Statistics Anxiety and Misconceptions: University Students Investigated

Belinda V. de CastroCenter for Educational Research and Development

University of Santo TomasManila, Philippines

bvdecastro@mnl.ust.edu.ph

Abstract

This paper dwelling on the determination of the causes of statistics anxiety and the underlying misconceptions of statistics of university students. The study made use of both qualitative and quantitative methods. Qualitatively, indepth interviews were done on master’s degree graduates concerning their experiences when they were enrolled in a Statistics course and how they were able to make use of it in their thesis. Interview transcripts served as basis for the survey instrument. Three hundred six students from the undergraduate and graduate school levels were surveyed. Factor analysis results showed six factor dimensions causing statistics anxiety, namely: inherent fear, preconceptions, dependency, task-generated difficulties, lack of interest and perfectionism. Three misconception dimensions were identified: concept-related, schema-related and model-related misconceptions. T-test for independent samples was used to identify significant differences in the anxiety levels and the misconceptions perceived by the two groups of students. Pearson correlation coefficients determined relationships between these two constructs and their willingness to learn statistics.

Keywords: Statistics anxiety, Statistics misconceptions, learning Statistics

Introduction

Anxiety had long been a focus of research in the area of learning and academic performance. Previous studies dealing with anxiety as a behavioral phenomenon in the field of mathematics include the following approaches: studies relating anxiety to testing conditions within the classroom (Rosenfeld, 1978; Spielberger et al, 1980), research analyzing anxiety in relation to learning approaches, cognitive processes and affective dispositions (Bessant, 1995; Yunis, 2006) and instructional procedures (Pan, W. & Tang, M, n.d.) and research dealing with the relationship of anxiety to academic performance (Cates and Rhymer, 2003; Onwuegbuzie, 2000) and their attitudes towards statistics (Lawson et al, 2003). Although researchers seem to agree that anxiety affected learning, a review of related literature suggests two potential inherent limitations of past researches. It is apparent that the source of that anxiety had not been exhausted in connection to the beliefs and misconceptions that arise as a result of this anxiety.

Anxiety refers to the body’s way of telling that there is something in the environment in need of one’s attention. High levels of anxiety cause the body to prepare for a fight or flight response from the perceived threat. Statistics anxiety is defined as a performance characterized by apprehension (Onwuegbuzie, 2004) or extensive worry, intrusive thoughts, mental disorganization, tension, and physiological arousal (Zeidner, 1990) when exposed to statistics content, problems, instructional situations, or evaluative contexts, and is commonly claimed to debilitate performance in a wide variety of academic situations by interfering with the manipulation of statistics data and solution of statistics problems. It is noticeably common among students whose academic background includes little previous statistical or mathematical training (Pan, W. & Tang, M, 2005).

According to Onwuegbuzie (2000), around two-thirds to four-fifths of graduate school students appear to experience uncomfortable levels of statistics anxiety. It can be so great that students often delay enrolling in research methods and statistics courses as long as possible, which is clearly not the optimal time to pursue such courses.

Conners, Mccown and Roskos-Ewoldsen, in the study of D’Andrea and Waters (2002), stated that the statistics instructor faces four major challenges inside the classroom: to motivate students to value a topic they think is irrelevant to their life, to deal with the anxiety that is often associated with learning statistics, to effectively teach both high and low achievers and to make the learning memorable. The researcher added a fifth challenge, that is, to minimize misconceptions that arise from the anxiety of the students toward statistics.

Statistics misconceptions involve semantically-meaningful deviation from a correct procedure applied by students in solving statistical problems (Mavarech, 1983). Up to this time, there is still dearth on researches dealing with misconceptions in statistics and how it relates to the anxiety level of the individual.

The Present Study

The study sought to identify causes of statistics anxiety among Filipino university students. To capture the local setting, a researcher-made survey instrument was developed based on indepth interviews with master’s graduates. Findings in the interviews were used to evolve a survey questionnaire which dealt with the underlying factors causing statistics anxiety and the misconceptions causing or arising from it among undergraduate and graduate school students. This researches hopes to assist teachers determine the roots of statistics anxiety and the misconceptions generated by / causing it so they could match instructional strategies needed for the situation. On the part of curriculum planners, this could help them sequence course content in Statistics to help reduce the level of anxiety and misconceptions of the students.

Review of Related Literature

Factors Affecting Statistics Anxiety

Statistics anxiety had been conceptualized as multidimensional (Cruise, et al, 1985). Onwuegbuzie & Wilson (2003) identified four general components of statistics anxiety, namely: instrument anxiety, content anxiety, interpersonal anxiety and failure anxiety. Instrument anxiety consists of computational self-concept and statistical computing anxiety. Content anxiety comprises fear of statistical language, fear of application of statistical knowledge, perceived usefulness of statistics and recall anxiety. Interpersonal anxiety is composed of fear of asking for help and fear of statistics instructors. Finally, failure anxiety consists of study-related anxiety, test anxiety and grade anxiety.

