donnell, C. D., & McNally, R. J. (1989). Anxiety sensitivity and history of panic as predictors of response to hyperventilation. Behaviour Research and Therapy, 27, 325–332. Easterbrook, J. A. (1959). The effect of emotion on cue utilization and the organization of behavior. Psychological Review, 66, 183–201. Eysenck, M. W. (1992). Anxiety: the cognitive perspective. Hove, UK: Erlbaum. Eysenck, M. W., & Calvo, M. G. (1992). Anxiety and performance: the processing efficiency theory. Cognition and Emotion, 6, 409–434. Faust, M. W. (1992). Analysis of physiological reactivity in mathematics anxiety. Unpublished doctoral dissertation, Bowling Green State University, Ohio. Faust, M. W., Ashcraft, M. H., & Fleck, D. E. (1996). Mathematics anxiety effects in simple and complex addition. Mathematical Cognition, 2(1), 25–62. Forsyth, J. P., Eifert, G. H., & Thompson, R. N. (1996). Systemic alarms in fear conditioning-II: an experimental methodology using 20% carbon dioxide inhalation as an unconditioned stimulus. Behavior Therapy, 27, 391–415. Gorman, J. M., Papp, L. A., Coplan, J. D., & Martinez, J. M. (1994). Anxiogenic effects of carbon dioxide and hyperventilation in patients with panic disorder. American Journal of Psychiatry, 151, 547–553. Griez, E., & van den Hout, M. A. (1986). Carbon dioxide inhalation in the treatment of panic attacks. Behaviour Research and Therapy, 2, 145–150. Harrington, P. J., Schmidt, N. B., & Telch, M. J. (1996). Prospective evaluation of panic potentiation following 35% carbon dioxide challenge in nonclinical subjects. American Journal of Psychiatry, 153, 823–825. Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33–46. D.R. Hopko et al. / Anxiety Disorders 17 (2003) 647–665 665 Hopko, D. R., Ashcraft, M. H., Gute, J., Ruggiero, K. J., & Lewis, C. (1998). Mathematics anxiety and working memory: support for the existence of a deficient inhibition mechanism. Journal of Anxiety Disorders, 12, 343–355. Hopko, D. R., McNeil, D. W., Zvolensky, M. J., & Eifert, G. H. (2001). The relation between anxiety and skill in performance-based anxiety disorders: a behavioral formulation of social phobia. Behavior Therapy, 32, 185–207. Hugdahl, K. (1981). The three-systems-model of fear and emotion: a critical examination. Behaviour Research and Therapy, 19, 75–85. Kellogg, J. S., Hopko, D. R., & Ashcraft, M. H. (1999). The effects of time pressure on arithmetic performance. Journal of Anxiety Disorders, 13, 591–600. Kucera, H., & Francis, W. N. (1967). Computational analysis of present day American English. Providence, RI: Brown University Press. Lang, P. J. (1968). Fear reduction and fear behavior: problems in treating a construct. In: J. M. Schlien (Ed.), Research in psychotherapy (Vol. III). Washington, DC: APA. Lejuez, C. W., Eifert, G. H., Zvolensky, M. J., & Richards, J. B. (2000). Preference between onset predictable and unpredictable administrations of 20% carbon-dioxide-enriched air: implications for better understanding the etiology of panic disorder. Journal of Experimental Psychology: Applied, 6, 349–358. Lejuez, C. W., Forsyth, J. P., & Eifert, G. H. (1999). Two devices for administering carbon dioxideenriched air in laboratory studies of aversive conditioning. Behavior Therapy and Experimental Psychiatry, 29, 239–248. Lejuez, C. W., O’ Donnell, J., Wirth, O., Zvolensky, M. J., & Eifert, G. H. (1998). Avoidance of 20% carbon dioxide-enriched air with humans. Journal of the Experimental Analysis of Behavior, 70, 79–86. Martinez, J. M., Coplan, J. D., Browne, S. T., Goetz, R., Welkowitz, L. A., Papp, L. A., Klein, D. F., & Gorman, J. M. (1998). Hemodynamic response to respiratory challenges in panic disorder. Journal of Psychosomatic Research, 44, 153–161. McNeil, D. W., Vrana, S. R., Melamed, B. G., Cuthbert, B. N., & Lang, P. J. (1993). Emotional imagery in simple and social phobia: fear versus anxiety. Journal of Abnormal Psychology, 102, 212–225. Papp, L. A., Martinez, J. M., Klein, D. F., Coplan, J. D., Norman, R. G., Cole, R., de Jesus, M. J., Ross, D., Goetz, R., & Gorman, J. M. (1997). Respiratory psychophysiology of panic disorder: three respiratory challenges in 98 subjects. American Journal of Psychiatry, 154, 1557–1565. Perna, G., Barbini, B., Cocchi, S., & Bertani, A. (1995). Thirty-five percent carbon dioxide challenge in panic and mood disorders. Journal of Affective Disorders, 33, 189–194. Plake, B. S., & Parker, C. S. (1982). The development and validation of a revised version of the Mathematics Anxiety Rating Scale. Educational and Psychological Measurement, 42, 551–557. Rapee, R., Brown, T. A., Antony, M. M., & Barlow, D. H. (1992). Response to hyperventilation and inhalation of 5.5% carbon dioxide-enriched air across the DSM-III-R anxiety disorders. Journal of Abnormal Psychology, 101, 538–552. Reiss, S., Peterson, R. A., Gursky, D. M., & McNally, R. J. (1986). Anxiety sensitivity, anxiety frequency, and the prediction of fearfulness. Behavior Research and Therapy, 24, 1–8. Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale. Journal of Counseling Psychology, 19, 551–554. Richardson, F. C., & Woolfolk, R. T. (1980). Mathematics anxiety. In: I. G. Sarason (Ed.), Test anxiety: theory, research, and application (pp. 271–290). Hillsdale, NJ: Erlbaum. Salame, R. F. (1984). Test anxiety: its determinants, manifestations, and consequences. In: H. M. van der Ploeg, R. Schwarzer, & C. D. Spielberger (Eds.), Advances in test anxiety research (pp. 83– 119). Hillsdale, NJ: Erlbaum. Sheehy, J. B., Kamon, E., & Kiser, D. (1982). Effects of carbon dioxide inhalation on psychomotor and mental performance during exercise and recovery. Human Factors, 24, 581–588. 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.