measuring education science students‘ statistics anxiety · schneider & preckel, 2017)....

Leibniz University Hannover

Faculty of Humanities

Institute of Psychology

Measuring Education Science Students‘

Statistics Anxiety Conceptual Framework, Methodological Considerations, and Empirical Analyses

Research Report Leibniz University Hannover: Institute of Psychology 2018

Dr. Günter Faber Leibniz University Hannover, Institute of Psychology

Dr. Heike Drexler Leibniz University Hannover, Institute of Psychology

MA Alexander Stappert University of Vechta, Department of Social and Education Sciences

BA Joana Eichhorn Leibniz University Hannover, Education Science Master’s Programme




URL: http://www.psychologie.uni-hannover.de/guenter_faber.html

Mail: [email protected]

Copyright © Faber, Drexler, Stappert, Eichhorn 2018

DOI: 10.13140/RG.2.2.18109.31201

Measuring education students’ statistics anxiety.

Conceptual framework, methodological considerations, and empirical analyses.

Research report

Günter Faber

Heike Drexler

Alexander Stappert

Joana Eichhorn




Copyright © Faber, Drexler, Stappert, Eichhorn 2018

Measuring Education Science Students’ Statistics Anxiety

Leibniz University Hannover:Institute of Psychology 2018

© Faber, Drexler, Stappert, Eichhorn

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Table of contents

1 Abstract ................................................................................................................. 2

2 Introduction ........................................................................................................... 3

2.1 Conceptual perspectives on statistics anxiety ....................................................... 4

2.2 Methodological perspectives on statistics anxiety measures ................................ 8

2.3 Approaching refined measurement ....................................................................... 9

3 Validation framework and objectives ................................................................. 11

4 Method

4.1 Participants and procedure .................................................................................. 15

4.2 Measures ............................................................................................................. 16

4.3 Data analyses ....................................................................................................... 18

5 Results

5.1 Scale formation ................................................................................................... 18

5.2 Validation results ................................................................................................ 21

5.3 Additional multivariate analyses ......................................................................... 23

6 Conclusion .......................................................................................................... 25

7 References ........................................................................................................... 29

8 Appendix ............................................................................................................. 46

Günter Faber, Heike Drexler, Alexander Stappert & Joana Eichhorn



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1 Abstract

At higher education levels, the acquisition and application of research methods appears to

represent a great challenge for a considerable number of students. As relevant empirical find-

ings consistently demonstrated, many students in social or human science programmes tend to

evolve and maintain negative attitudes against compulsory method courses and, in particular,

perceive statistical demands as threatening study events – thus, being at risk of developing a

heightened level of statistics anxiety. Therefore, university settings need to pay attention to

this phenomenon and strive for a sound analysis of the students’ concern. Accordingly, over

the past decades several questionnaires had been developed to assess university learners’ sta-

tistics anxiety in order to get appropriate information for conceptualizing most adaptive

instructional and guidance strategies. However, against theoretical and methodological back-

ground of test anxiety research, current instruments for assessing university students’ statistics

anxiety prevailingly emphasize the affective construct component. In order to unfold the con-

struct in a more exhaustive and differentiated manner, a scale for measuring university stu-

dents’ worry, avoidance, and emotionality cognitions was developed. In two samples of edu-

cation science majors the present study aimed at analyzing the scale’s psychometric properties

and at gaining preliminary validation results. In both samples, principal component analysis

led to the formation of a unidimensional scale which appeared to be sufficiently reliable. Its

relations to domain-specific self-belief and background variables turned out as theoretically

expected – thus, for the time being the scale should claim criterion validity. In particular, the

scale’s total sum score was demonstrated to substantially correlate with the students’ math-

ematical self-concept, entity beliefs, and negative instrumental values.

Keywords: statistics anxiety, math self-concept, implicit entity beliefs, utility values




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2 Introduction

Higher education settings usually need to manage a broad range of students’ individual

background, learning approaches, and study outcomes. Therefore, in order to ensure a most

adaptive and effective academic environment, they must rely on appropriate conceptualiza-

tions of the students’ learning processes which should help to analyze the individual and con-

textual factors of university achievement and to explain existing differences in the students’

performance – and, eventually, to access reliable and valid information about the substantial

determinants of university success or failure. For that purpose, educational research had offer-

ed several modeling perspectives to unfold the complexity of learning processes being typical

for university contexts. Though each of them focusing on learning and achievement in a

different manner, all these conceptualizations widely agree in stressing the importance of

students’ individual aptitudes, body of knowledge, and motivational characteristics (Credé &

Kunzel, 2008; De Clercq, Galand, Dupont, & Frenay, 2013; Entwistle, 2007; Price, 2014; van

Rooij, Brouwer, Bruinsma, Jansen, Donche, & Noyens, 2018). For the most part, empirical

research in the field had verified and further differentiated these conceptual assumptions. In

particular, relevant meta-analyses unanimously demonstrated the crucial role of students’

cognitive abilities, prior knowledge, and latest school grades to predict academic outcomes at

university level. Furthermore, they evidenced the impact of students’ motivational orientations

on their academic attainment (Richardson, Abraham, & Bond, 2012; Robbins, Lauver, Le,

Davis, Langley, & Carlstrom, 2004; Schneider & Preckel, 2017).

Especially, the motivational orientations cover various types and levels of academic self-

beliefs which essentially may regulate the students’ learning approach and, thus, affect their

academic outcomes (Pintrich, 2004). The students’ competence and control beliefs must be

recognized as cognitve-motivational key constructs (Krampen, 1988; Schunk & Zimmerman,

2006). Competence beliefs refer to an individual’s perceived capabilities to succeed in a given

academic activity or task (Eccles & Wigfield, 2002). Control beliefs refer to an individual’s

perceived likelihood of accomplishing desired academic outcomes or of avoiding undesired

academic outcomes by means of his or her own behavioral attempts (Perry, Hall, & Ruthig,

2005). Both types of beliefs result from an individual’s cumulative success or failure exper-

iences and must be seen as important personal resources to cope with academic requirements

in a certain educational setting. Over time, competence and control beliefs will operate in a

mutually reinforcing manner and contribute to implement the students’ more or less adaptive

learning approach (Drew & Watkins, 1998; Robbins, Lauver, De, Davis, Langley, & Carl-

strom, 2004; van Overvalle, 1989). Accordingly, students with high competence and control

beliefs will develop a strong sense of self-efficacy and evolve learning strategies to persistently

endeavor successful outcomes – whereas students with low competence and control beliefs

will develop strong concerns not to master the academic tasks at hand and possibly rely on

less adaptive learning strategies. In the latter case, students are seriously prone to increasingly

experience feelings of personal threat and, in the long term, to stabilize trait-like test anxieties

(Putwain, 2018; Respondek, Seufert, Stupnisky, & Nett, 2017). As empirical findings from

various university settings consistently substantiated, an individually heightened level of test

anxiety predicts less useful learning strategies (Spada, Nikcevic, Moneta, & Ireson, 2006; Vir-

tanen, Nevgi, & Niemi, 2013) and leads to significantly lowered learning outcomes (Credé &




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Kunzel, 2008; Feinberg & Halperin, 1978; Hancock, 2001; Kassim, Hanafi, & Hancock, 2007;

Schneider & Preckel, 2017). Hence, the emergence, maintenance, and consequences of sust-

ained test anxieties indicate a potential risk factor of the students’ learning – which foreseeably

threatens to impede their academic perspectives in a certain study domain or programme. Con-

sequently, higher education settings should carefully pay attention to this phenomenon and

strive for the implementation of appropriate instructional or guidance strategies.

With all that, the learning of research methods, most notably the acquisition of statistical

knowledge and competencies, appears to represent a stress or anxiety provoking domain in

higher education contexts. Quite a number of undergraduate and graduate students of social

sciences, education, psychology and business programmes struggles with statistics (Mji & On-

wuegbuzie, 2004; Onwuegbuzie & Wilson, 2003). Moreover, in comparison with other acad-

emic courses their individually reported level of anxiety appears to be highest in the statistics

domain (Dykeman, 2011). When dealing with the requirements of quantitative method courses

which commonly are compulsory for earning their degree, these students mostly suffer from

strong failure expectations and frequently experience feelings of apprehension and personal

threat. As well, they perceive methodological competencies difficult to acquire and less useful

for current studies and later professional development (Murtonen & Lehtinen, 2003; Murto-

nen, Olkinuora, Tynjälä, & Lehtinen, 2008; Zeidner, 1991). As a result, they are at risk for

developing and maintaining a heightened level of anxiety in the face of statistical analyses –

in particular, when being confronted with statistical tasks of data gathering, processing, and

interpreting (Cruise, Cash, & Bolton, 1985). Over the past decades, numerous empirical

analyses from most diverse conceptual, methodological, and institutional backgrounds had

yielded a vast amount of insights into the development, the structure, and the consequences of

higher education students’ statistics anxiety – and, thus, advancingly established a broad-based

research line to clarify and elaborate the construct.

2.1 Conceptual perspectives on statistics anxiety

Structurally, the students’ emerging statistics anxiety has to be considered a multidimen-

sional construct reflecting the complex interplay of several cognitive, motivational, and phy-

siological components (Rost & Schermer, 1989a). Against the background of relevant empiri-

cal findings from test anxiety research it can be defined as a domain-specific form of perfor-

mance or evaluation anxiety which manifests as repeatedly occuring worry cognitions, task-

irrelevant and interfering thoughts, marked states of emotional tension and physiological arou-

sal (Zeidner, 1991). The worry component of test anxiety refers to the students’ mental antici-

pation of failure and its negative consequences, whereas the emotionality component refers to

their feelings of tenseness, nervousness or distress, and the physiological component refers to

their perceptions of bodily symptoms. As in some conceptual approaches the emotionality

component includes physiological reactions, other conceptual approaches differentiate or ex-

tend these components (Cassady & Johnson, 2002; Schwarzer & Quast, 1985; Zeidner, 1998).

