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Edited by: Natasha Kirkham, Birkbeck, University of London, UK

Reviewed by: Camilla Gilmore, Loughborough University, UK; Alessandro Pepe, University of Milano-Bicocca, Italy

*Correspondence: Emma Carey

Dénes Szűcs

This article was submitted to Developmental Psychology, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Mathematics anxiety (MA) can be observed in children from primary school age into the teenage years and adulthood, but many MA rating scales are only suitable for use with adults or older adolescents. We have adapted one such rating scale, the Abbreviated Math Anxiety Scale (AMAS), to be used with British children aged 8–13. In this study, we assess the scale's reliability, factor structure, and divergent validity. The modified AMAS (mAMAS) was administered to a very large (

Math is an important skill not only for academic success, but also for efficient functioning in everyday life. Yet, a significant proportion of the population experience fear and apprehension when faced with numerical problems (Hembree,

MA is by definition distinct from other forms of anxiety, since it is defined in terms of an emotional response elicited

On the other hand, general anxiety is a much less specific type of anxiety and refers to an individual's disposition toward anxiety about events, behaviors, and competence (Spence,

The definitional uniqueness of MA may seem at odds with its consistent empirical association with test and general anxiety. However, it is important to bear in mind that these associations are small to moderate and account for only some individual variability in MA level. For example, Hembree (^{2}-value of 0.37 between MA and test anxiety. This means that 37% of variation in MA can be explained by variation in test anxiety scores: in other words, 63% of the variability in individuals' levels of MA comes from other sources. These sources have been highly debated in the math anxiety literature and go beyond the scope of this paper (for review see Maloney and Beilock,

Several anxiety measures have been developed for use with children; however, many of these measures are excessively age-restricted or adequate statistics supporting their validity are not provided. For example, Ramirez et al. (

The same problem regarding age specificity applies to the Scale for Early Mathematics Anxiety (MA; Wu et al.,

An alternative measure of MA in children is the Math Anxiety Questionnaire (Thomas and Dowker,

Several measures of MA have been used in adult research, including the Abbreviated Math Anxiety Scale (AMAS; Hopko et al.,

The modified AMAS (mAMAS) was developed in response to the need for a brief and appropriate scale to assess MA in British children and adolescents. Adjustments were made to the content of the AMAS in order to make the language appropriate to children speaking British English. Furthermore, the language and content of the scale has been adapted such that it is applicable across a broader age range (from middle childhood across adolescence), by altering references to specific topics in math (e.g., equations and algebra) and altering an item which refers to using tables in the back of a textbook, something which primary school aged British children have not encountered. Table

1 | Having to use the tables in the back of a math book | Having to complete a worksheet by yourself |

2 | Thinking about an upcoming math test 1 day before^{*} |
Thinking about a maths test the day before you take it |

3 | Watching the teacher work an algebraic equation on the blackboard | Watching the teacher work out a maths problem on the board |

4 | Taking an examination in a math course^{*} |
Taking a maths test |

5 | Being given a homework assignment of many difficult problems that is due the next class meeting^{*} |
Being given maths homework with lots of difficult questions that you have to hand in the next day |

6 | Listening to a lecture in math class | Listening to the teacher talk for a long time in maths |

7 | Listening to another student explain a math formula | Listening to another child in your class explain a maths problem |

8 | Being given a “pop” quiz in math class^{*} |
Finding out that you are going to have a surprise maths quiz when you start your maths lesson |

9 | Starting a new chapter in a math book | Starting a new topic in maths |

To evaluate construct validity of the mAMAS, we conduct confirmatory factor analysis to show for the first time that the mAMAS used with children and adolescents has the same factor structure as the AMAS used with adults. Furthermore, our unusually large sample size enabled us to divide the sample to conduct both exploratory and confirmatory factor analysis on items from the mAMAS alongside items from two other anxiety scales—the Child Test Anxiety Scale (CTAS; Wren and Benson,

We tested 1849 students in schools across Cambridgeshire (eight schools), Hertfordshire (seven schools), Suffolk (seven schools), Norfolk (two schools), and Bedfordshire (one school). Demographics of the schools varied widely. Using the number of children receiving Free School Meals (FSM) as an indicator of socioeconomic status, schools in our sample ranged from 2.9 to 36.5% receiving FSM (Department for Education,

Our sample consisted of students from two different age groups. The first of these (aged 8–9 years) consisted of students in year 4 of primary school. This group was chosen because they are old enough to complete standardized tests and questionnaires but are still in the early stages of education, therefore enabling us to capture MA in fairly young children. The second age group (age 11–13) consisted of students in years 7 and 8 of secondary school. This group was chosen in order to investigate how students' MA has developed by early secondary school.