Onwuegbuzie and Wilson (2003) classified the literature dealing with the antecedents of statistics anxiety into three categories: situational, environmental, and dispositional. As for the situational antecedents, statistics anxiety was found to be related to factors such as performance parameters of statistics and mathematics prior knowledge, instructors’ evaluation, course grades, whether the course is required or elective, and whether statistics is a major or a minor subject. As for environmental antecedents, gender (female reporting higher anxiety), age (older students reporting higher anxiety), race, and learning styles were some of the important variable related to statistics anxiety. As to dispositional antecedents, the most frequently studied variables related to

self-esteem, perceived scholastic competence, perceived intellectual ability, perfectionism, procrastination, hope and coping strategies.

Several instruments had already been developed to measure anxiety such as the Mathematics Anxiety Rating Scale (MARS) (Bessant, 1995), the Fennema-Sherman Mathematics Anxiety Scale (FSMAS) (Cates and Rhymer, 2003), Statistics Anxiety Rating Scale (STARS) (D’Andrea and Waters, 2002; Bell, 2005), Attitude Towards Statistics (ATS) (D’Andrea and Waters, 2002, Lawson et al, 2003), Encouraged about Statistics (EncStat) (Watson, et al, 2003) – that aimed to identify the negative attitudes of students regarding math / statistics and the CAOS test (Delmas, et al, 2006), designed to measure students’ conceptual understanding of important statistical ideas at the end of an introductory course in statistics.

Statistics Anxiety Rating Scale (STARS) has been the most widely used measure of statistics anxiety (Onwuegbuzie and Wilson, 2003) and subjected to extensive reliability and validity studies. It is made of up two types of items: the first type is considered a measure of anxiety, while the second type measures attitudes and beliefs. Six factor dimensions emerged namely: worth of statistics, interpretation anxiety, test and class anxiety, computational self-concept, fear of asking for help, and fear of statistics teachers (Bell, n.d.; Cruise, 1985).

Factors contributing to students’ anxiety are broad. Several factor dimensions were evolved in the previous studies on statistics anxiety. Forte (1995) identified factors affecting social work students’ anxiety towards statistics through a questionnaire which includes minimal previous math preparation, late in career introduction to quantitative analysis, general anti-quantitative bias, lack of appropriation for the power of analytical models, and lack of mental imagery useful in thinking about quantitative concepts. Pan & Tang (2005) made use of focus group interviews (FGI) of seven (7) social science graduate students and found out that contributory to statistics anxiety are math phobia, lack of connection to daily life, pace of instruction and instructor’s attitude. Yunis (2006), for his part, identified five (5) reasons for statistics difficulties of psychology students, namely: course content, teaching, examinations, relevance of statistics, and student characteristics.

Approaches Addressing Reduction of Anxiety

Past researches have documented a negative relationship between statistics anxiety and course performance, thus manifesting a debilitative phenomenon (Onwuegbuzie & Wilson, 2003). A variety of teaching approaches had been experimented to address reduction of anxiety in learning statistics: cooperative learning (Borresen, 1990), real data sets (Filebrown, 1994), humor (Forte, 1995; Berk & Nanda, 1998), journal writing (Sgoutas-Emch & Johnson, 1998), short stories (D’Andrea & Waters, 2002) and real-world applications (Forte, 1995; Pan & Tang, 2005). Forte (1995) argued that statistics can be effectively taught when incorporated with computer usage, statistical language practice and group learning principles. Pan & Tang’s study (2004) also proved that combining application-oriented teaching methods with teacher attentiveness to student’s anxiety was significantly effective in reducing anxiety.

Method

Analysis is based on 306 students, both from the graduate and undergraduate school level of a reputable school, enrolled in Basic Statistics course within a span of one year. Five master’s degree graduates were subjected to indepth interviews regarding their experiences when they were taking up statistics course and their realizations when they were doing their thesis. Significant statements from the transcripts from these interview sessions evolved a survey

questionnaire reduced into two major themes: the first concerned with the causes of anxiety among students taking up statistics and the second concerning the misconceptions causing or brought about by this anxiety.

Cronbach Alpha was used to test the instruments’ reliability and internal consistency. A 95.9% reliability coefficient was achieved which indicated that the construct was internally consistent. Profile of student respondents was shown to identify their background in Statistics. Factor analysis was then employed as a data reduction tool to derive the underlying cause dimensions on statistics anxiety and the misconceptions on the course. One way analysis of variance was employed to ascertain differences in student respondents’ causes of anxiety and misconceptions on statistics when grouped according to their demographic profile. ANOVA was also used to determine statistical differences in their perceptions. T-test for independent samples was used to compare and contrast the levels of anxiety and misconceptions of the two groups of students.