Over the past decades, across a wide range of student samples and measurements there has

been ample evidence for these components being distinguishable but mutually reinforcing

(Deffenbacher, 1980; Hodapp & Benson, 1997; Kieffer & Reese, 2009; Liebert & Morris,




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1967; Sarason, 1984). In most cases, they had been demonstrated to negatively affect the stu-

dents’ learning processes and achievement outcomes. However, the worry component ge-

nerally turned out to most strongly predict academic performance or test results (Cassady &

Johnson, 2002; Deffenbacher, 1980; McIlroy, Bunting, & Adamson, 2000; Rana & Mahmood,

2010; Schwarzer & Jerusalem, 1992; Seipp, 1991; Steinmayr, Crede, McElvany, & Wirth-

wein, 2016; von der Embse, Jester, Roy, & Post, 2018). The debilitating effect of worry cog-

nitions on students’ performance appears to be mainly caused by their strongly biased and

task-irrelevant mode of information processing. High-anxious students usually tend to per-

ceive threatening cues within a certain evaluation setting in an extremely attentive or even

sensitive manner (Wine, 1982; Fernández-Castillo & Caurcel, 2015; Putwain, Connors, & Sy-

mes, 2010). They produce more and stronger self-doubts which interfere with the process of

task completion – in particular, by thinking more frequently and intensely about the inevitable

failure they expect (Sarason, 1984; Schwarzer, 1996). Thus, high-anxious students’ attention

and cognitions operate more self-focused than task-focused. As a result, their cognitive re-

sources are to be seen heavily preoccupied and notedly impeded (Ashcraft & Moore, 2009;

Hopko, Ashcraft, Gute, Ruggiero, & Lewis, 1998; Richards, French, Keogh, & Carter, 2000).

In the long term, high-anxious students tend to use less adaptational coping strategies. They

prefer behavioral responses to immediately reduce their cognitive worries and emotional ap-

prehension – rather than basically enhancing their task-relevant knowledge and learning ap-

proach (Rost & Schermer, 1989b; Zeidner, 1998). However, these strategies neither will con-

tribute to handle their feelings of threat and distress, nor will they facilitate their mastery of

the academic task. Instead they will most likely lead to the failure outcome the students already

fear for. From a transactional perspective, the emergence and maintenance of test anxiety cru-

cially contributes to establishing a self-reinforcing circle of negative anxiety-outcome relations

(Spielberger & Vagg, 1995; Zeidner, 1998).

Based on this conclusive body of evidence a theoretically and methodologically sound fra-

mework for the statistics anxiety construct should implicitly take into account its cognitive,

emotional, and physiological components. In particular, it is essential that it addresses the issue

of relevant worry cognitions as it is assumed that they are closely linked to the debilitating

effects of statistics anxiety on statistical learning and performance.

To date, however, most empirical analyses in the field have emphasized the emotional and

physiological components of statistics anxiety (Cruise, Cash, & Bolton, 1985). They define

the construct as feelings of anxiety or as habitual anxiety in the face of statistically loaded

situations (Macher, Paechter, Papousek, & Ruggeri, 2012; Onwuegbuzie & Wilson, 2003).

Admittedly, the measurement items used in these empirical analyses cover a wide range of

statistical tasks that students typically encounter in everyday study or the context of their

course. These items can be empirically assigned to various situation- or task-specific dimen-

sions.

Thus, factor analyses of the task- and course-related items of Zeidner’s (1991) Statistics Anx-

iety Inventory led to the development of a content- and a test-specific subscale. Likewise,

factor analyses of the widely used Statistics Anxiety Rating Scale (Cruise, Cash, & Bolton,

1985) and the conceptually related Statistical Anxiety Scale (Vigil-Colet, Lorenzo-Seva, &

Condon, 2008) provided separate subcomponents concerning the students’ interpretation and




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test anxiety, their fear of asking for help and fear of statistics teachers (Baloğlu, 2002; Chew

& Dillon, 2014a; Chiesi & Primi, 2010; Chiesi, Primi, & Carmona, 2011; DeVaney, 2016;

Hanna, Shevin, & Dempster, 2008; Liu, Onwuegbuzie, & Meng, 2011; Oliver, Sancho, Ga-

liana, & Cebrià i Iranzo, 2014; Macher, Paechter, Papousek, & Ruggeri, 2012; Papousek, Rug-

geri, Macher, Paechter, Heene, Weiss, Schulter, & Freudenthaler, 2012; Sesé, Jiménez, Mon-

tano, & Palmer, 2015).

Similarly, the Statistics Anxiety Measure (Earp, 2007; Vahedi, Farrokhi, & Bevrani, 2011)

and the Statistics Comprehensive Anxiety Response Evaluation (Griffith, Mathna, Sapping-

ton, Turner, Evans, Gu, Adams, & Morin, 2014) revealed some distinct task- or situation-

specific subcomponents referring to statistically relevant course requirements and situations.

In summary, these approaches to measuring the construct of statistics anxiety undoubtedly

represent typically anxiety-evoking task features and test situations in a most elaborate way.

However, with the exception of the Statistics Anxiety Measure (Earp, 2007) and the short

research scale Hong and Karstensson (2002) used – both of which include some worry items

– it is notable that all the other instruments fail to integrate students’ cognitive, emotional, and

physiological anxiety reactions, in particular with regard to the critical worry component.

Williams’s (2013, 2015) findings provide support to this conceptual shortcoming, as they de-

monstrated that scores on the interpretation and test/class anxiety subscales of the Statistics

Anxiety Rating Scale (Cruise, Cash, & Bolton, 1985) were only moderately correlated with

students’ tendency to worry.

In contrast, a concurrently operating research line in the test anxiety field had already decom-

posed the statistics anxiety construct and assessed the students’ worry and emotionality res-

ponses separately. However, in most cases a composite score including both components was

used because of both components’ high interrelation (Benson, 1989; Benson, Bandalos, &

Hutchinson, 1994; Finney & Schraw, 2003; González, Rodrígez, Faílde, & Carrera, 2016;

Hong & Carstensson, 2002). That way, albeit merely having total anxiety scores available, the

interpretation of students’ responses explicitly allowed for a traceable cognitive perspective.

Furthermore, one relevant study had analyzed the relations of both the worry and emotionality

component with several cognitive-motivational and achievement variables. According to the

findings of test anxiety research, its results demonstrated the worry component to better ex-

plain the students’ performance in a statistics exam (Bandalos, Yates, & Thorndike-Christ,

1995).

As this research line essentially contributes to refine the statistics anxiety construct with re-

spect to its motivationally operating components, its task- or situation-specific references ap-

pear less differentiated. That is, in all studies the items for assessing statistics anxiety referred

exclusively to the taking of a statistical test or exam. This contextual limitation, hence, should

challenge the representativity or content validity of the worry and emotionality measures, be-

cause their scores account only for a particular part of the relevant learning setting (Cohen,

Manion, & Morrison, 2011; Haynes, Richard, & Kubany, 1995).

A most appropriate framework of the statistics anxiety construct should merge the concep-

tual strengths of both research lines and, therefore, consider the relevant worry, emotionality,

and bodily reactions students will experience when dealing with the typically occurring task




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features and examination procedures of their statistics course or of any other course – if ne-

cessarily requiring statistical knowledge and skills. Refining the construct that way, research

in the field should advance in developing measurement tools which will help to determine the

students’ statistics anxiety in a psychologically as well as contextually more differentiated and,

thus, in a more representative manner. Consequently, their construction should thoroughly

specify the construct’s key facets (Guttman & Greenbaum, 1998) and transform its a priori

assumptions into most concrete operationalizations mapping out both relevant anxiety reac-

tions and typically threatening situations (Zeidner, 1998).

Moreover, another issue crucial to the conceptualization of the statistics anxiety construct

refers to the role of the students’ avoidance tendencies. Already in the very first beginning of

empirical test anxiety research, Mandler and Sarason (1952) posited anxiety responses to ma-

nifest as “implicit attempts at leaving the test situation” (166). Subsequently, empirical find-

ings provided support for this assumption and yielded sound evidence for students’ avoidance

cognitions being substantially related to their anxiety responses (Blankenstein, Flett, & Wat-

son, 1992; Galassi, Frierson, & Sharer, 1981; Genc, 2017; Hagtvet & Benson, 1997; Middleton

& Midgley, 1997; Skaalvik, 1997; Zeidner, 1998). In particular, the analyses of Elliot and

McGregor (1999), Pekrun, Elliot and Maier (2009), and Putwain and Symes (2012) demon-

strated clearly that students with heightened avoidance orientations reported a higher extent of

worry cognitions and lower scores on subsequent exam performance. Conceptually, these em-

pirical findings primarily originate from achievement motivation research, in most cases from

goal orientation theories which had developed several instruments to assess the students’ striv-

ing no to perform worse than others in a certain academic setting (Elliot & Murayama, 2008).

Though not unfolding the avoidance issue in an exhaustive manner, this motivation approach

should unarguably contribute to broadening and refining the test anxiety construct – and, thus,

offer promising perspectives to integrate the role of students’ avoidance tendencies (Putwain,

2008).

Heretofore, only few conceptualizations of the test anxiety construct had addressed this

issue and claimed the students’ escape or avoidance cognitions to constitute an essential part

of their worries and to represent an important factor to elicit interfering, task-irrelevant

thoughts (Pekrun, Goetz, Kramer, Hochstadt, & Molfenter, 2004; Schwarzer & Quast, 1985).

Future research efforts are required to further determine the relevance of avoidance thoughts

within the worry component. Accordingly, in order to strive for a most differentiated analysis

of the construct, research in the field should benefit from an enhanced emphasis on students’

avoidance cognitions. Hence, it should provide appropriate measurements being designed not

only to assess the students’ worries about threatening failure outcomes, but also to inquire their

thoughts to preferably avoid getting involved with threatening tasks or situations. Currently

available questionnaires either do not consider the students’ avoidance cognitions at all (Grif-

fith, Mathna, Sappington, Turner, Evans, Gu, Adams, & Morin, 2014; Onwuegbuzie & Wil-

son, 2003; Vigil-Colet, Lorenzo-Seva, & Condon, 2008) or include just a single item assessing

avoidance behavior (Earp, 2007). They do not allow for a proper clarification of their role

within the students’ worry responses. The same applies to one single study which had exam-

ined the students’ avoidance goals as predictors of statistics anxiety and, thus, demonstrated a

moderate association (Zare, Rastegar, & Hosseini, 2011).




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Research in the field should refine its conceptualization of students’ worry responses and

develop instruments that explicitly capture avoidance cognitions with respect to statistically

loaded tasks and situations. That way, an important step to refine the substantive and structural

stage of construct validation would be done (Benson, 1998).