Dealing with missing data appropriately and splitting of the sample for some analyses resulted in different sized samples for each analysis. Assessments of the reliability and factor structure of the mAMAS have a sample size of 1746 after casewise deletion of those with missing relevant data. Of the 824 primary school (year 4) students, there were 419 boys and 405 girls, with a mean age of 109.4 months (

Analysis of the divergent validity of the mAMAS relied on item-level data from the mAMAS, RCMAS, and CTAS. The sample size after casewise deletion of those with missing items on any of these measures was 1469. The sample was stratified by school and then divided randomly to form two subsamples. The first of these was used for the exploratory factor analysis. This sample consisted of 735 students, 365 of whom were male, and 370 female. Three hundred and fifty-seven students were in year 4 and 378 in year 7 or 8. The mean age of this sample was 129.4 months (

MA was measured using a modified version of the Abbreviated Math Anxiety Scale (AMAS; Hopko et al.,

Test anxiety was measured using the Children's Test Anxiety Scale (CTAS; Wren and Benson,

General anxiety was measured using the Short Form of the Revised Children's Manifest Anxiety Scale: Second Edition (RCMAS-2; Reynolds and Richmond,

Researchers went to schools to administer the testing in group settings (either as a class or whole year group). As well as completing the questionnaires analyzed here, students also completed the age-appropriate Hodder Group Reading Test (Vincent and Crumpler,

The reliability of the mAMAS was assessed using both ordinal alpha and Cronbach alpha (as in Cipora et al.,

As well as making an assessment of the reliability of the mAMAS, we investigated its validity by carrying out a confirmatory factor analysis based on the two-factor structure of the original AMAS (Hopko et al.,

Mplus was used to conduct this analysis, employing theta parameterization and weighted least squares means and variance adjusted (WLSMV) estimation due to the categorical nature of Likert-scale variables (Muthén and Asparouhov,

R was used to conduct all analyses (R Core Team,

Principal axis factoring was used; this was favored over maximum likelihood extraction, because of its insensitivity to violations of the assumption of multivariate normality (Osborne,

Two methods were used to determine the optimal number of factors to extract. We chose to use Horn's parallel analysis (Horn,

We conducted confirmatory factor analysis to yield a model for the mAMAS, CTAS, and RCMAS with the number of factors which had emerged from the exploratory factor analysis. Mplus was used for this analysis (Muthén and Muthén,

The average mAMAS total score was 19.67 (_{(1746)} = 0.95, _{(1746)} = 0.96, _{(1746)} = 0.87,

With a Bonferroni corrected significance level of 0.008 for six comparisons (0.05/6 = 0.008; all _{(1744)} = −2.07, _{(1744)} = −2.95, _{(1744)} = −0.75, _{(1744)} = 7.29, _{(1744)} = 9.33, _{(1744)} = 3.78,

Year 4 | Female | 404 | 20.70 | 7.49 | 11.14 | 4.17 | 9.56 | 4.08 |

Male | 420 | 17.88 | 7.87 | 9.21 | 4.29 | 8.67 | 4.26 | |

Year 7 and 8 | Female | 459 | 21.25 | 7.69 | 11.68 | 4.37 | 9.57 | 4.29 |

Male | 463 | 18.80 | 7.11 | 9.85 | 3.98 | 8.95 | 3.98 |

First we examined ordinal alpha for the entire sample. Ordinal alpha for the total scale was 0.89, for the Learning subscale was 0.83 and for the Evaluation subscale was 0.83. Ordinal alpha was not increased by removing any item from either subscale or the total scale.

We then looked at ordinal alpha for each age group separately. In year 4 students, ordinal alpha for the total scale was 0.89, for the Learning subscale was 0.81, and for the Evaluation subscale was 0.83. In year 7/8 students, ordinal alpha for the total scale was 0.89, for the Learning subscale was 0.85 and for the Evaluation subscale was 0.84. Ordinal alpha-values were not increased by removing any item from either subscale or the total scale in either age group.