Results

Respondents’ Demographic Characteristics

Table 1 indicates that student respondents are mostly undergraduate students (85.6%), 18 to 19 years of age (56.2%), female (61.8%) and in the business field (85.9%). Majority are full time students (85.9%), have earned only three (3) units of statistics (72.5%) and devotes one to two hours a day in studying statistics (24.5%).

Table 1.Profile of University Student Respondents (n=306)

Profile N % Profile N %Age 16 to 17 15 4.9 Hours Spent < 1 hr. 25 8.2

18 to 19 172 56.2 Studying ≥ 1 to < 2 hrs. 75 24.520 to 21 89 29.1 Stat in a day ≥ 2 to < 3 hrs. 56 18.322 and above 19 6.2 ≥ 3 to < 4 hrs. 34 11.1

Gender Male 117 38.2 ≥ 4 hrs 31 10.1Female 189 61.8 Units Earned 3 units 222 72.5

Program Undergraduate 262 85.6 6 units 18 5.9MA/MS 44 14.4 9 units 12 3.9

Field Business 263 85.9 12 units 2 0.7Education 27 8.8 Student Part 38 12.4Medical 16 5.2 Time Full 263 85.9

Table 2 indicates the significant differences in the student respondents’ perception of their statistical skills. Computational , graph construction and

interpretation were among the three topmost skills identified by both graduate and undergraduate students as their cutting edge in statistics. Results also show how inept both groups are with respect to the use of statistical software. Notably, these two groups of respondents differed significantly on three aspects namely: formula recall (t-value = 2.58, p-value<0.05), dummy table (t-value = -2.13, p-value<0.05) and composite table presentation (t-value = -2.18, p-value<0.05).

Table 2.

Significant Differences in the Student Respondents’ Statistical Skills (n=306)

SkillsUndergraduate Graduate

t-valueMean SD Rank Mean SD Rank

Formula recall 2.54 0.64 6 2.27 0.67 8 2.58*Computational 2.88 0.63 1 2.76 0.71 2 1.20Data analysis 2.60 0.65 5 2.64 0.65 5 -0.40Data interpretation 2.64 0.63 4 2.69 0.70 4 -0.49Graph construction 2.78 0.70 2 2.71 0.73 3 0.60Graph interpretation 2.67 0.69 3 2.78 0.64 1 -0.96Dummy table presentation 2.33 0.72 7 2.58 0.66 6 -2.13*Composite table presentation 2.29 0.72 8 2.55 0.70 7 -2.18*Use of Statistical software 2.07 0.88 9 2.22 0.74 9 -1.11*significant at 0.05 level

Table 3 shows the significant differences in the difficulty level of statistics content as perceived by the student respondents. Notably, there is agreement in the rankings made by the respondents on the four easiest topics for them, namely: (from easiest) measures of central tendency , variability , testing for significant differences and relationships . They were also akin in their rankings that testing for significant agreement is the most difficult. Results provide evidence that difficulty level were found to be significantly different on only three topic contents, namely: testing for significant differences (t-value = 2.32, p-value<0.05), relationships (t-value = 2.95, p-value<0.01) and time series analysis (t-value = -1.08, p-value<0.01).

Table 3.Significant Differences in the Difficulty Level of Statistical Topics as Perceived by Student Respondents

SkillsUndergraduate Graduate

t-valueMean SD Rank Mean SD Rank

Measures of Central Tendency 2.39 2.21 1 2.15 1.89 1 0.67Measures of Variability 3.20 2.02 2 2.85 1.53 2 1.04Testing for Significant Differences 4.17 1.87 3 3.45 1.43 3 2.32*Testing for Significant Relationships 4.30 1.69 4 3.48 1.32 4 2.95**Regression Analysis 5.33 1.62 6 4.90 1.52 5 1.55Testing for Significant Agreement 6.32 1.72 8 6.33 1.61 8 -0.05Time Series Analysis 4.45 2.35 5 6.05 1.68 7 -4.08**Multivariate Analysis 5.58 2.30 7 5.82 2.41 6 -0.61*significant at 0.05 level, **significant at 0.01 level

The Survey instrument was a two-pronged questionnaire: Part I, consists of 40 items, deals with the causes of statistics anxiety among college students and Part II, a 17-item instrument, deals with their misconceptions on statistics as a course. These items are scored on a Likert-type scale from one to eight, with “one” indicating disagreeing to a much extent while “eight” indicating agreement to the statement to a much extent. Hence, the higher the score, the more the item is a cause of their anxiety (Part I) and the more the student believes on the wrong notions on Statistics (Part II). Factor analysis using principal component analysis with varimax rotation was applied to this two-part questionnaire to determine the underlying dimensions to the college students’ perception of Statistics. Prior to factor analysis, Kaisier Meyer Olkin (KMO) Measure of Sampling Adequacy and Bartlett’s Test of Sphericity were applied to test the fitness of data. The KMO were found to be 0.873 and 0.763 and Bartlett’s Test of Sphericity were found to be 1868.345 and 1758.5 respectively, with significance lower than 0.001. Both statistical data supported the use of factor analysis.