2.2 Methodological perspectives on statistics anxiety measures

Students’ statistics anxiety is commonly assessed using questionnaires consisting of items

in Likert-scale format. With respect to statistically relevant task features or situations, they

usually offer response categories which ask the students for each task- or situation-related item

to rate the subjectively experienced intensity of being anxious. The response alternatives range

from “no anxiety” to “high anxiety” in the Statistics Anxiety Rating Scale (Cruise, Cash, &

Bolton, 1985), likewise from “not at all anxiety evoking” to “extremely anxiety evoking” in

the Statistics Anxiety Inventory (Zeidner, 1991), from “not anxious” to “very anxious” in the

Statistics Anxiety Measure (Earp, 2007), from “no anxiety” to “considerable anxiety” in the

Statistical Anxiety Scale (Vigil-Colet, Lorenzo-Seva, & Condon, 2008), and from “no anx-

iety” to “severe anxiety” in the Statistics Comprehensive Anxiety Response Evaluation (Grif-

fith, Mathna, Sappington, Turner, Evans, Gu, Adams, & Morin, 2014).

Thereby, it is left up to the student to interpret the meaning of these categories and to decide

implicitly, to what extent the answer would reflect her or his cognitive worries, negative emo-

tions, or bodily reactions. Although these anxiety components have been demonstrated to be

substantially associated, the ambiguity of anchor labels (Podsakoff, MacKenzie, Lee, & Pod-

sakoff, 2003) should hinder a most differentiated and valid clarification of the students’ anx-

ious reactions and, hence, should not sufficiently comply with the conceptual perspectives on,

and the empirical knowledge about, the test anxiety construct (Rost & Schermer, 1989a).

Rather, these response categories appear to be principally at risk for compressing or even

covering the students’ actual understanding of the response she or he has individually decided

for (Krosnick & Presser, 2010). As a consequence, this response format potentially might con-

tribute to establish a method-driven restriction in the interpretation of research data. Therefore,

from both a conceptual and methodological perspective for future scale development in the

field, it is recommended to apply response labels asking for the students’ agreement with clear-

ly and distinguishably worded items to assess their cognitive, emotional, and physiological

reactions (Cohen, Manion, & Morrison, 2011; Rost & Schermer, 1989a).

Furthermore, the anchors currently in use might be considered emotionally loaded and hence

to have the potential to trigger biased responses (Lee, 2006; Podsakoff, MacKenzie, Lee, &

Podsakoff, 2003). Principally, this biased responses will operate in different ways and produce

contradictory effects: on the one hand, those students experiencing a heightened level of sta-

tistics anxiety should be prone to avoid extreme statements such as “high anxiety”, “extremely

anxiety evoking”, or “considerable anxiety” and, thus, tend to report a socially and emotionally

more acceptable extent of statistics anxiety (Lunneborg, 1964; Zeidner, 1998) – inasmuch as

they would judge their anxious feelings as manifestation of personal weakness. Therefore, they

should be motivated to report a somewhat lowered or trivialized level of anxiety and, thus, to

protect their sense of self-worth (Harter, 1990). They might also feel embarrassed by the

response wording and try to repress their anxiety symptoms. Hence, the response wording




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would provoke a certain kind of coping strategy (Rost & Schermer, 1989b). On the other hand,

students with a heightened level of statistics anxiety should process these anchor labels in a

most sensitive way as threatening stimuli (Bar-Haim, Lamy, Pergamin, Bakermans-Kranen-

burg, & Ijzendorn, 2007; Fernández-Castillo & Caurcel, 2015; Lawson, 2006) and, accord-

ingly, report an inflated level of statistics anxiety (Mathews & MacLeod, 2002).

Although there is only scarce empirical evidence to reasonably clarify the prevalence and di-

rection of that emotional response bias, no matter what, its potentially confounding effect on

research data must be seen as most plausible (Gaye-Valentine & Credé, 2013). In particular,

possible response bias should affect the students’ responses in an uncontrollable way and se-

riously diminish their validity, eventually. Work on developing new measurement instruments

in the field should take this methodological flaw into account and use unloaded response cate-

gories as a precaution.

2.3 Approaching refined measurement

To overcome the conceptual limitations and methodological shortcomings of current

instruments as a very first attempt a new scale to assess university students’ statistics anxiety

was developed. Nevertheless, it should adopt the particular strengths of existing instruments.

Thus, it was assigned to approach a refined measure of the construct by meeting the following

criteria: Its items should (1) specifically take into account the students’ anxiety responses in a

most differentiable way and, hence, consider their worry and avoidance cognitions as well as

their emotional reactions. Thereby, its items should embed the various anxiety reactions (2)

into a representative range of statistically loaded task features and course situations the stu-

dents would typically encounter. In all this, its items should use (3) statements and response

labels which do not offer emotionally or motivationally biasing wording.

The construction of this scale for measuring university students’ “Worry, Avoidance, and

Emotionality Cognitions Encountering Statistical Demands” (WAESTA) largely followed the

procedure of facet theory using a mapping sentence (Guttman & Greenbaum, 1998). This map-

ping sentence served as a heuristic device to cover all major facets of the construct and, thus,

to achieve sufficient content validity (Edmundson, Koch, & Silverman, 1993). A pool of eli-

gible items was drawn up using this constitutive mapping sentence which included con-

ceptually relevant anxiety components, situational references, and intended response catego-

ries (Zeidner, 1998).

In particular, each item to represent the statistics anxiety domain was specified with respect to

four key facets: a relevant reaction facet referring to the worry, avoidance, and emotionality

component, and three contextual facets referring to the (1) outcome in a statistics exam, the

(2) individual learning of statistical procedures and handling of statistical demands, and the

(3) public mastering of statistical content. Furthermore, an additional range facet defined the

response categories to assess the students’ perceived magnitude of individual anxiety re-

actions. As seemingly appropriate response range a four-point format was decided – in order

to avoid artificial complexities in the respondents’ decision making (Lee & Paek, 2014; Lo-

zano, Garcia-Cueto, & Muñiz, 2008) but instead to ensure a cognitive-motivationally realistic

as well as just manageable number of rating references.

For instance, statistics anxiety should be more or less manifest as a student’s experienced or




10

anticipated worries about the anticipated exam outcome, the understanding of a certain statis-

tical formula and the presentation of research findings.

This four-facet mapping sentence was used as a cross-classification template to systemati-

cally operationalize the statistics anxiety construct as it allowed to combine the various ele-

ments of facets in a most differentiated manner (Hox, 1997). That way, a final scale version

with 17 four-point Likert-type rating items was built (Table 1).

All items concerned a mentally imaginable situation the students should easily manage to

anticipate. Eight items referred to the students’ worries about their potentially expected failure

to master the course exam and to cope with several statistical requirements. Four items con-

cerned their cognitions to preferably avoid the statistics course and particular statistical de-

mands. Five items are related to their emotional tension when being confronted with a certain

statistical task (Appendix).

Table 1. WAESTA items assessing relevant anxiety reactions to statistically loaded task

features and course situations

Test Anxiety

Component

Course

Exam

Outcome

Understanding

Explanation

Application

Oral Task

Presentation

Explanation

Worry 01, 14, 16 05, 08 10, 11, 12

Avoidance 03 06, 17 04

Emotionality 02, 07, 09, 13 15

Example (Item 07):

quite nervous explain a chart

“I would be quite nervous if I were asked to explain a chart from a research

report.”

Response range Does not apply (1) … … Applies in full (4)

As statistically indicated task requirements for the understanding of course contents, the

interpretation of quantitative research results as well as the application of statistical formulas

and procedures were considered. Likewise, the oral presentation and explanation of statistical

content in the public course situation was included. To warrant conceptual clarity, the avoid-

ance items should neither tap the students’ avoidance reactions by suppressing or substituting

individually occurring threat cognitions (Williams, 2015), nor should they refer to the stu-

dents’ actual avoiding strategies to cope with disliked or threatening academic events (On-

wuegbuzie, 2004; Rost & Schermer, 1989b). Rather they should operationalize the students’

mentally processed avoidance thoughts or even escape illusions before or during statistical

task completion – and, thus, might indicate a specific subcomponent of worry cognitions.

Moreover, the component of physiological symptoms or bodily tensions was not explicitly

addressed. Instead it was thought to be indirectly inferred from the emotionality items. Con-

ceptually, this restriction seemed to be justifiable, since the students’ perceived affective state

should always reflect their actual physiological arousal (Zeidner, 1998).




11

3 Validation framework and objectives

As the WAESTA scale should be examined for the first time, the present study was in-

tended as an exploratory investigation of its structural and criterion validity (John & Benet-

Martinez, 2000). A further aim was to describe its psychometric properties.

As test anxiety is assumed to be a multifaceted construct (Zeidner, 1998), the first step was to

analyze the factor structure of the WAESTA scale. As the WAESTA items were theoretically

designed to tap either the worry, avoidance or emotionality component of the statistics anxiety

construct. As the WAESTA items were theoretically designated to represent each the worry,

avoidance, and emotionality component of the statistics anxiety construct, a clear three factor

solution appeared to be expectable, at best. However, relevant research findings in the test

anxiety field had demonstrated these components being substantially correlated (Deffen-

bacher, 1980; Cassady & Johnson, 2002; Chin, Williams, Taylor, & Harvey, 2017; Gaye-

Valentine & Credé, 2013; Hodapp & Benson, 1997; Hong & Karstensson, 2002; Sarason,

1984; Sparfeldt, Schilling, Rost, Stelzl, & Peipert, 2005; von der Embse, Jester, Roy, & Post,

2018). Furthermore, in certain research contexts dealing with school students’ domain- or sub-

ject-specific test anxieties, all worry, avoidance, and emotionally items repeatedly loaded on

one common anxiety factor (Faber, 1993, 1995a, 2012b, 2015). Therefore, an accurate pre-

diction of the scale’s ultimate factor structure seemed difficult. Rather the present study should

explore the scale’s underlying structure in a most tentative way – and should, thus, take into

account three alternatives: a three factor solution separating the worry, avoidance, and emo-

tionality components, a two factor solution with the worry and avoidance items loading on a

first factor and the emotionality items loading on a second factor, and a one factor solution

subsuming all items. Presuming the avoidance component to represent a specific worry ele-

ment, the two factor solution definitely revealed a reasonable perspective, in particular. With

the reservation of this initially performed analysis, the final version of the WAESTA scale

should be determined and its psychometric properties examined.

The second step was to test the scale’s external validity, in particular its relationships with

selected convergent and discriminant criterion variables. For this purpose, the validation

framework included variables representing the students’ cognitive-motivational orientations

and the statistically relevant background.