Cronbach alpha for the whole scale was 0.85 (95% confidence interval 0.83–0.87), for the Learning subscale was 0.77 (95% confidence interval 0.74–0.80) and for the Evaluation subscale was 0.79 (95% confidence interval 0.76–0.83). Cronbach alpha was not increased by removing any item from either subscale or the total scale.

For year 4 students, Cronbach alpha for the total scale was 0.85 (95% confidence interval 0.82–0.87), for the Learning subscale was 0.74 (95% confidence interval 0.69–0.79) and for the Evaluation subscale was 0.78 (95% confidence interval 0.73–0.83). For year 7/8 students, Cronbach alpha for the total scale was 0.86 (95% confidence interval 0.83–0.88), for the Learning subscale was 0.80 (95% confidence interval 0.76–0.84) and for the Evaluation subscale was 0.81 (95% confidence interval 0.76–0.85). Cronbach alpha-values were not increased by removing any item from either subscale or the total scale in either age group.

Figures ^{2}-test of model fit suggested that the model was significantly different from the ideal model: χ^{2} = 466.95(84,

Ordinal α for the RCMAS was 0.73 and Cronbach α was 0.74 (95% confidence interval 0.71–0.76), suggesting adequate reliability. Ordinal α for the CTAS was 0.92 and Cronbach α was 0.92 (95% confidence interval 0.91–0.93), suggesting excellent reliability.

Horn's parallel analysis and Velicer's MAP test suggested that a 5-factor model would be optimal: thus we opted to examine the 5-factor model, in which all extracted factors had loadings >0.4 on 3 or more variables. Eigen-values of the five factors in this model ranged from 2.1 to 5.3. Items were easily clustered into factors.

The factors identified were perceived to represent: Test Anxiety, MA, Physical Anxiety, Off-Task Behaviors in Tests and Social Anxiety. These factors largely related to specific anxiety scales or subscales. The MA factor consisted of all mAMAS items and one item of the CTAS. Test Anxiety consisted largely of CTAS items and the two mAMAS items which addressed math tests. Items from the Autonomic Reactions subscale of the CTAS and the Physiological subscale of the RCMAS clustered onto the Physical Anxiety factor. Items from the Off Task Behaviors subscale of the CTAS formed the factor Off-Task Behaviors in Tests. Finally, items loading onto Social Anxiety were all from the RCMAS, with the highest loading items making reference to social situations. For a detailed view of each item's factor loadings, see Table

mAMAS | Finding out that you are going to have a surprise maths quiz… | 0.60 | ||||

mAMAS | Watching the teacher work out a maths problem on the board | 0.70 | ||||

mAMAS | Starting a new topic in maths | 0.65 | ||||

mAMAS | Having to complete a worksheet by yourself | 0.61 | ||||

mAMAS | Being given maths homework with lots of difficult questions… | 0.51 | ||||

mAMAS | Listening to another child in your class explain a maths problem | 0.67 | ||||

mAMAS | Listening to the teacher talk for a long time in maths | 0.55 | ||||

mAMAS | Thinking about a maths test the day before you take it | 0.25 | 0.45 | |||