To validate the internal reliability of each of the statements in the factors identified, an internal reliability test (Cronbach Alpha) was conducted. All factors with a reliability coefficient above 0.7 were considered acceptable in the study. Relatively high reliability coefficients ranging

from 0.737 to 0.932 were indicated by all factors. Part of the decision rule was done by discarding all items the factor loadings and communalities of which were less than 0.40 and eigenvalues less than 1.0. These decision rules resulted to a 39-item instrument for Part I that measured 6 anxiety cause dimensions, namely Inherent Fear, Preconception, Dependency, Task-generated Difficulties, Lack of Interest and Perfectionism.

Table 4.Results of Factor Analysis on the Causes of Statistics Anxiety

Anxiety Cause Factor DimensionsFactor

LoadingEigenvalue

Variance(%)

Reliability Coefficient

Inherent Fear 3.92 15.62 92.76I don’t like numbers even before, that’s why I am afraid of Statistics.

.833

I do not feel confident enough to deal with numbers. .768Statistics had been difficult for me because I had very limited background when it comes to numbers.

.638

I was able to develop fear of Statistics because of what others say about it.

.575

I feel uneasy when taking the test in Statistics. .565I find it difficult to associate symbols used in statistical formulas to its functions.

.550

The sight of graphs and charts irritate me. .540I am terrified with the sight of formulas in Statistics. .522When I take the test, I can feel how poorly I am doing as compared to my classmates

.519

I find it hard to see the meaning and implications of the numbers in Statistics.

.492

It’s a torture for me to analyze and interpret statistical computations.

.453

Preconception 2.57 10.61 91.73I always have the feeling that I would fail in Statistics even if I study well.

.602

I’m afraid to ask questions when there is something not clear to me because I might be asking the wrong questions.

.585

I am hesitant to start analyzing things in Statistics. .581Stat had always been a complicated thing for me. .574I was getting low grades even if I studied very well. .559Just hearing the word Statistics stirs up my emotions. .512I have to force myself to like Statistics because it is a required subject.

.488

I feel like groping in the dark whenever I am in my Stat class.

.443

There is a feeling of uncertainty in my answers in Stat. .434Dependency 2.87 10.08 76.79I give more time to study Statistics than the other courses. .681I rely so much on the book for explanations. .671I put double effort whenever I solve Statistical problems. .652I seek the assistance from friends when I encounter difficulty in Statistics.

.640

I feel that my teachers in Statistics were not able to exert the effort to motivate us.

.631

I need to see the step by step procedure of how to go about statistical formulas before I can solve it.

.583

Given a chance, I always have the tendency of asking another person solve a statistical problem for me and not do it myself.

.463

I am very dependent on the way my teacher presents the lesson.

.412

Task-generated Difficulties 1.52 9.85 79.27Taking one step at a time and not taking the problem as a .612

whole alleviates my tension in solving statistical problems.I need to see the step by step procedure of how to go about statistical formulas before I can solve it.

.583

Statistical problem situations are quite lengthy to read and understand.

.532

Dealing with Statistics computations is a tough challenge. .519I can only answer statistical problems if I am basing my solution to the examples given by my teacher.

.500

Lack of interest 1.72 8.96 61.47More focus is needed for me to study Statistics. .831The teachers are giving us examples with which we could not really identify ourselves.

.785

I felt that we were burdened with too much manual computations when there are existing software which can do it to give us more time for analysis and interpretation.

.545

I do not see the relevance of Statistics in my field of work .347Perfectionism 1.28 8.49 66.11When I take the test, I am bothered about items on other parts of the test I wasn’t able to answer.

.691

When I take the test I think of the consequences of failing. .672Our teacher wants us to learn the lesson the way he wants us to learn.