As relevant cognitive-motivational variables the students’ competence and control beliefs

were considered. Both types of beliefs are well proven to regulate the students’ engagement

and learning approach in the long term. In particular, they essentially affect the students’ anx-

iety experience. As unfavorable competence and control beliefs usually come along with in-

creased expectancies of failure, they will provoke a strong sense of personal threat and, thus,

lead to an individually heightened level of anxiety. For the purpose of scale validation, as

relevant competence beliefs their domain-specific self-concepts, as relevant control beliefs

their implicit competence theories were assessed.

There is sound evidence that domain-specific academic competence beliefs and self-con-

cepts substantially predict the individually existing magnitude of test anxiety (Ahmed, Min-

naert, Kuyper, & van der Werf, 2012; Faber, 2012a; Goetz, Pekrun, Hall, & Haag, 2006).




12

Correspondingly, in the statistics domain the crucial role of self-concepts had been well esta-

blished. In most cases, high-anxious students reported a lowered self-concept of own ma-

thematics or statistical competencies (Bandalos, Yates, & Thorndike-Christ, 1995; Benson,

1989; González, Rodrígez, Faílde, & Carrera, 2016; Macher, Paechter, Papousek, & Ruggeri,

2012; Onwuegbuzie & Wilson, 2003; Williams, 2014, Zeidner, 1991). Therefore, it should be

assumed the WAESTA scale scores to correlate negatively and substantially with the students’

mathematics self-concept. As well, to sufficiently clarify the domain-specificity of the

WAESTA scale, its relation to the students’ verbal self-concept should be concurrently anal-

yzed. According to the multidimensional feature of academic self-beliefs (Green, Martin, &

Marsh, 2007; Marsh & O’Mara, 2008), research in the field had consistently demonstrated the

students’ mathematics anxiety being substantially related to their performance and motivation

in the mathematics but not in the verbal domain (Arens, Becker, & Möller, 2017; Faber, 1995b,

2015; Goetz, Frenzel, Pekrun, Hall, & Lüdtke, 2007; Gogol, Brunner, Preckel, Goetz, &

Martin, 2016; Hembree, 1990; Hill, Mammarella, Devine, Caviola, Passolunghi, & Szücs,

2016; Marsh, 1988; Marsh & Yeung, 1996; Sparfeldt, Schilling, Rost, Stelzl, & Peipert, 2005;

Streblow, 2004). Across most diverse educational settings a clear subject-specific pattern of

relations between mathematics anxiety and performance or motivation variables had been sub-

stantiated – thus evidently indicating the convergent and discriminant validity of mathematics

anxiety measures. From this validation perspective, the WAESTA scale should claim prelimi-

nary subject-specificity if its correlation with the verbal self-concept variable would turn out

to be distinctly weaker than with the mathematics self-concept variable.

Besides, the students’ control beliefs largely manifest as causal attributions to explain indi-

vidually experienced outcomes (Skinner, 1996) which, in turn, affect their expectancies of

future attainment. Students who attribute their failure to stable, internal factors are less likely

to strive to improve their competence – for instance, by increasing their learning effort or

altering their learning strategies (Weiner, 1985). In a narrow sense, students’ control beliefs

may essentially refer to their perceived malleability of own abilities or competencies. Accord-

ingly, the students develop implicit theories or mindsets which may stress an entity view of

more or less fixed and unchangeable abilities – or an incremental view of more or less modi-

fiable and changeable abilities (Dweck & Leggett, 1988; Yeager & Dweck, 2012). Though

these implicit theories have been demonstrated to correlate with the student’s actual ability

level only marginally (Spinath, Spinath, Riemann, & Angleitner, 2003), they significantly

affect their motivationally relevant goal orientations, effort beliefs, learning strategies and,

eventually, their task performance (Blackwell, Trzesniewski, & Dweck, 2007; Burnette,

O’Boyle, VanEpps, Pollack, & Finkel, 2013; Cury, DaFonseca, Zahn, & Elliot, 2008; Jones,

Wilkins, Long, & Wang, 2012). These implicit theories principally might not only concern an

individual’s cognitive ability but also might emerge in a domain-specific manner and refer to

the perceived malleability of certain skills or competencies (Dweck & Molden, 2005) – e.g.,

in the areas of mathematics and language (Davis, Burnette, Allison, & Stone, 2011; Räty, Ka-

sanen, Kliskinen, Nykky, & Atjonen, 2004; Vogler & Bakken, 2007), foreign language learn-

ing (Lou & Noels, 2017), academic writing (Karlen & Compagnoni, 2017), music (Smith,

2005), physical activities (Ommundsen, 2003), biology and science (Chen & Pajares, 2010;

Dai & Cromley, 2014). Consequently, they should also play a motivationally crucial role in

the students’ learning of statistics. With respect to the statistics domain, an entity view of own




13

competencies would diminish or even suspend any control perspective. Following the findings

of attribution analyses, this loss of control should increase the students’ expectancies of in-

evitable failure and, thus, should heighten their statistics anxiety (Bandalos, Yates, & Thorn-

dike-Christ, 1995; Carden, Bryant, & Moss, 2004; Covington, 1986; Faber, 2012a; Leppin,

Schwarzer, Belz, Jerusalem, & Quast, 1987).

Unfortunately, previous studies in the field had seldom analyzed the role of implicit theories.

If at all, they had referred to the students’ general ability beliefs, but not to specific beliefs

about statistical competencies (Zonnefeld, 2015) or had only considered the students’ beliefs

to master statistical demands through strategy use and effortful behavior (Schutz, Drogosz,

White, & Distefano, 1998) – thus, reflecting an incremental view of learning approach. How-

ever, these learning control beliefs had been demonstrated to significantly predict course

grades. Moreover, in another study the students’ implicit beliefs concerning the malleability

of their methodological competencies had been analyzed. Though not directly tapping the

issue of statistics, the findings demonstrated a certain motivational type of students showing

stable negative perceptions of method learning and, in particular, reporting lowered incre-

mental scores (Lapka, Wagner, Schober, Gradinger, Reimann, & Spiel, 2010).

Accordingly, against the background of overall research findings the WAESTA scale scores

should be reasonably assumed to correlate positively and substantially with the students’ entity

view of less or not malleable statistical competence.

Furthermore, as another motivational criterion variable, the students’ task values were consid-

ered. Conceptually, from an expectancy-value perspective on achievement motivation task

values concern the students’ perceived importance or adequacy of a certain activity to fulfill

their personal needs and to attain their personal goals (Eccles & Wigfield, 2002). In particular,

these task values may manifest as attainment, intrinsic, or utility components and have been

demonstrated to regulate the students’ motivational orientations, learning strategies, and aca-

demic choices (Wigfield, Hoa, & Klauda, 2009). Task values evidently emerge in a task- or at

least domain-specific manner (Gaspard, Häfner, Parrisius, Trautwein, & Nagengast, 2017; Ko-

sovich, Hulleman, Barron, & Getty, 2015; Selkirk, Bouchey, & Eccles, 2011). Thus, they

should characteristically affect the students’ learning and performance in the statistics domain

as well. Previous research in the field had primarily analyzed the students’ perceived utility or

worth of statistical knowledge and competencies as an attitudinal construct (Nolan, Beran, &

Hecker, 2012) – focusing on the usefulness of statistics in personal and professional contexts

(Cruise, Cash, & Bolton, 1985; Dauphinee, Schau, & Stevens, 1997; Ramirez, Emmioğlu, &

Schau, 2010; Schau, Stevens, Dauphinee, & Del Vecchio, 1995). As relevant empirical find-

ings consistently showed, the students’ ratings of the worth of statistics appeared to positively

correlate with their statistical achievement as well as with their self-reported learning strategies

to a slight extent only (Arumugam, 2014; Emmioǧlu & Capa-Aydin, 2012; Hood, Creed, &

Neumann, 2012; Kesici, Baloğlu, & Deniz, 2011; Nasser, 2004; Slootmaeckers, 2012). In

comparison, the relations of utility perceptions with domain-specific measures of academic

self-concept were stronger. Students with low competence beliefs valued statistics as less im-

portant (Baloğlu, 2002; Chiesi & Primi, 2009; Dauphinee, Schau, & Stevens, 1997; Dempster

& McCorry, 2009; Stanisavljevic, Trajkovic, Marinkovic, Bukumiric, Cirkovic, & Milic,

2014; Vanhoof, Kuppens, Sotos, Verschaffel, & Onghena, 2011). Similarly, students’ statistics

anxiety was also moderately correlated with their utility ratings – indicating those students




14

suffering from a heightened level of statistics anxiety tendentially perceived statistics to a les-

ser extent as useful (Baloğlu, 2002; Chew & Dillon, 2014c; Nasser, 2004; Papanastasiou,

2005; Papanastasiou & Zembylas, 2008; Papousek, Ruggeri, Macher, Paechter, Heene, Weiss,

Schulter, & Freudenthaler, 2012; Tremblay, Gardner, & Heipel, 2000).

In summary, these correlational findings draw a pattern which is completely in line with the

social-cognitive processing of task values (Bornholt & Wilson, 2007; Guo, Parker, Marsh, &

Morin, 2015). They will operate both as mediating and mediated variables among the students’

actual competencies and self-beliefs (Chiesi & Primi, 2010; Lalonde & Gardner, 1993; Nasser,

2004; Ratanaolarn, 2016; Sesé, Jiménez, Montano, & Palmer, 2015).

Accordingly, the WAESTA scale scores should be assumed to correlate inversely and sub-

stantially with the students’ perceived value of statistical competence.

As a relevant background variable to explain the students’ statistical self-beliefs and compe-

tencies their prior mathematical learning, in particular their latest school grade had been well

proven. From the perspective of self-concept development (Marsh & O’Mara, 2008), previous

failure experience in mathematics will evidently lead to form low competence beliefs in the

statistics domain and, eventually, contribute to strengthening the emergence of domain-speci-

fic anxiety responses. In various studies students with poor school grades in mathematics re-

ported a heightened level of statistics anxiety (Beurze, Donders, Zielhuis, de Vegt, & Verbeek,

2013; Birenbaum & Eylath, 1994; Chiesi & Primi, 2010; Galli, Ciancaleoni, Chiesi, & Primi,

2008; Lalonde & Gardner, 1993).

Accordingly, the WAESTA scale scores should be assumed to correlate inversely and sub-

stantially, but low in magnitude with the students’ mathematics grade they had last earned at

school.