mAMAS | Taking a maths test | 0.40 | 0.45 | |||

CTAS | It is hard for me to remember the right answers | 0.25 | 0.28 | |||

CTAS | I wonder if my answers are right | 0.58 | ||||

CTAS | I think about what my grade will be | 0.60 | ||||

CTAS | I worry about how hard the test is | 0.55 | ||||

CTAS | I worry about doing something wrong | 0.66 | ||||

CTAS | I think about what will happen if I fail | 0.72 | ||||

CTAS | I worry about failing | 0.85 | ||||

CTAS | I worry about what my parents will say | 0.39 | ||||

CTAS | I wonder if I will pass | 0.58 | ||||

CTAS | I think that I should have studied more | 0.38 | ||||

CTAS | I think most of my answers are wrong | 0.56 | ||||

RCMAS | I am nervous | 0.27 | ||||

CTAS | I think I am going to get a bad grade | 0.70 | ||||

CTAS | I think about how poorly I am doing | 0.48 | ||||

CTAS | My heart beats fast | 0.38 | 0.52 | |||

CTAS | I feel nervous | 0.59 | 0.31 | |||

CTAS | I feel scared | 0.48 | 0.46 | |||

CTAS | My hand shakes | 0.56 | ||||

CTAS | I feel warm | 0.60 | ||||

CTAS | My face feels hot | 0.56 | ||||

RCMAS | I have too many headaches | 0.34 | ||||

CTAS | My belly feels funny | 0.64 | ||||

RCMAS | Often I feel sick in my stomach | 0.44 | ||||

CTAS | My head hurts | 0.50 | ||||

RCMAS | I wake up scared sometimes | 0.35 | ||||

CTAS | I find it hard to sit still | 0.63 | ||||

CTAS | I tap my feet | 0.56 | ||||

CTAS | I look around the room | 0.68 | ||||

CTAS | I have to go to the bathroom | 0.22 | ||||

CTAS | I try to finish up fast | 0.41 | ||||

CTAS | I stare | 0.56 | ||||

CTAS | I play with my pencil | 0.72 | ||||

CTAS | I look at other people | 0.57 | ||||

CTAS | I check the time | 0.22 | 0.42 | |||

RCMAS | I often worry about something bad happening to me | 0.20 | 0.20 | |||

RCMAS | I feel someone will tell me I do things the wrong way | 0.25 | ||||

RCMAS | I get nervous around people | 0.28 | ||||

RCMAS | I worry that others do not like me | 0.53 | ||||

RCMAS | I fear other kids will laugh at me in class | 0.83 | ||||

RCMAS | I fear other people will laugh at me | 0.95 |

Standardized root mean square residual (SRMR) for the model was 0.06, RMSEA was 0.04 (90% CI 0.039–0.043) and CFI 0.94. Whilst CFI was just below Hu and Bentler's (

Math anxiety | 0.67 | |||||

Physical anxiety | 0.69 | 0.57 | ||||

Off-task behaviors | 0.49 | 0.57 | 0.51 | |||

Social anxiety | 0.58 | 0.50 | 0.51 | 0.37 | ||

mAMAS | Finding out that you are going to have a surprise maths quiz… | 0.72 | ||||

mAMAS | Watching the teacher work out a maths problem on the board | 0.65 | ||||

mAMAS | Starting a new topic in maths | 0.66 | ||||

mAMAS | Having to complete a worksheet by yourself | 0.73 | ||||

mAMAS | Being given maths homework with lots of difficult questions… | 0.75 | ||||

mAMAS | Listening to another child in your class explain a maths problem | 0.65 | ||||

mAMAS | Listening to the teacher talk for a long time in maths | 0.56 | ||||

mAMAS | Thinking about a maths test the day before you take it | 0.43 | 0.42 | |||