.595

Total Variance Explained 63.59*Kaiser-Meyer Olkin Measure of Sampling Adequacy = 0.926

Six factor dimensions were identified among the 39 statements (Table 4), labeled in the order of decreasing explained variance. Factor 1, labeled as Inherent Fear refers to the students’ phobia of anything that is associated with mathematics such as numbers, formulas, charts and graphs, triggered by situations in their past. This fear lingers up to this time that blocks their confidence when dealing with statistical computations. This relates to classical mathematics anxiety. Factor 2 refers to the Preconceptions of the individual of his lacking capabilities and the demands of his environment. These preconceptions obstruct the development of self-confidence in dealing with the difficulties brought about by studying Statistics. Factor 3 refers to the Dependency of the person on the teacher’s explanations, their friends’ assistance and the textbook’s examples in order to proceed computing a statistical problem. They would always seek for affirmation before they could move on. Factor 4 depicts Task-Generated Difficulties encountered in Statistics as a cause of anxiety among students. The sight of lengthy solutions and interpreting them makes them anxious. This could also arise from deciding which statistical test to use and what to do with the null hypothesis. Lack of Interest, as shown by Factor 5, had always been a cause of anxiety among students. This deals with the student’s perception of the relevance of Statistics in their lives. They feel that statistics does not fit their personality. A person’s brain is not wired for logical thinking so we could not expect everybody to be interested with numbers. Lastly, Factor 6, labeled as Perfectionism, refers to the ardent desire of the individual not to commit any mistake and get the best grade he could ever get.

Table 5 exemplifies significant differences in the statistics anxiety level of student respondents based on the factors affecting it. T-test results show that graduate and undergraduate students showed significantly different anxiety levels on three factor dimensions, namely: preconceptions (t-value = 1.99, p-value<0.05), lack of interest (t-value = 1.96, p-value<0.05) and perfectionism (t-value = 2.06, p-value<0.05). it is interesting to note that graduate school students manifested a higher anxiety level than undergraduate students on only one factor dimension, that is, inherent fear .

Table 5.Significant Differences on the Statistics Anxiety Level of University Students

Factors Affecting Statistics Anxiety

Undergraduate Graduatet-value

Mean SD Mean SDInherent Fear 4.16 1.20 4.26 1.24 -0.52Preconception 4.63 1.60 4.12 1.63 1.99*Dependency 5.13 1.19 4.79 1.43 1.77Task-generated Difficulties 5.37 1.47 5.07 1.59 1.26Lack of Interest 4.83 1.31 4.42 1.43 1.96*Perfectionism 5.43 1.53 4.92 1.69 2.06*

*significant at 0.05 level

Table 6 depicts results of factor analysis done on the misconceptions perceived by university students. Four items were discarded in part II, so the resulting 13-item instrument measured 3 misconception factor dimensions: Concept-related, Schema-related and Instrument-related, labeled in the order of decreasing explained variance. Factor 1 labeled as Concept-Related nature of statistical misconception refers to the wrong concept of students on certain fundamental concepts in statistics, arising from misuse of their reasoning power; Factor 2, labeled as Schema-Related nature refers to misconceptions related to their prior perceptions or beliefs induced by some situations of the past which had not been corrected for so many years and lastly, Factor 3, labeled as Model-related nature, refers to the misconceptions arising from the use of certain instruments or softwares in learning statistics.

Table 6.Results of Factor Analysis of the Statistics Misconceptions Perceived by University Students

Statistics Misconception Factor DimensionsFactor

LoadingEigenvalue

Variance(%)

Reliability Coefficient

Concept Related 1.92 16.649 74.16Two variables which are significantly related are also significantly different.

.729

Parametric Statistics can be used for variables which are nominal in nature.

.709

There should be an interval of at least 15 days for the test-retest method.

.707

A randomly selected sample is needed to avoid bias. .625Schema Related 2.38 16.013 76.44My fear of Statistics was due to my fear of numbers. .776Numbers in Statistics is meaningless. .770My fear of numbers can be attributed to my elementary / high school teachers.

.746

Artistic people are more inclined to Statistics. .669Only those who are mathematically inclined would enjoy Statistics.

.430

Model Related 1.69 13.656 80.14It would be more beneficial to learn statistical software than manual computations.

.727

A reliable instrument is valid. .633A valid instrument is also reliable. .625The normal curve determines a reliable and consistent survey instrument.

.611

Total Variance Explained 46.317*Kaiser-Meyer Olkin Measure of Sampling Adequacy = 0.840

Table 7 shows significant differences in the misconceptions of the student respondents

regarding statistics using t-test for independent samples. Results indicate that no significant differences were found in any of these factor dimensions. However, it could be noted that graduate school students manifested a higher mean misconception level than the undergraduate students in all factor dimensions.

Table 7.Significant Differences in the Statistics Misconceptions Perceived by University Students

Misconception DimensionsUndergraduate Graduate

t-valueMean SD Mean SD

Concept Related 5.51 1.30 5.56 1.23 -0.26Schema Related 3.62 1.50 3.79 1.40 -0.68Model Related 5.52 1.40 5.66 1.30 -0.61

*significant at 0.05 level

Table 8 exhibits the relationships between causes of statistics anxiety, perceived misconceptions and willingness to learn statistics by student respondents using pearson correlation coefficients. Factors dimensions relating to causes of statistics anxiety exhibited moderate to strong positive relationships with each other, with the weakest existing between inherent fear and perfectionism (r=0.36**) and the strongest existing between dependency and preconceptions(0.72**). The same pattern of relationship exists among the misconception factor dimensions ranging from 0.29 to 0.58. Relationships between cause of anxiety and misconceptions ranges from weak (inherent fear and concept-related, r=0.13) to moderate relationships (inherent fear and schema-related, r=0.49), with the exception of perfectionism and concept-related misconceptions which did not manifest any relationship (r=0.06). willingness to learn posted significant negative relationships to inherent fear (r= -0.15), preconceptions (r=-0.27), lack of interest (r=-0.210 and perfectionism (r=-0.20). it relates positively to the misconception factor dimensions concept-related (r=0.22) and model-related (r=0.16).

Table 8.Relationship between Causes of Statistics Anxiety, Perceived Misconceptions and Students’ Willingness to Learn Statistics

Factor Dimensions

Causes of Statistics AnxietyMisconceptions Factor

Dimensions

Inhe

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Fea

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Pre

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Dep

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Tas

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nera

ted

Dif

ficu

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s

Lac

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In

tere

st

Per

fect

ioni

sm

Con

cept

R

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ed

Sch

ema

Rel

ated

Mod

el R

elat

ed

Preconception 0.63**Dependency 0.56** 0.72**Task-generated Difficulties 0.49** 0.69** 0.77**Lack of Interest 0.58** 0.71** 0.70** 0.57**Perfectionism 0.36** 0.56** 0.53** 0.49** 0.48**Concept Related 0.13* 0.19** 0,28** 0.31** 0.19** 0.06Schema Related 0.49** 0.48** 0.44** 0.35** 0.48** 0.18** 0.29**Model Related 0.22** 0.28** 0.38** 0.36** 0.27** 0.16** 0.58** 0.34**Willingness to Learn -0.15* -0.27** -0.04 -0.02 -0.21** -0.20** 0.22** -0.02 0.16**

*significant at 0.05 level

Discussion

Statistics anxiety has six causality typologies- inherent fear, preconceptions, dependency, task-generated difficulties, lack of interest and perfectionism. Methods of reducing anxiety depend on its cause. Inherent fear and preconceptions that prevent a person from focusing on and successfully completing statistical work, such as predictions of failure, self-degrading thoughts

and preoccupation with the consequences of doing poorly can be managed by using positive mental imagery, disputing negative and self-defeating thoughts with more productive, realistic thoughts and self-hypnosis.

Like all fears and phobias, statistics anxiety is created by the unconscious mind linking a statistics attribute to an emotional trauma which happened in the past. Inherent Fear as a cause of anxiety my have a real-life scare as the original catalyst, the condition can also be triggered by myriad, benign events like tests, solving statistical situational problems, or perhaps seeing someone else experience trauma. But as long as negative association is powerful enough, the unconscious mind thinks he still could not make it. Results are similar to the Everyday Numerical Anxiety typology identified by Bessant (1995) for which inherent fear of numbers had contributed much to the anxiety felt by the students on Statistics. Yet it runs contrary to the findings of Onwuegbuzie (2000) wherein some students with high levels of statistics anxiety have had positive experiences in their previous mathematics courses and did not encounter undue levels of mathematics anxiety, making mathematics anxiety not a precursor of statistics anxiety.

Statistics anxiety is not only due to lack of training or to insufficient skills from which emanates task-generated difficulties. It can also be due to misperception about statistics and the negative experiences in previous statistics classes (Pan, W. & Tang, M, 2005). These situations could have caused their preconceptions about statistics. Lawson et al (2003) suggests that a simple statistical reasoning handout could assist in improving the statistical reasoning of the students so as to rectify their wrong notions about statistical concepts and models and their schema about the course.

Hand (1998) stressed that an undue emphasis on the mathematical foundations of statistics had been detrimental to the discipline. This triggers two opposing causes of statistics anxiety, lack of interest on one hand and perfectionism, on the other hand. This actually hinders the individual to see the relevance of statistics in his field, similar to the worth of statistics factor dimension identified by Cruise (1985) using STARS. Hand (1998) stated further that the discipline of statistics should not be marginalized by an apparent obsession with mathematical necessities.

High levels of anxiety interfere with concentration and memory, which are critical to academic success. But without any anxiety, however, would result to lack of motivation to study for exams, participate in class discussions and do daily assignments. A moderate amount of anxiety actually helps academic performance by creating motivation.

Contributory to statistics anxiety was the lack of connection to the real world (Pan & Tang, 2005). When lectures and assignments gear towards real-life problems and illustrate how statistics can be useful, misconceptions about statistics can be dispelled. Applying the class contexts to daily life and actual research articles makes learning of statistics more meaningful. Their lack of interest, inherent fear and preconceptions may be addressed by considering actual problem situations, actual dummy sets from a survey questionnaire to be used as examples in statistics lectures. Participants in the study of Pan & Tang (2005) stressed the importance and effectiveness of having this carried through so that students can clearly see how statistics can address different aspects of the problem. Applying statistical concepts to solve real-life problems also give students opportunities to reinforce what they have learned, which also addresses the pace issues they felt as a problem (Pan & Tang, 2005).

Suggestions for reduction of anxiety

Despite the prevalence of statistics anxiety and its debilitative nature (Onwuegbuzie and Wilson, 2003), it is interesting to note only a few researches had been done on ways to reduce statistics anxiety. For their part, Garfeld & Chance (2000) posited that students must understand the purpose and logic of statistical investigations. They must know the reason and rigor of statistical inquiries in any problem situation. The situation must be crystal clear in their minds so as to make certain of the appropriate statistical procedure that can respond to it. Problems must be given, not as isolated cases, but as parts of a whole situation where solutions to each problem make use of statistical procedures that contribute to the solution of a bigger problem. Students also need to understand the nature of sampling, why samples are used instead of populations and how to make inferences from samples to population.

Students must understand the process of statistical investigation. They should be familiar with all specific phases of a statistical inquiry, which includes identifying the problem/question, creating a plan, collecting, organizing, analyzing and displaying data, presenting and interpreting results and discussing conclusions and implications of the study. Statistics must not only deal with the application of the formulas but more importantly the reason for using them and the interpretation of the results. As Garfeld and Chance (2000) argues, students must develop statistical literacy. They must know how to pose critical, reflective questions about numerical arguments, data reported in the media and the reports of their classmates. They should be able to distinguish the reliability of the measurement scale used, the representation adequacy of their sample and the sensibility of the claims being made out of the results.

Students must be able to develop useful statistical disposition. They should be able to appreciate the role of and randomness in the world and the role of statistical methods and planned experiments as useful scientific tools and powerful means for making personal, social and business-related decisions in the face of uncertainty (Garfeld & Chance, 2000). They must be able to make use of reason with statistical ideas and make sense of statistical information when making inferences and interpreting results. This could help them see the relevance of statistics in their field and later apply its procedures in their line of work.

Other researchers advocated the use of humor (Wilson, 1999), humorous cartoon examples (Schacht and Stewart, 1990), journal writing (Sgoutas-Emch and Johnson, 1998; Onwuegbuzie et al, 1997; Wilson, 1999), untimed and open notes examinations (Wilson, 1999; Onwuegbuzie, 2000), performance assessments (Elliot, 1995) and working with a partner in the computer lab (Wilson, 1999) as effective ways of reducing statistics anxiety.

Students tend to develop a shallow and isolated understanding of key concepts and do not develop the deep understanding needed to integrate these concepts and use these in making inferences about the population. They might be able to give correct answers and even get good grades, yet still not understand the statistical ideas and maintain misconceptions (Garfeld & Chance, 2000).

In the study of Delmas et al (2006), results revealed that students still had difficulty in identifying appropriate types of graphic representations such as interpreting boxplots and did not demonstrate a good understanding of important design principles and concepts related to probability, sampling variability and inferential statistics.

Conclusion

The prevalence of statistics anxiety and misconceptions among university students can be addressed from both supportive environment and multidimensional instructional strategies. The supportive environment helps students reduce their anxiety and misconceptions and the application oriented instruction makes it easier for them to learn statistics more effectively.

General orientation to learning combines study strategies and motivational dispositions, which individually and jointly impact academic performance. Differences in approach can affect students’ learning preferences, beliefs about the discipline, feelings of self confidence, attitudes and anxiety levels. Clarity as to what the teacher expects and how the students will be evaluated is necessary. Uncertainty about teacher expectations can lead to anxiety, concern with unimportant details, inability to see the whole of the material and other impediments to learning about the subject.

References

Bell, J. (2001). Length of course and levels of statistics anxiety. Education, 121(4), 713-716.

Bell, J. (1998). International students have statistics anxiety too! Education, 118(4), 634-637.

Berk, R.A. & Nanda, J.P. (1998). Effects of jocular instructional methods on attitudes, anxiety and achievement in statistics courses. Humor, 11, 383-409.

Bessant, K.C. (1995). Factors associated with types of mathematics anxiety in college students. Journal of Research in Mathematics Education, 26(4), 327-345.

Birenbaum, M. & Eylath, S. (2004). Who is afraid of statistics? Correlates of statistics anxiety among students of educational sciences. Educational Research 36(1), 93-98.

Borresen, C.R. (1990). Success in introductory statistics with small groups. College Teaching, 38, 26-28.

Cates, C. & Rhymer, K. (2003). Examining the relationship between mathematics anxiety and mathematics performance: an instructional hierarchy perspective. Journal of Behavioral Education, 12(1), 23 – 34.

Cruise, R., Cash, R. & Bolton D. (1985). Development and validation of an instrument to measure statistical anxiety. Proceedings of the American Statistical Association, 92-96.

D’Andrea, L. & Waters, C. (2002). Teaching Statistics using short stories; reducing anxiety and changing attitudes. International Conference on Teaching Statistics Icots6.

Delmas, R., Garfield, J., Ooms, A. and Chance, B. (2006). Assessing students’ conceptual understanding after a first course in statistics. A paper presented at the Annual Meetings of The American Educational Research Association, San Francisco, California.

Filebrown, S. (1994). Using projects in elementary statistics course for non-science majors. Journal of Statistics Education, 2(2).

Forte, J.A. (1995). Teaching statistics without sadistics. Journal of Social Work Education, 31, 204-218.

Garfeld, J. & Chance, B. (2000). Assessment in statistics education: issues and challenges. Mathematical Thinking and Learning, 2(1&2), 99-125.

Hand, D. (1998). Breaking misconceptions – statistics and its relationship to mathematics. The Statistician, 47, 245-250.

Lawson, T., Schiers, M., Doellman, M., Grady, G. & Kelnhofer, R. (2003). Enhancing students’ ability to use statistical reasoning with everyday problems. Teaching of Psychology, 30(2), 107-110.

Mevarech, Z. (1983). A deep structure model of students’ statistical misconceptions. Educational Studies in Mathematics, 14, 415-429.

Murtonen, M. and Lehtinen, E (2003). Difficulties experienced by education and sociology students in quantitative methods courses. Studies in Higher Education, 28(2), 171-185.

Onwuegbuzie, A.J. (2004). Academic procrastination and statistics anxiety. Assessment and Evaluation in Higher Education, 29(1), 3-18.

Onwuegbuzie, A. & Wilson, V. (2003). Statistics anxiety: Nature, etiology, antecedents, effects, and treatments—a comprehensive review of the literature. Teaching in Higher Education, 8(2), 195–209.

Onwuegbuzie, A.J. (2000). Attitudes toward statistics assessments. Assessment and Evaluation in Higher Education, 25(4), 321-339.

Onwuegbuzie, A.J. (2000). Statistics anxiety and the role of self perception. The Journal of Educational Research, 93(5), 323-330.

Onwuegbuzie, A.J., Daros, D & Ryan, J. (1997). The components of statistics anxiety: a phenomenological study. Focus on Learning Problems in Mathematics, 19(4), 11-35.

Pan, W. & Tang, M. (2005). Students’ perception on factors of statistics anxiety and instructional strategies. Journal of Instructional Psychology, 32(3), 205-214.

Pan, W. & Tang, M. (2004). Examining the effectiveness of innovative instructional methods on reducing statistics anxiety for graduate students in the social sciences. Journal of Instructional Psychology, 31(2), 149-159.

Rosenfeld, RA. (1978). Anxiety and learning. Teaching Sociology, 5(2), 151 – 166.

Schacht, S. & Stewart,B.J. (1990). What’s funny about statistics? A technique for reducing student anxiety. Teaching Sociology, 18, 52-56.

Sgoutas-Emch,S.A. & Jonhnson, C.J. (1998). Is journal writing an effective method of reducing anxiety toward statistics? Journal of Instructional Psychology, 25, 49-57.

Watson, F., Kromrey, J., Ferros, J., Lang, T. & Hogarty, K. (2003, April). An assessment blue-print for EncStat: a statistics anxiety intervention program. Paper presented at the annual meeting of the American Educational Research Association, Chicago, II.

Wilson, V.A. (1999). Reducing statistics anxiety: a ranking of sixteen specific strategies. Paper presented at the annual meeting of the Mid-South Educational Research AssociationPoint Clear, AL, November.

Yunis, F.A. (2006). Factors influencing the psychology students in dealing with statistics courses. International Conference on Teaching Statistics Icots-7.

Zeidner, M. (1990). Does test anxiety bias scholastic aptitude test performance by gender and socio-cultural group? Journal of Personality Assessment, 55(1 and 2), 145-160.