Students’ prior experience of statistics should also be considered as a relevant background

variable. Following the analysis of Sutarso (1992) who demonstrated significantly lower anx-

iety scores in the subgroup of students with more statistics courses taken before the exam,

Onwuegbuzie (2003) also substantiated a small but significant relation between prior statistics

experience and self-concept. Unfortunately, he did not explicitly assess the statistics anxiety

variable. Instead he had used the computational self-concept subscale from the STARS instru-

ment (Cruise, Cash, & Bolton, 1985). Although there is theoretical and empirical overlap be-

tween the self-concept and anxiety variables they represent distinct constructs and should not

be treated as interchangeable. This is particularly important as the STARS subscale does not

measure self-concept in a particularly sophisticated way and includes several items that are

unrelated to competence beliefs. In another study the students’ previous experiences did not

significantly predict their grades in a statistics exam (Slootmaeckers, 2012). These findings

seemingly suggest the potential role of prior statistics experiences to explain rather the stu-

dents’ self-beliefs than their actual attainment. The study of Dempster and McCorry (2009)

clearly lent support to this perspective. Being more frequently and persistently involved with

learning statistics might increase the students’ confidence with typical requirements and meth-

ods (Waples, 2016). Thereby, they might reduce their feelings of apprehension and fear of

failure. However, other relevant studies did not substantiate any significant impact of prior

statistics experiencies on the students’ statistics anxiety (Birenbaum & Eylath, 1994; Chew &

Dillon, 2012; 2014b; Schutz, Drogosz, White, & DiStefano, 1998; Townsend, Moore, Tuck,




15

& Wilton, 1998). Most noteworthy, in some cases advanced students’ anxiety level did not

decrease after completion of a statistics course or program (Chau, 2018; van der Westhuizen,

2014). In order to further clarify their role to predict the individually existing level of statistics

anxiety, the scale validation of the WAESTA scale included the students’ prior statistics ex-

periences.

According to the exposure or contact hypothesis, the WAESTA scale scores should be as-

sumed to correlate inversely and substantially, but low in magnitude with the students’ prior

statistics experience.

4 Method

4.1 Participants and procedure

In order to conceptually and methodologically extend the scope of preliminary analyses

(Faber, Drexler, Stappert, & Eichhorn, 2018), in the present study the data of both a construc-

tion sample and a validation sample were further analyzed.

The construction sample consisted of 113 graduate students (n = 94 females, n = 19 males)

from a German university Master’s course in educational sciences (n = 80) and special edu-

cation (n = 33). They all were enrolled in a compulsory course on empirical research methods

and theory of science. Therefore, the participation rate was sufficiently high at 82 per cent.

Seventy-four of the students had already acquired elementary statistical knowledge during

their first degree, whereas 39 were required to attend a course in basic descriptive and

inferential statistics. Both the subgroup with and without statistical knowledge did not signi-

ficantly differ with respect to gender (chi-square test, p > .05) and age (Mann-Whitney U-test,

p > .05). Also, there was no significant difference of gender ratio within each subgroup

(binomial test, p > .05).

The validation sample was thought to scrutinize the findings from the construction sample

one year later. It consisted of 87 graduate students from the same Master’s courses: educational

sciences (n = 59) and special education (n = 28). The sample was predominantly female (n =

74). As with the construction sample all the students were enrolled on a compulsory course on

empirical research methods and theory of science. The participation rate was rather high at 89

per cent. Fifty of the students had acquired statistical knowledge during their first degree

whereas 37 had to attend an introductory statistics course. Once again there were no subgroup

differences in gender, gender ratio, or age (Stappert, 2017).

In both samples all relevant data concerning the self-belief and background variables under

consideration were gathered on the course’s first term. For that purpose, a questionnaire in-

cluding all items to measure the students’ self-concept, statistics anxiety, implicit theories, task

values, and relevant background information was administered.

Whereas the background items as well as the self-concept items were presented separately and

blockwise, the other self-belief items were all presented in a mixed order (Schriesheim, Ko-

pelman, & Solomon, 1989). Furthermore, to prevent a priming effect of the self-concept items,

they were presented at the end of the questionnaire (Podsakoff, MacKenzie, Lee, & Podsakoff,

2003).




16

4.2 Measures

The students’ academic self-concepts in mathematics and language (German) were as-

sessed using nine six-point rating items for each subject. These items referred to the students’

most recent learning experiences at school and addressed their competence beliefs with regard

to meeting subject-specific demands – also in comparison with former classmates. The

wording of the items was strictly parallel. In the majority, the items originate from well proven

instruments (Faber, 2012a; Möller, Streblow, Pohlmann, & Köller, 2006; Rost, Sparfeldt, &

Schilling, 2007). For the purpose of this study they were adapted, phrased retrospectively, and

presented in an economical grid style format. Sample item: “I tried hard in mathematics/

German, but I did not perform very well.” Exploratory factor analysis (with varimax rotation)

revealed a two-factor solution allowing for a clear distinction between the subject-specific

self-concept facets. Hence, it was possible to build two scales for measuring the subject-

specific academic self-concepts. In both samples, their reliability was most appropriate for

both the mathematics and the language self-concept scale (Table 2). According to the

multifaceted feature of the construct, the self-concept variables appeared to lowly correlate in

the construction sample (r = .14, p > .05) and in the validation sample (r = -.05, p > .05). High

scale scores indicated the students’ competence beliefs being positive. For the construction

sample, an additionally conducted confirmatory factor analysis using three item parcels for

each subject revealed an appropriate fit of the measurement model (χ2/df = 1.143, TLI = 0.989,

CFI = 0.997, RMSEA = 0.036). Here again, the latent mathematics and language variable

correlated to a low extent (r = -.25, p < .01). Remarkably, the relation between both self-

concept measures turned out to be negatively signed. However, from the perspective of self-

concept development, this particular finding might be explainable as it indicates a dimensional

comparison effect in the students’ academic self-perceptions across non-matching domains or

subjects (Arens, Becker, & Möller, 2017; Marsh, Kuyper, Seaton, Parker, Morin, Möller, &

Abduljabbar, 2014).

To assess students’ implicit theory of statistical competencies, a short scale with five four-

point rating items was administered in the construction sample. As current instruments in the

field only allowed for measuring the students’ implicit intelligence theory (İlhan & Cetin,

2013; Kooken, Welsh, McCoach, Johnston-Wilder, & Lee, 2016), a new scale was created.

Following the recommendations of Hong, Chin, Dweck, Lin and Wan (1999), all items tapped

an entity view of personal statistical competence. Unfortunately, due to their insufficient item-

test correlation (rit < .22) two items had been deleted. With an average item intercorrelation of

Fisher’s z’ = .44 and an average item-test correlation of Fisher’s z’ = .52 the final scale’s

reliability appeared to be just acceptable (John & Benet-Martinez, 2000). Sample item: “To

work with statistics, you need a talent that I simply do not have.” High scale scores indicated

the students to perceive their statistical ability being fixed, hence as less malleable in nature.

In the validation sample, a slightly revised scale with four four-point Likert items was used

(Stappert, 2017). In view of sample size and item number its reliability appeared to be

sufficient (Table 2).

The utility value students attributed to statistical competence was measured by means of a

short scale. In the case of the construction sample it consisted of five four-point rating items

dealing with the perceived utility of statistics for the students’ current studies and intended




17

career. To reduce acquiescence or social desirability bias in the students’ responses, scale

items were both positively and negatively worded. Sample item: “Statistics will not play an

important role in my future professional life”. With an average item intercorrelation of Fisher’s

z’ = .40 and an average item-test correlation of Fisher’s z’ = .49 the scale’s reliability was just

acceptable (Table 2). High scale scores indicated the students to consider statistics being less

important. In the validation sample, an extended version of the scale was used (Eichhorn,

2018). It consisted of eight four-point Likert items. Its reliability was once more just acceptable

(Table 2). Here again, high sum scores indicated the students to perceive statistics as being

less useful for their current studies and later professional development.

Table 2. Descriptive statistics and reliabilities of the scales for measuring self-belief and

background validation variables

Items AM SD zS zK α

Latest School Grade in Mathematics

Construction Sample 1 3.06 0.91 0.76 -0.15

Validation Sample 1 3.11 1.36 -0.50 -2.28*

Prior Statistics Experiences

Construction Sample 1 1.15 0.91 1.46 -1.62

Validation Sample1 1 2.0

Academic Self-Concept in Mathematics

Construction Sample 9 29.81 9.81 1.37 -2.04 .93

Validation Sample 9 31.01 11.43 -0.33 -1.84 .94

Academic Self-Concept in Language (German)

Construction Sample 9 45.52 7.32 -3.61*** -0.01 .92

Validation Sample 9 41.45 8.53 -2.12* -0.16 .90

Implicit Entity Beliefs

Construction Sample 3 5.43 2.02 3.59*** 0.13 .70

Validation Sample 4 7.87 2.61 2.15* -0.32 .81

Negative Utility Value of Statistics

Construction Sample 5 11.06 2.89 0.41 -1.18 .72

Validation Sample 8 16.18 3.95 0.55 -0.10 .75

1In the validation sample, a binary response format was used. Therefore, the item’s

mode is reported.

Significance: *p < .05, ***p < .001

Note. AM = arithmetic mean, SD = standard deviation, zS = z-standardized skewness,

zK = z-standardized kurtosis, α = internal consistency (Cronbach’s coefficient alpha)

Finally, as relevant background variable students’ most recent school grade in mathematics

was inquired in both samples. Students were also asked to report the experience of statistics in

the course of their first degree. The construction sample used a four-point Likert scale ranging

from “no experience” to “a lot of experience”. As this response format turned out to be too

ambiguous in the students’ understanding, in the validation sample their previous experience




18

with statistics was assessed with a dichotomous format – which referred to the successful pas-

sing of a statistics exam (response categories “yes” = 2 and “no” = 1).

4.3 Data analyses

According to the conceptual difficulty to unequivocally predict the WAESTA scale’s ulti-

mate factorial feature, a series of principal component analyses (PCA) was conducted in order

to explore and clarify the latent structure underlying the relations among all worry, avoidance,

and emotionality items (Kline, 2013). Following the methodological recommendations of Pi-

tuch and Stevens (2016), only factor loadings equaling or exceeding an absolute value of |0.4|

and, thus, explaining around 16% of the item variance, should be accepted and interpreted –

and consequently used for the purpose of final scale formation.