mAMAS | Taking a maths test | 0.55 | 0.26 | |||

CTAS | It is hard for me to remember the right answers | 0.32 | 0.30 | |||

CTAS | I wonder if my answers are right | 0.59 | ||||

CTAS | I think about what my grade will be | 0.55 | ||||

CTAS | I worry about how hard the test is | 0.75 | ||||

CTAS | I worry about doing something wrong | 0.74 | ||||

CTAS | I think about what will happen if I fail | 0.78 | ||||

CTAS | I worry about failing | 0.83 | ||||

CTAS | I worry about what my parents will say | 0.67 | ||||

CTAS | I wonder if I will pass | 0.49 | ||||

CTAS | I think that I should have studied more | 0.62 | ||||

CTAS | I think most of my answers are wrong | 0.79 | ||||

RCMAS | I am nervous | 0.62 | ||||

CTAS | I think I am going to get a bad grade | 0.74 | ||||

CTAS | I think about how poorly I am doing | 0.77 | ||||

CTAS | My heart beats fast | 0.32 | 0.41 | |||

CTAS | I feel nervous | 0.51 | 0.28 | |||

CTAS | I feel scared | 0.41 | 0.49 | |||

CTAS | My hand shakes | 0.65 | ||||

CTAS | I feel warm | 0.52 | ||||

CTAS | My face feels hot | 0.68 | ||||

RCMAS | I have too many headaches | 0.39 | ||||

CTAS | My belly feels funny | 0.73 | ||||

RCMAS | Often I feel sick in my stomach | 0.64 | ||||

CTAS | My head hurts | 0.69 | ||||

RCMAS | I wake up scared sometimes | 0.44 | ||||

CTAS | I find it hard to sit still | 0.72 | ||||

CTAS | I tap my feet | 0.56 | ||||

CTAS | I look around the room | 0.59 | ||||

CTAS | I have to go to the bathroom | 0.66 | ||||

CTAS | I try to finish up fast | 0.58 | ||||

CTAS | I stare | 0.72 | ||||

CTAS | I play with my pencil | 0.51 | ||||

CTAS | I look at other people | 0.56 | ||||

CTAS | I check the time | 0.21 | 0.24 | |||

RCMAS | I often worry about something bad happening to me | 0.16 | 0.36 | |||

RCMAS | I feel someone will tell me I do things the wrong way | 0.59 | ||||

RCMAS | I get nervous around people | 0.74 | ||||

RCMAS | I worry that others do not like me | 0.70 | ||||

RCMAS | I fear other kids will laugh at me in class | 0.88 | ||||

RCMAS | I fear other people will laugh at me | 0.93 |

Ordinal alpha, the most appropriate measure for items on an interval scale, suggests that the internal consistency of the scale as a whole is very good (0.89) and that the subscales have good internal consistency (both 0.83). These high alpha-values suggest that, regardless of the factor structure of the scale, the mAMAS reliably measures one construct. This suggests that our modifications of the AMAS did not decrease the scale's internal consistency, and that the mAMAS is reliable even when children and adolescents are being tested. Furthermore, these alpha-values remained high when year 4 and year 7/8 students' results were analyzed separately. This suggests that the mAMAS is a reliable scale of MA both in middle childhood and early adolescence. This indicates that the mAMAS is preferable to other childhood MA scales such as the Child MA Questionnaire (Ramirez et al.,

Our confirmatory factor analysis of the mAMAS based on the subscales identified in the original mAMAS and confirmed to exist in Polish, Iranian, and Italian translations of the AMAS (Hopko et al.,

All factor loadings were at an acceptable level (≥0.60) which, alongside adequate measurements of model fit, suggests that the mAMAS can be conceptualized in terms of the same two subscales which comprise the original AMAS. This was the case for both younger (year 4) and older (year 7 and 8) children, suggesting that the mAMAS has good construct validity when used for children aged 8–13. This represents a very broad age range compared with other childhood MA scales, and highlights the utility of the mAMAS when researchers wish to investigate MA across development.

In order to assess convergent and divergent validity of the mAMAS we analyzed children's scores on mAMAS items alongside items from the CTAS and the RCMAS-II short form. MA, test anxiety and general anxiety have previously been shown to be related, but should be dissociable. Thus, we had the expectation that if the mAMAS truly measures MA, mAMAS items should load onto one or more unique factors.

We first ran exploratory factor analysis on data from half of the sample, to explore how items were related without relying on prior theoretical assumptions. This was followed up with a confirmatory factor analysis (using the factors identified in exploratory factor analysis) on the other half of the sample. Adding a confirmatory factor analysis enabled us to confirm that the factor structure determined through exploratory factor analysis was not subject to overextraction of spurious factors and to gain measures of model fit.

The exploratory and confirmatory factor analyses of item-level data from the RCMAS, CTAS and mAMAS suggest that an individual's scores on each item of these questionnaires is influenced by multiple, unique but related factors. A 5-factor solution best explained the variance in the data without unnecessary complexity. These five factors were interpreted as representing: test anxiety, MA, off-task behaviors, physical anxiety, and social anxiety. This 5-factor solution was used to conduct confirmatory factor analysis, and it was determined that the model had a good fit to the data.

It is notable that all items in the mAMAS loaded relatively highly on the MA factor (all items had a factor loading >0.40 in the exploratory factor analysis, and all but one item had a factor loading >0.40 in the confirmatory factor analysis). This suggests that the mAMAS taps into a unique area of anxiety, even in children aged 8–13. If MA could be explained in terms of other anxiety forms, such as test anxiety and general anxiety, one would expect no unique MA factor to emerge from a factor analysis. Therefore, the analysis suggests that the mAMAS shows divergent validity: it measures a form of anxiety which can be differentiated from test and general anxiety.