That way, principal component analyses were calculated for the construction sample. The

Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett’s test of sphericity demon-

strated the inter-item correlations being appropriately strong (KMO = .878, BTS p < .001). In

spite of the small number of participants in the validation sample, a principal component ana-

lysis of the scale items was also conducted. As the items’ communalities ranged from h = .412

to h = .660 (Costello & Ossbourne, 2005) and the Kaiser-Meyer-Olkins measure revealed an

appropriately high score (KMO = .901), this procedure appeared to be most reasonable (de

Winter, Dodou, & Wieringa, 2009; MacCallum, Widaman, Zhang, & Hong, 1999).

In order to further clarify possible differences in the statistics anxiety variable and to dis-

close potential nonlinear relations, a series of two-way analyses of variance (ANOVA) with

the students’ mathematics self-concept, implicit entity beliefs, and negative utility values as

factor variables was additionally run. In each case, the independent variables were factorized

using median split, thus, leading to the identification of lowered and heightened level

subgroups. In particular, separate 2�2 analyses and a comprehensive 2 �2 �2 analysis for

the construction sample were conducted.

Both samples had missing data (5.7% and 7.3%). As they did not produce any systematic

pattern in the construction (MCAR test p = .182) and in the validation sample (MCAR test p

= .178), they were treated as “missing completely at random” (Little, 1988). The missing

values were estimated by means of the two-step iterative expectation-maximization (EM)

algorithm. Though this method appears to be at risk to underestimate the standard errors of

imputed data, in view of the small number of missings, its use was considered justified (Gra-

ham, 2012).

5 Results

5.1 Scale formation

For determining the final version of the WAESTA scale in the construction sample, first

of all, descriptive item statistics were calculated. To test significant deviations from normal

distribution their z-standardized skewness and kurtosis scores were utilized (Field, 2009). The

avoidance item 04 as well as the worry item 11 showed a significant negative skew indicating

most students to agree with the statements – in detail they would preferably give a presentation

without any statistical content and during a presentation they would strongly hope not being




19

asked statistical questions. Furthermore, as the analysis revealed a significant negative kurtosis

score for the items 03, 06, 14, and 15, their distribution appeared to be platykurtic. Accord-

ingly, the students’ relevant item responses denoted a heightened variance or difference among

them (Table 3).

Table 3. Descriptive statistics, factor loadings and corrected item-test correlations of

WAESTA items (WR = worry, AV = avoidance, EM = emotionality): Results from the

construction sample (Faber, Drexler, Stappert, & Eichhorn, 2018)

Item AM SD zS zK a rit

01 WR 2.37 0.82 1.49 -0.67 .486 .436

02 EM 2.71 0.94 -1.30 -1.69 .688 .645

03 AV 2.74 1.08 -1.33 -2.61** .581 .515

04 AV 2.88 0.97 -2.12* 1.65 .719 .664

05 WR 2.51 0.91 -0.50 -1.68 .725 .663

06 AV 2.50 0.97 -0.21 -2.08* .758 .697

07 EM 2.17 0.96 1.71 -1.78 .697 .620

08 WR 2.24 0.84 1.49 -0.83 .718 .670

09 EM 2.20 0.87 1.59 -1.04 .668 .583

10 WR 2.69 0.93 -1.63 -1.43 .647 .694

11 WR 2.91 0.97 -2.09* -1.75 .740 .676

12 WR 2.26 0.80 1.52 -0.45 .734 .618

13 EM 2.96 0.93 -1.51 -0.45 .683 .493

14 WR 2.69 1.07 -0.67 -2.18* .551 .474

15 EM 2.87 0.84 -1.30 -2.77** .532 .637

16 WR 2.75 0.84 -1.45 -0.83 .689 .442

17 AV 2.07 0.87 1.55 -1.52 .488 .442

Total Sum Score (Items 01-17)

WAESTA 42.66 10.20 -0.49 -1.34

Significance: *p < .05, **p < .01

Note. AM = arithmetic mean, SD = standard deviation, zS = z-standardized

skewness, zK = z-standardized kurtosis, a = factor loading, rit = corrected item-

test correlation

For the data of the construction sample, principal component analyses did not statistically

separate the three anxiety components. Due to the eigenvalues (e1 = 7.385, e2 = 1.219, e3 =

1.132), neither a varimax nor an oblique rotation procedure yielded any loading pattern to

separate the worry, avoidance, and emotionality items in a conceptually proper way. Rather

all analyses led to a unidimensional structure (Table 3). This solution revealed sufficiently

high factor loadings and explained 43.59 per cent of extracted variance.

Nonetheless, for further clarification, three provisional subscales representing the students’




20

worry, avoidance, and emotionality cognitions were formed, and their interrelations as well as

their relations with criterion variables were examined. In line with the PCA result, the sub-

scales strongly correlated. Furthermore, using Steiger’s Z formula (Hoerger, 2013; Steiger,

1980) to compare dependent correlation coefficients, no difference between coefficients reach-

ed statistical significance (p > .05). Accordingly, the worry, avoidance, and emotionality sub-

scales appeared to be equally associated with the achievement and motivation variables under

consideration (Table 4).

Table 4. Correlations between provisory WAESTA subscales and with criterion variables

(in the construction sample)

AV EM SGM MSC VSC IEB NUV

WAESTA-

Worry .72*** .80*** -.23* -.38*** .03 .58*** .41***

WAESTA-

Avoidance

(AV)

.69*** -.28** -.43*** .05 .56*** .57***

WAESTA-

Emotionality

(EM)

-.22* -.34*** .12 .49*** .32***

Significance: *p < .05, **p < .01, ***p < .001

Note. SGM = Most Recent School Grade in Mathematics, MSC = Mathematics Self-Con-

cept, VSC = Verbal Self-Concept, IEB = Implicit Entity Beliefs, NUV = Negative Utility

Value

Consequently all WAESTA items were used to build the scale’s final version. For its total

score, neither the z-standardized scores of skewness and kurtosis nor the Shapiro Wilk W-test

(W = .988, df = 113, p = .443) evinced any significant deviation from the normal distribution

assumption. High total scores indicated the students’ to report stronger worry, avoidance, and

emotionality cognitions. The scale’s reliability was estimated in various ways and turned out

to be adequate: Its internal consistency (Cronbach’s coefficient alpha) amounted to α = .92, its

split-half reliability (odd-even method using Spearman-Brown correction) to r12 = .89, and its

standard error (based on coefficient alpha) was se = 2.67.

In the validation sample, the PCA results revealed eigenvalues (e1 = 8.422, e2 = 1.216, e3 =

1.006) which indicated a solution with one common factor. All factor loadings appeared to be

considerably high (ranging from amin = .612 to amax = .812). Accordingly, the unidimensional

scale feature was fully replicated and explained 52.64 per cent of extracted variance. For the

total sum score, z-standardized skewness (zS = -0.096) and kurtosis values (zK = -0.173) did

not indicate any significant deviation from the normal distribution assumption. Here again, the

scale’s reliability was estimated in various ways and turned out to be adequate: its internal

consistency (Cronbach’s coefficient alpha) amounted to α = .94, its split-half reliability (odd-

even method using Spearman-Brown correction) to r12 = .91, and its standard error (based on

coefficient alpha) was se = 2.45.




21

5.2 Validation results

As an initial approach to analyze the external validity of the WAESTA scale, its zero-order

correlations with the criterion variables under consideration were first analyzed. Due to the

non-normal distribution of criterion variables, Pearson and Spearman correlation coefficients

were precautionally calculated. However, as both types of coefficients revealed quite similar

information, the construct relations were preferably described in terms of Pearson’s r.

As the results consistently demonstrated (Table 5), the WAESTA scores were closely and

significantly associated with the students’ mathematics self-concept but not with their lan-

guage self-concept. This particular finding might be considered to provide preliminary evid-

ence that the WAESTA scale measures rather a domain-specific than a general facet of the

students’ test anxiety experience.

Table 5. Relations of WAESTA sum scores with background and self-belief variables

(zero-order correlations): Results from the construction and the validation sample

Most Recent

School Grade

Mathematics

Prior

Experiences

Statistics

Academic

Self-Concept

Mathematics

Academic

Self-Concept

Language

Implicit

Entity

Beliefs

Negative

Utility

Value

Construction Sample

-.29*** -.23* -.43*** .09 .62*** .49***

Validation Sample

-.22* -.18* -.38*** -.08 .80*** .32***


Furthermore, the scale scores were most strongly correlated with the students’ entity views

of own statistical competence. A heightened level of statistics anxiety came along with a deep

understanding of own statistical competencies being less or even not malleable in nature. With

the negative instrumental value of statistics the WAESTA sum score correlated moderately

positive. Students reporting a higher level of statistics anxiety tendentially perceived statistical

competencies as less important. Finally, the relation between the WAESTA score and the most

recent school grade in mathematics appeared to be positive and significant, though low in

magnitude. Hence, students with a heightened level of statistics anxiety had been less success-

ful in the mastery of mathematical demands at school. Similarly, students with prior exper-

iences with statistics displayed a lower level of statistics anxiety. Overall, the analysis in both

the construction and the validation sample revealed a most comparable pattern of criterion-

related correlations.

To get most differentiated validation results, a series of regression analyses with the

WAESTA scale as dependent variable were computed for both samples. As this procedure

allowed for controlling the covariations among all predictor variables with respect to their

empirical overlap and multicollinearity (Field, 2009), it should help to unravel the complexity

of construct relations. In particular, a sequence of regression models including an advancing

number of predictor variables was consecutively tested (Table 6). In both samples the stand-

ardized residuals of WAESTA sum scores did not violate the normal distribution assumption.

In each case, the Shapiro Wilk W-test demonstrated the standardized residuals being normally




22

distributed (construction sample: W = 986, df = 113, p = .308, validation sample: W = 979, df

= 87, p = .182).

Table 6. Multiple regression of WAESTA sum scores on background and self-belief vari-

ables (standardized beta weights and squared multiple regression coefficients): Results

from the construction and the validation sample

Model

Most Recent

School Grade

Mathematics

Prior

Experiences

Statistics

Academic

Self-Concept

Mathematics

Implicit

Entity

Beliefs

Negative

Utility

Value

R2

Construction Sample

A -.039 -.449*** .177

Validation Sample

A .184 -.533*** .154 Construction Sample

B -.005 -.244** -.436*** .236 Validation Sample

B .180 -.144 -.519*** .165 Construction Sample

C -.136 -.221*** -.014 .592*** .478 Validation Sample

C .030 .036 -.087 .772*** .616 Construction Sample

D -.158 -.248*** .031 .487*** .313*** .559 Validation Sample

D .023 .032 -.081 .799*** -.059 .614


Note. R2 = adjusted multiple regression coefficient squared

The results for regression models A and B clearly demonstrated the mathematics self-con-

cept to explain the most part of anxiety variance. However, adding the entity beliefs to the

regression equation in model C and D, the predictive power of the students’ mathematics self-

concept was reduced to a minimal and insignificant extent. Instead, the students’ entity beliefs

largely contributed to the WAESTA sum score. As the mathematics self-concept and the entity

belief variable in both samples were substantially correlated (r = -.51 in the construction

sample and r = -.45 in the validation sample), but the entity belief variable in both samples

was more strongly related to the anxiety variable (r = .63 in the construction sample and r =

.80 in the validation sample) – the massive decline in the self-concepts’ beta weight must be

seen as a result of multicollinearity (Marsh, Dowson, Pietsch, & Walker, 2004). This predic-

tive pattern occurred in both samples.

Moreover, only in the construction sample the students’ negative value of statistics sub-

stantially and independently explained additional variance in the WAESTA sum score. The

difference between samples might be due to the fact, that the methods for assessing the value

variable were not comparably formatted. Similarly, it was only in the construction sample that

that prior experience of statistics contributed incrementally to variance in WAESTA score.




23

Students with more experience reported statistics anxiety to a lesser degree. Once again the

difference between samples should be traced back to the scale format. In the validation sample

the dichotomous experience score was treated as a dummy variable which might have reduced

empirical variance and, thus, lowered correlation coefficients. Apart from this, all regression

analyses demonstrated the students’ statistics anxiety to be essentially and most closely pre-

dicted by their control beliefs – as reflecting their perceived malleability of individual compe-

tencies in the statistics domain.

Finally, for further clarification of the WAESTA scale’s validity, their mean differences

between both the educational science and the special education students were analyzed. As the

comparison groups were small and unequal in size the nonparametric Mann-Whitney U-test

for independent samples was used (Zimmerman, 1987). In the construction sample a signifi-

cantly higher level of statistics anxiety in the special education subgroup were be found (Z =

-2.314, p = .021, effect size r = 0.22). In the validation sample, the level of statistics anxiety

did not significantly differ between educational science and special education students (Z = -

0.374, p > .05). However, with the small size of the validation sample in mind, this finding

should be considered cautiously.

5.3 Additional multivariate analyses

In order to scrutinize the role of the WAESTA scores within the multivariate context of

relevant self-belief variables, their mean differences depending on the students’ domain-spe-

cific self-concept, implicit entity, and negative value responses were analyzed.

As the result of the first two-way analysis of variance demonstrated, mean differences in the

students’ statistics anxiety appeared to be significantly explained by a main effect of both the

entity belief and the self-concept variable (Table 7). Accordingly, those students reporting a

lowered sense of malleability of their statistical competencies and having a poorer math-

ematical self-concept apparently displayed a heightened level of worry, avoidance, and emo-

tionality cognitions (Figure 1). The interaction effect of the self-concept and implicit entity

beliefs variable was statistically not significant.

A quite similar effect pattern was found with regard to the negative value variable. Mean

differences in the WAESTA responses were significantly explained by a main effect of both

the negative value and the self-concept variable (Table 7). Those students who perceived the

availability of statistical competencies as less useful and, besides, reported a poorer math-

ematical self-concept, showed a heightened level of statistics anxiety (Figure 1). Thus, in both

analyses the students’ statistics anxiety appeared to be substantially predicted by distinct ef-

fects of the domain-specific self-beliefs under consideration – whereas the effect of the math-

ematics self-concept was less powerful in each case. Here again, the interaction effect of both

independent variables was statistically not significant.

Bringing together both perspectives by concurrently analyzing the role of all self-belief

variables, the result of a three-way analysis of variance revealed significant main effects of

the entity beliefs and the negative value but not anymore for the self-concept variable (Table

6). Rather, the students with strong entity beliefs and negative utility values reported a con-

siderably heightened level of statistics anxiety (Figure 2).




24

Figure 1. Mean statistics anxiety scores depending on the students’ implicit entity theory,

negative utility value, and mathematics self-concept: separate two-way analyses of vari-

ance from the construction sample.

Figure 2. Mean statistics anxiety scores depending on the students’ implicit entity theory,

negative utility value, and mathematics self-concept: comprehensive three-way analysis

of variance from the construction sample.

Though this effect pattern obviously appeared somewhat more pronounced for the sub-

group with a poorer mathematical self-concept, this difference did not reach statistical signi-

ficance. Therefore, the additive impact of lowered expectations to improve one’s own statis-

tical skills and negative perceptions of the utility of statistical skills allowed for best predicting

the interindividually existing level of statistics anxiety. All interaction effects were statistically

not significant. This finding is completely in line with the regression results (Table 5). How-

ever, it may yield a more descriptive look on the relations among constructs. That is, within

the cognitive-motivational interplay of all self-belief variables, the explanative role of the




25

mathematical self-concept was largely mediated by the students’ entity beliefs and utility va-

lues.

Table 7. Differences in students’ statistics anxiety depending on their mathematics self-

concept, implicit entity beliefs, and negative instrumental value. Results from the con-

struction sample.

WAESTA Sum Scores (Statistics Anxiety)

Factor Variables df F p η2

Mathematics Self-Concept (MSC) 1,112 5.749 .018 .050

Implicit Entity Beliefs (IEB) 1,112 48.671 .000 .309

MSC × IEB 1,112 0.875 .352 .008


Negative Utility Value (NUV) 1,112 24.349 .000 .183

MSC × NUV 1,112 0.260 .611 .002


Implicit Entity Beliefs (IEB) 1,112 35.411 .000 .252

Negative Utility Value (NUV) 1,112 13.469 .000 .114

MSC × IEB 1,112 1.339 .250 .013

MSC × NUV 1,112 0.774 .381 .007

IEB × NUV 1,112 0.268 .606 .003

MSC × IEB × NUV 1,112 0.003 .956 .000

Note. df = degree of freedom, F = F-value, p = probability, η2 = partial eta

squared (effect size)

6 Conclusion

The present study should examine the internal and external validity as well as the psycho-

metric properties of the newly developed WAESTA scale for measuring educational science

students’ worry, avoidance, and emotionality cognitions in the domain of statistics learning.

Conceptually, this measurement approach should integrate both the strengths of a more situa-

tion- and a more response-focused research line in the field. Data were gathered in a construc-

tion sample as well, one year later, in a validation sample of education science majors. As a

substantive result, this scale was demonstrated to represent the construct in a unidimensional

manner. Using principal component factor analysis, all scale items were empirically support-

ed. Accordingly, the final scale version included all items as initially administered in both

samples. Its internal consistency was most sufficient. Furthermore, its relations with various

self-belief and background variables most widely turned out as theoretically predicted. Spe-

cifically, total WAESTA score was more strongly correlated with the students’ mathematics

than with their language self-concept – and, thus, the scale should claim domain-specific va-

lidity. These findings correspondingly held for both the construction and the validation sample.

For the time being, the WAESTA scale can be considered internally and externally valid as




26

well as having adequate psychometric properties. Nevertheless, some results definitely deserve

further attention.

In particular, the scale’s underlying structure consistently appeared to be unidimensional.

This finding indicates the strong empirical overlap among the worry, avoidance, and emo-

tionality responses – and, thus, the cognitive-motivational interplay of anxiety components.

Similarly, close relations had been already found elsewhere (Deffenbacher, 1980; Hodapp &

Benson, 1997; Cassady & Johnson, 2002; Chin, Williams, Taylor, & Harvey, 2017; Hong &

Karstensson, 2002; Sarason, 1984; Sparfeldt, Schilling, Rost, Stelzl, & Peipert, 2005),

especially with respect to domain- or task-specific facets of test anxiety (Faber, 1993, 1995a,

2012b, 2015). Nonetheless, in most cases worry and emotionality cognitions were demon-

strated to differently correlate with students’ performance and motivation scores (Faber, 2000,

2002; Seipp, 1991; von der Embse, Jester, Roy, & Post, 2018). By no means, this result does

challenge the need for a separate assessment of worry, avoidance, and emotionality cognitions.

Rather this approach should ensure to obtain a most differentiated measuring of statistics anx-

iety and, thereby, should contribute to reducing the interpretation ambiguity of item responses.

In that regard, it should certainly increase the scale’s cognitive-motivational representativity

and content validity. Likewise, the students’ avoidance cognitions were found to be most clo-

sely related to their worry, but only slightly less closely related to their emotionality cogni-

tions. Therefore, according to relevant findings (Galassi, Frierson, & Sharer, 1981; Hagtvet &

Benson, 1997), avoidance cognitions must be seen as an important feature within the students’

anxiety experience and, thus, should have contributed to completing and differentiating the

measuring of statistics anxiety. Hence, future research should more strongly pay attention to

this issue and reconsider its theoretical framework as well as its methodological implications.

Apart from this conceptual perspective, the WAESTA scale’s content and format should be

further refined. In particular, the proportion of worry, avoidance, and emotionality items

should be more balanced – in particular, the number of avoidance items should be extended.

Furthermore, given the ambiguous research findings (Lee & Paek, 2014; Lozano, Garcia-

Cueto, & Muñiz, 2008; Wakita, Ueshima, & Noguchi, 2012; Weng, 2004), subsequent scale

analyses should also compare various scale versions with different numbers of response cate-

gories in order to examine their psychometric and validity properties.

With respect to the validation results, both the correlation and regression analyses suggest,

at first glance, that students’ implicit entity beliefs are sufficient to explain their statistics anx-

iety. Without any doubt, the entity beliefs appear to obviously play a crucial role in the pre-

diction of statistics anxiety – as should be expected from the view of social-cognitive theories

(Dweck & Leggett, 1988; Schunk & Zimmerman, 2006; Zeidner, 1998). However, in the stu-

dents’ cognitive-motivational processing, they will operate in a more complex manner. Ac-

cording to relevant theoretical conceptions and empirical findings in the field (Blackwell,

Trzesniewski, & Dweck, 2007; Chiesi & Primi, 2010; Emmioǧlu, 2011; Onwuegbuzie, 2003;

Sesé, Jiménez, Montano, & Palmer, 2015), it should be assumed that implicit beliefs actually

mediate the effects of students’ self-concept and their learning background on the dependent

anxiety variable (Baron & Kenny, 1986). The massive decline in the self-concept variable’s

beta weights, when adding the entity belief variable to the regression equation, apparently




27

supports this assumption (Table 5). The same applies for the results of additionally run anal-

yses of variance (Table 6). Indeed, within the validation framework this indirect effect cannot

be adequately substantiated with correlational or regression analysis, but only with multivar-

iate modeling method (Kline, 2011). Future research should make every effort to apply such

modelling techniques in order to clarify the role of entity beliefs in the statistics domain.

Beyond the purpose of scale validation, the empirical findings concerning the students’

entity beliefs might even extend the previous research in two respects: at the level of construct

specificity, the measuring of entity beliefs did not refer to the perceived malleability of general

cognitive abilities but enquired the perceived malleability of statistical competencies. As this

entity belief variable was only very weakly correlated with language self-concept (construc-

tion sample r = .07; validation sample r = -.12) it should be considered domain-specific.

Hence, for the domain of statistical learning, this particular finding appears to be in line with

the recommendations of the implicit theories approach (Dweck & Molden, 2005). Accord-

ingly, at the level of construct relations, the results allow for refining the nomological scope

of the statistics anxiety framework – at least, as it refers to the type and role of self-belief

variables (Bandalos, Yates, & Thorndike-Christ, 1995; González, Rodrígez, Faílde, & Carrera,

2016; Onwuegbuzie & Wilson, 2003; Zeidner, 1991).

The present study undeniably suffers from some conceptual and empirical limitations and

shortcomings. First of all, composition and size of both student samples do not allow for ge-

neralizing the empirical findings as should be required. Instead, the findings reported here

might claim a sort of local validity – all the more, as their data basis referred to a certain

university setting. Their external validity must, therefore, be considered weak. Further anal-

yses should necessarily remedy this problem and examine the WAESTA scale with other stu-

dent samples from other educational science contexts.

Moreover, the validation framework is still lacking in several respects and should be fur-

ther completed (Benson, 1998). The number of items for measuring the students’ implicit

entity theory and utility value should be extended – not least, in order to enhance their internal

consistencies. However, simply increasing the number of items will not necessarily improve

reliability and criterion validity to a considerable extent (Gogol, Brunner, Goetz, Martin,

Ugen, Keller, Fischbach, & Preckel, 2014). Further validation efforts should carefully explore

options to broadening the constructs’ operationalizations in a conceptually and contextually

adequate manner – but not only to enhance statistical variance of item responses. Especially

the construct of entity beliefs might allow for response variability merely in its context or

situation facet. Therefore, as relevant studies in the field correspondingly showed, its potential

operationalization space will be conceivably restricted (Blackwell, Trzesniewski, & Dweck,

2007; Hong, Chiu, Dweck, & Wan, 1999; Lou & Noels, 2017). One way to refine the construct

should be its extension with the students’ beliefs about perceived effort and learning control

(Blackwell, Trzesniewski, & Dweck, 2007; Schutz, Drogosz, White, & Distefano, 1998;

Tempelaar, Rienties, Giesbers, & Gijselaers, 2015). Furthermore, this study assessed students’

mathematics self-concept retrospectively. As a proportion of both samples did not have any

prior experience of statistics using a measure of statistical self-concept would have been

misguided. However, provided that further research would include participants being most

comparable in their statistical background, their self-concept in the statistics domain should




28

be absolutely used to elaborate scale validation (González, Rodrígez, Faílde, & Carrera, 2016;

Sproesser, Engel, & Kuntze, 2016). Likewise, concurrent measures of the students’ self-effi-

cacy to master certain statistical tasks should help to further differentiate the scale’s criterion

validity (Finney & Schraw, 2003; Olani, Harskamp, Hoekstra, & van der Werf, 2010; Pere-

piczka, Chandler, & Becerra, 2011). Not least, an appropriate validation of the WAESTA scale

will require an analysis of its relations with other instruments for measuring statistics anxiety

– for instance, by comparing it with the German adaptation of the STARS questionnaire (Pa-

pousek, Ruggeri, Macher, Paechter, Heene, Weiss, Schulter, & Freudenthaler, 2012).

As another crucial point the measuring of the students’ prior statistics experience might be

considered. In both samples, this variable had been differently operationalized. Therefore, its

relations to the statistics anxiety score cannot be compared across samples. However, the

multivariate findings indicate the students’ informally experienced exposure to statistics (as

assessed in the construction sample) being stronger related to their anxiety scores than their

prior passing of a formal exam (as assessed in the validation sample). Possibly, this particular

result should be traced to both the binary item format and the number of students in the va-

lidation sample. Moreover, in line with research findings reported elsewhere (Dempster &

McCorry, 2009), this particular result might also indicate the everyday encounter with sta-

tistical demands to play a more important role for the emergence and maintenance of anxious

reaction patterns. Further validation efforts should bear this perspective in mind and always

analyze the informal experiences with statistics as cognitive-motivationally decisive

background variable – instead of merely focussing on structural information (Hannigan, He-

garty, & McGrath, 2014; Onwuegbuzie, 2003). However, as additional analyses of the data

from both samples showed, the relation between students’ prior statistics experiences and their

statistics anxiety appeared to be largely superposed by the domain-specific self-concept and

value variable (Faber & Drexler, 2018).

Another considerable lack of the present study concerns the missing of a relevant perfor-

mance measure. As only a certain part of students in both samples had yet to pass an exam in

introductory statistics, sufficiently robust data were not available. Further validation studies

should analyze the relation between the WAESTA scores and suitable measures of students’

actual statistics performance (Hanna & Dempster, 2012). Especially, this relation should be

most instructive – in as much as relevant studies commonly reported low to moderate correla-

tions (Bandalos, Yates, & Thorndike-Christ, 1995; Finney & Schraw, 2003; Macher, Paechter,

Papousek, & Ruggeri, 2012; Sesé, Jiménez, Montano, & Palmer, 2015; Tremblay, Gardner, &

Heipel, 2000; Vigil-Colet, Lorenzo-Seva, & Condon, 2008; Zeidner, 1991). However, these

results do not really indicate a general flaw in the measures’ criterion validity. Rather, they

reflect the motivational consequences of statistics anxiety within a strongly restricted setting

(Pekrun, 1988). As the successful passing of statistical requirements in the Master’s degree is

mandatory, the students’ increasingly experienced worry, avoidance tendencies, and feelings

of apprehension should dispose them to strengthen their learning effort in order to avoid an

impending failure outcome (Macher, Papousek, Ruggeri, & Paechter, 2015; Martin & Marsh,

2003). Accordingly, for the WAESTA scale, also a moderate relation with the students’ statis-

tical performance should be assumed. Moreover, in order to further elucidate the relation be-

tween students’ statistics anxiety and actual achievement, it should be also enlightening to




29

analyze their domain-specific learning approach (Chiesi, Primi, Bilgin, Lopez, del Carmen

Fabrizio, Gozlu, & Tuan, 2016; Markle, 2017).

Finally, as both samples in this study were small and predominantly female, gender was

not included in the validation analyses. Relevant findings in the field consistently demon-

strated the females to report a higher level of statistics anxiety (Benson, 1989; Hong & Kar-

stensson, 2002; Macher, Paechter, Papousek, & Ruggeri, 2012; Onwuegbuzie & Wilson,

2003). Interestingly, despite the apparently heightened anxiety level of female students, some

studies did not substantiate any significant disadvantage in their exam performance (Bradley

& Wygant, 1998; Macher, Paechter, Papousek, Ruggeri, Freudenthaler, & Arendasy, 2013).

This finding needs further clarification with respect to the underlying motivational and behav-

ioral processes. Hence, female students might have overrated their individually existing

anxiety level (Zeidner, 1998) – possibly due to a self-derogatory gender stereotyping effect

(Bieg, Goetz, Wolter, & Hall, 2015; Pomerantz, Altermatt, & Saxon, 2002). As well, pursuing

a more adaptive coping strategy to avoid feared failure, they might have ramped up their learn-

ing approach (Martin & Marsh, 2003). Given a larger sample size with a more adequately

balanced gender ratio, this issue should also be examined with respect to the WAESTA scale.

In summary, the present findings yield important information concerning the internal and

external validity of the newly developed WAESTA scale. However, they must be seen as pre-

liminary in nature. Therefore, they should represent just a very first step in method devel-

opment.

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8 Appendix

WAESTA scale for measuring education science students’ worry (WR), avoidance (AV), and

emotionality (EM) cognitions encountering statistical demands (from Faber, Drexler, Stappert,

& Eichhorn, 2018) – originally worded in German (Faber, Drexler, & Stappert, 2018).

01 WR I will hardly be able to meet my degree program's statistics requirements

right away.

02 EM I would be very uncomfortable if I had to work on a statistical problem.

03 AV If I could, I would rather take two other courses than do one statistics

course.

04 AV When presentation topics are being assigned in the course, I would make

sure that I receive a topic that doesn't involve statistics.

05 WR It would be difficult for me to discuss statistical content adequately in my

papers.

06 AV When preparing presentations, I would rather omit anything that has to do

with statistics.

07 EM I would be quite nervous if I were asked to explain a chart from a research

report.

08 WR I have difficulty understanding statistical content in a lecture.

09 EM I would have trouble extracting the relevant information from a table of

statistical values.

10 WR If I had to comment on statistical data in a course, I would be worried that

I would make a fool of myself.

11 WR If I had to give a presentation including statistical findings in a course, I

would hope that no one had any follow-up questions.

12 WR I would hardly be able to present a report on statistical research findings

adequately.

13 EM I would feel very tense if I had to apply a statistical formula.

14 WR Despite careful preparation for a statistics exam, I would worry about not

passing it.

15 EM The thought of having to explain a statistical problem in a course makes

me quite nervous.

16 WR If I took a statistics course, I would be concerned that I would quickly

forget everything I had learned.

17 AV In scientific texts, I would skip over statistical tables and diagrams if pos-

sible.




47

Recommended citation:

Faber, G., Drexler, H., Stappert, A. & Eichhorn, J. (2018). Measuring education science students‘ statistics anxiety.

Conceptual framework, methodological considerations, and empirical analyses. Leibniz University Hannover, Fa-

culty of Humanities, Institute of Psychology: Research report.

measuring education science students‘ statistics anxiety · schneider & preckel, 2017)....

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