Two items in the mAMAS had a similar loading on the Test Anxiety factor as they did on the MA factor. These items, “Thinking about a math test the day before you take it” and “Taking a math test,” make explicit references to both mathematics and evaluative situations. It is unsurprising that they load similarly onto MA and Test Anxiety factors, because being high in either MA

Our findings that items from the mAMAS almost all loaded onto a unique factor representing MA provide strong empirical evidence for two things. Firstly, MA appears to exist as a unique anxiety form. Some items measured by MA questionnaires might measure two different forms of anxiety (MA and test anxiety), but other items measure MA alone, suggesting that MA can be considered as a separate construct to test anxiety. This calls into question how much of the relationship between MA and test anxiety would remain if questions which tap into both anxiety forms were removed from MA questionnaires. Secondly, the mAMAS taps into this unique MA factor, rather than merely reflecting another form of anxiety. Thus, we have shown both that MA exists in its own right in children and adolescents and that we are able to capture it using the mAMAS.

Having a valid and reliable scale with which to measure MA is of vital importance to researchers, psychiatrists, and educational psychologists. MA is associated with a variety of negative outcomes, including avoidance of math-related situations and poorer outcomes in math (Hembree,

This larger age span of the mAMAS compared with other child MA questionnaires could be very beneficial to both educational practitioners and researchers. In the school or educational psychology setting, having different measures for each age group is likely to cause confusion. It also raises questions around which measure is appropriate for a child who functions at a lower or higher academic level than their peers: is it more appropriate to administer a questionnaire suitable for their chronological age or their academic level? For example, a child with very strong mathematical ability may be anxious in response to a question they find challenging. If the sample questions in an anxiety questionnaire are those which would stretch the average child of their

In addition, the AMAS is a very common tool for researchers of adult MA. The fact that the mAMAS is similar to the AMAS in both style, content and factor structure may enable researchers to better study how math anxiety changes from childhood to adulthood, by using two closely related scales.

Assessing the test-retest reliability of the mAMAS would be useful, but practically challenging with a large sample such as used here. Taking another measure of MA could confirm the convergent validity of the mAMAS. However, as discussed, neither the Child MA Questionnaire (Ramirez et al.,

Further studies of the mAMAS may wish to investigate more specific properties of the test, such as whether its factor structure is invariant across various groups of children. For example, average levels of MA have consistently been shown to be lower in boys than girls (see Hembree,

Our analyses suggest that the mAMAS provides a valid and reliable measurement of MA in children aged 8–13. The mAMAS appears to have the same factor structure as the original AMAS. It also appears to tap uniquely into MA, forming a unique factor when items were factor analyzed alongside items from the CTAS and RCMAS. The questions in the mAMAS are phrased as broadly as possible and should be applicable to all English-speaking children and adolescents, as long as they are learning math in school and have the questions explained or read aloud to them when necessary. Thus, the mAMAS provides a useful assessment of MA, which may be utilized by researchers, educational psychologists, and educational practitioners.

Cambridge Psychology Research Ethics Committee.Children took an opt-out consent form home from school in their book bags, for their parents/guardians to return if they did not want their child to participate in the research. We worked with children whose parents/guardians did not opt-out of participation, as approved by Cambridge Psychology Research Ethics Committee.We made arrangements for any participant who appeared distressed or expressed that they did not wish to participate to leave with no penalty and return to other activities in school (testing carried out in the main school halls or classrooms). Students generally found the tasks (maths and reading tests and filling in questionnaires) within the realm of what they normally do in the school day.

AD and DS made substantial contributions to the conception and design of the work. AD, FH, and EC made substantial contributions to the acquisition and interpretation of the data. EC and DS were involved in analysis of the data. EC drafted the work with contributions from FH. AD and DS were involved in critical revisions and discussion of intellectual content.

This project has been funded by the Nuffield Foundation (EDU/41179), although the views expressed are those of the authors and not necessarily those of the Foundation. The project also received funding from the James S. McDonnel Foundation (220020370).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors thank Florence Gabriel, Timothy Myers, Jack Clearman, and Swiya Nath for help with data collection and Kayleigh Fawcett for her help modifying the AMAS.

The Supplementary Material for this article can be found online at: