CONFERENCE PAPER: Presented at the 4th International Conference on Education and
New Learning Technologies (EDULEARN12), Barcelona (Spain)
TOO AFRAID TO LEARN?! ATTITUDES TOWARDS STATISTICS AS
A BARRIER TO LEARNING STATISTICS AND TO ACQUIRING
QUANTITATIVE SKILLS
Koen Slootmaeckers1
1
University of Leuven (Belgium)
Koen.slootmaeckers@soc.kuleuven.be
Abstract
Quantitative skills are important for social science students to study and understand social reality.
Students, however, tend to avoid quantitative methods and that they even fear them. This study aims
to understand the negative feelings students have toward statistics. By drawing on a recent survey
among political science students, we simultaneously assess the influence of dispositional, courserelated, and person-related factors on the different dimensions of statistics anxiety. Secondly, and
more importantly, this study aims to provide insights in the relation between these attitudes and the
learning statistics, and the long-term retention of quantitative skills. Our findings suggest that the
introduction of quantitative methods throughout the curriculum increase student’s interest in statistics,
and can foster learning and long-term retention.
Keywords: Statistics anxiety, Learning statistics
1
INTRODUCTION
Why are social science students afraid of statistics? In society, numbers are omnipresent. Media,
corporations and politicians overwhelm people with quantitative information. Numeric skills are
important to avoid deception and to function in society. By consequence, these skills are also
important for social science students to grasp and understand social reality [1]. We see, however, that
these students tend to avoid quantitative methods and even fear them. If quantitative skills are
becoming more important in society and social science, how can we understand this statistics anxiety?
And more importantly, to what extent is this statistics anxiety a barrier preventing students from
developing a constructive and critical attitude toward data?
In light of the ‘Educational Project on Overcoming Statistics anxiety’, – initiated in the Political Science
department of our university – we conducted a survey with all students enrolled in the political science
programme [2]. This survey contained the Survey of Attitudes Toward Statistics (SATS) scale. For the
third year of the Bachelor programme and for the Master programme a measure of quantitative skills
was included as well; this data is used to map statistics anxiety and its covariates.
For the second and main goal of the paper, the focus shifts from statistics anxiety as dependent
variable to statistics anxiety as an independent variable and as a barrier to learning statistics.
Whereas most studies focus on the relationship between attitudes and achievement in statistics
course, we expand the focus to the relation of statistics anxiety with long-term retention of statistics.
This cross-sectional study will provide new insights into statistics anxiety as a barrier to long-term
learning of quantitative methods
This paper, a first step in a longitudinal analysis of statistics anxiety, contributes both to the
understanding of the origin and the effects of statistics anxiety. Furthermore, it provides first insights
into the evolution of statistics anxiety throughout the programme and more importantly, into statistics
anxiety as a barrier to long-term learning. A longitudinal follow-up study will test the causality of these
findings.
After a brief overview of the literature on statistics anxiety, this paper will present the results of the
analyses of the antecedents of statistics anxiety, followed by the results of the test for the effect of
attitudes towards statistics on the learning of statistics and the long-term retention.
CONFERENCE PAPER: Presented at the 4th International Conference on Education and
New Learning Technologies (EDULEARN12), Barcelona (Spain)
2
ON THE CAUSES AND EFFECTS OF STATISTICS ANXIETY
Students perceive statistics as ‘the worst course taken in College’ [3] or as ‘inherently uninteresting,
quite difficult and, like immunization injections they received as children, a necessary but quite
unpleasant aspect of growing up’ [4, p.15]. Statistics courses are not only a negative experience, but
students often are ‘scared to death’ by the idea [5], [6]. Onwuegbuzie and Wilson [5, p.196] describe
statistics anxiety as the ‘anxiety that occurs when a student encounters statistics in any form or at any
level’. This anxiety does not necessary have to rise from bad training or insufficient skills [7], but from
students’ misperceptions about both statistics and their (lack of) mathematical skills, from warnings
from their peers, or from the ‘horror stories’ they have heard [1], [4], [5], [7]. For an extensive review
see Onwuegbuzie and Wilson [5].
There is a vast amount of studies studying the antecedents of statistics anxiety [7], [8]. Factors
inducing statistics anxiety are often classified in three categories [5], [7], [9]: dispositional, courserelated, and person-related factors [9]. The ‘dispositional factors’ [5], [7], [10] are those factors dealing
with psychological and emotional characteristics of students, such as attitudes, perceptions, and
(perceived mathematical) self-concept [9].
The course-related elements influencing statistics anxiety, also referred to as the ‘situational factors’
[5], [7], [8], [10], are factors that immediately result from statistics courses [9]. These can be, for
example, the nature of the course (whether it is an elective course or a mandatory one) [5], prior
knowledge [8], course grade [8], and course and/or teacher evaluation [5], [8], [9]. Furthermore, these
situational or course-related factors expand to prior mathematical courses. It is been shown that e.g.
prior experiences with mathematics and mathematic grades are related with statistics anxiety as well
[5], [11].
The person-related antecedents, also called the ‘environmental’ factors [5], [9], are the sociodemographic characteristics, e.g. gender, age, and educational level, of the students.
Although all three clusters are deemed important in the study of statistics anxiety, studies taking the
tree categories together in one model are, to our knowledge, scarce. Most studies only focus on one
aspect at the time [9], [12], [13], [14], [15]. To address this lacuna, is exactly one of the aims of this
study.
At the same time, there is a small but growing body of studies showing a relation between attitudes
toward statistics and statistics achievement [16], [17], [18], [19], [20], [21]. The meta-analysis of
Emmioğlu and Çapa-Aydin [16] indicates a positive relationship between both students’ affect toward
statistics and their perception of their cognitive competence on the one hand, and obtained grades on
the other hand. The analysis also shows a positive but small effect on the grades of valuing of
statistics and the perception of difficulty, with all attitudes coded that a higher score means a more
positive attitude.
All studies that focus on the effects of statistics anxiety on the learning of statistics deal with the
achievements in statistics courses. To our knowledge, there is no study on the relation between
attitudes toward statistics and the long-term retention of statistics (or quantitative skills, more broadly).
To respond to the growing importance of statistics in the field, long-term retention of quantitative skills
should be a goal of higher education, as it will prepare students for their future careers. Hence the
second aim of this study, i.e. studying the attitudes toward statistics as a potential barrier for the
acquiring of quantitative skills in the long run.
3
DATA
In light of the educational project (EPOS), a survey has been conducted in al years of the political
science programme. A pen and paper survey has been handed out in the first class of the course
‘Research Methods’ in the first year (n= 630, all social sciences students and other programmes) and
in the first class of the course ‘Practicum for Political Science’ of the second year (n=39, all second
year political science students). As both classes are mandatory, we have a response rate of about
100% for the first two years of the Bachelor programme. For the third year students (n= 41, response
rate of 77,36%) and for the Master programme students (n=116, response rate of 63,74%), we
conducted a web-survey. In both surveys the Survey of Attitudes Toward Statistics (SATS-36) [22]
was included. In addition to the SATS-36 both surveys also contained questions about prior
experiences with mathematics and/or statistics, as well as questions on socio-demographic
parameters.
CONFERENCE PAPER: Presented at the 4th International Conference on Education and
New Learning Technologies (EDULEARN12), Barcelona (Spain)
3.1
Statistics anxiety
For the measurement of statistics anxiety, we make use of the SATS-36 of Schau et al. [22]. This
scale is described to consist of six subcomponents: Affect, Cognitive Capacity, Value, Difficulty,
Interest, and Effort. However, as the effort subscale does not fit the context of the Third bachelor and
Master students, they are not enrolled in a statistics course, this subscale is not included. We use thus
a reduced version of the scale. Contrary to the described structure of the SATS-scale, our factor
analysis (table 1) fails to distinguish the ‘affect’ subscale from the other factors.
Table 1: Factor Loadings SATS-32 (Pattern Matrix)
low scoring (threshold: 0,4) or ambiguous scoring items not shown
Factor
Interest
v3 I will like statistics
v12 I am interested in being able to communicate statistical
information to others
v19 I will enjoy taking statistics courses
v20 I am interested in using statistics
v23 I am interested in understanding statistical information
v29 I am interested in learning statistics
v4 I will feel insecure when I have to do statistics problems
v5 I will have trouble understanding statistics because of how
I think
v6 Statistics formulas are easy to understand
v26 I will make a lot of math errors in statistics
v32 I will understand statistics equations
v35 I will find it difficult to understand statistical concepts
v7 Statistics is worthless
v9 Statistics should be a required part of my professional
training
v10 Statistical skills will make me more employable
v13 Statistics is not useful to the typical professional
v16 Statistical thinking is not applicable in my life outside my
job
v21 Statistics conclusions are rarely presented in everyday life
v25 I will have no application for statistics in my profession
v33 Statistics is irrelevant in my life
v8 Statistics is a complicated subject
v15 I will get frustrated going over statistics tests in class
v18 I will be under stress during statistics class
v24 Learning statistics requires a great deal of discipline
Difficulty
Value
Cognitive
Capacity
-0,656
-0,506
-0,674
-0,729
-0,674
-0,867
-0,665
-0,843
0,430
-0,418
0,491
-0,479
0,535
-0,427
-0,487
0,628
0,476
0,456
0,674
0,689
0,400
0,504
0,538
0,583
Method: Principal Axis Factoring, Oblimin rotation with Kaiser Normalization
The obtained factor can be interpreted by using the original scoring scheme of Schau [23]. The
interest subscales means: “students’ level of individual interest in statistics” (Cronbach’s alpha = 0,87).
Difficulty can be understood as: “students’ attitudes about the difficulty of statistics as a subject”
(Cronbach’s alpha = 0,74). The value subscale can be defined as: “students’ attitudes about the
usefulness, relevance, and worth of statistics in personal and professional life” (Cronbach’s alpha =
0,81). Finally, Cognitive competence means: “students’ attitudes about their intellectual knowledge
and skills when applied to statistics” (Cronbach’s alpha = 0,82). For each factor we recoded the items
in order to construct mean scales, with range 1-7, ‘1’ meaning a negative attitude and ‘7’ meaning a
positive attitude toward statistics.
3.2
Antecedents of statistics anxiety
For the dispositional factors we include a measure for mathematics self-concept, i.e. students’
perception about themselves in relation to mathematics, and for the perception of use of statistics in
the future career. Regarding the latter, students were asked to answer on a 7-point Likert scale to
what extent they think they will use statistics in their future job, with 7 meaning ‘I’ll use statistics
frequently in my future job’. For mathematical self-concept, two measures were included. First,
CONFERENCE PAPER: Presented at the 4th International Conference on Education and
New Learning Technologies (EDULEARN12), Barcelona (Spain)
students were asked to evaluate their own mathematical skills (statistics skills for third bachelor and
master students) on a 7-point Likert scale. Second, a measure of students’ self-confidence about their
ability to learn statistics was included for the first and second bachelor students.
The course-related (situational) factors in this study probe the students’ experience with statistics. We
included both subjective and objective experience. For subjective experience, students were asked to
state how experienced they are with statistics on a 7-point Likert scale, with 7 meaning very
experienced. Objective experience was measured for the first and second year students by the
number of hours of mathematics classes each week in the last year of high school as a proxy. For the
third years and master students, it was measured by the amount of statistics classes taken in higher
education. For the third year and master students we also included experience with statistics in nonmethodological courses.
Finally, for person-related (environmental) factors gender, age and year of the programme the
students are enrolled in are included in the model.
3.3
Measurement of achievement in statistics
We have two measures of achievement in statistics. First, we have the grades the first year students
obtained for the exam of the course ‘introductory statistics’ taught in the first semester 2011-2012.
This grade serves as a proxy for the success in learning statistics.
For the third year and master students, we have a measure for the long-term retention of quantitative
methods. In collaboration with educational scientists, we constructed a questionnaire about
quantitative skills. These questions are based on exercises from the ARTIST-project
(https://app.gen.umn.edu/artist/); the Dutch translation of Garfield’s questionnaire ‘Statistical reasoning
Assessment’ [24] and the practice book of Moore & McCabe [25]. Questions of this section are dealing
with interpreting OLS regression results, significance tests, histograms etc. From the responses on
these questions a variable has been computed which represents the percentage of correct responses
relative to the number of answered questions (90% of the students answered 20 questions out of 25).
4
4.1
RESULTS
Antecedents of statistics anxiety
Table 2 shows the results of the OLS regressions testing the effects of the different anxiety inducing
factors on the attitudes toward statistics, for both groups of students, i.e. first and second year
bachelor students, and third year and master students.
Looking at the effect of the dispositional factors, the results show that the perception of
mathematical/statistical skills has, for the two groups, a positive effect on ‘interest’ (b=0,153 and
b=0,298), ‘cognitive competence’ (b=0,260 and b=0,461), and ‘difficulty’ (b=0,175 and b=0,442). The
perception of the future use of statistics is positively related with ‘interest’, ‘cognitive competence’ and
‘value’ for both groups, and for the third year and master students it has a positive effect on ‘difficulty’
too. For the first and second year bachelor, the self-confidence of the ability to learn statistics has a
positive effect on all four attitudes toward statistics, with the effect on value being rather small.
With regards to the course-related factors, the results show that subjective experience has a small
positive effect on the ‘value’ (b=0,046) for the first and second year students. For the third and master
students it has a negative effect on ‘difficulty’ (b=-0,167) and on ‘interest’ (b=-0,134, p<0,10). Students
who had more hours of mathematics classes in high school have more positive attitudes about their
cognitive competence (b=0,077). The number of statistics courses taken on the other hand, does not
have an effect on the attitudes towards statistics. Contrary to this, we find that encountering
quantitative methods during substantive courses has a positive effect on interest (b=0,305).
Last, we have the person-related factors. Age only has a small positive effect on ‘interest’ for the first
and second year students (b=0,044). Women are more negative about their ‘cognitive competence’
and the difficulty of statistics as a subject. Second year students are less interested in statistics than
first year students are, but they have more positive attitudes with regards to ‘value’ and ‘difficulty’.
Third year students have more negative attitudes toward all subscales except difficulty, than master
students do.
CONFERENCE PAPER: Presented at the 4th International Conference on Education and
New Learning Technologies (EDULEARN12), Barcelona (Spain)
Table 2: Results of regressions analyses with the 4 factors of the SATS-32 scale as dependent
variables. Statistics: Unstandardized regression coefficients (b), standardized coefficients (B)
2
and coefficient of determination (R ).
First and Second Bachelor students
Dispositional
factors
Perception of
mathematics/statistics
1
skills
Perception of use
statistics in future job
Self-confidence of
ability to learn
statistics
Course-related
factors
Subjective
experience with
statistics
Mathematic classes
in High School
Interest
Cognitive
Competence
Value
B
(B)
b
(B)
b
(B)
b
(B)
0,153***
(0,193)
0,260***
(0,349)
0,019
(0,028)
0,307***
(0,365)
0,056*
(0,071)
0,173***
(0,239)
Cognitive
Competence
Value
Difficulty
b
(B)
b
(B)
b
(B)
B
(B)
0,175***
(0,230)
0,298***
(0,346)
0,461***
(0,646)
0,076
(0,118)
0,442***
(0,571)
0,351***
(0,498)
0,001
(0,001)
0,449***
(0,440)
0,102
(0,121)
0,386***
(0,505)
0,136*
(0,148)
0,259***
(0,381)
0,093***
(0,154)
0,232***
(0,334)
-0,022
(-0,029)
0,024
(0,034)
0,046*
(0,073)
0,043
(0,060)
-0,134
(-0,151)
a
-0,052
(-0,074)
0,018
(0,029)
-0,167*
(-0,220)
0,003
(0,005)
0,077***
(0,110)
0,019
(0,030)
0,033
(0,046)
-0,024
(-0,021)
0,023
(0,025)
-0,077
(-0,092)
-0,021
(-0,021)
0,305**
(0,181)
-0,005
(-0,003)
0,114
(0,090)
-0,020
(-0,013)
Difficulty Interest
Number of statistic
courses taken
Quantitative material
in nonmethodological
courses
Person-related
factors
Age
0,044***
(0,118)
Women 0,130
(reference: Men) (0,060)
Second Bachelor
-0,346*
(reference: First
(-0,078)
Bachelor)
Third Bachelor
(reference: Masters
programme)
Constant
R²
N
a
Third Bachelor and Master students
0,599*
0,348***
a
0,002
(0,005)
0,008
(0,027)
-0,001
(-0,003)
0,030
(0,091)
0,006
(0,024)
0,024
(0,099)
-0,012
(-0,040)
-0,275***
(-0,136)
-0,008
(-0,004)
-0,293***
(-0,142)
-0,022
(-0,009)
-0,341**
(-0,173)
-0,166
(-0,093)
-0,258
(-0,121)
0,108
(0,026)
0,234*
(0,063)
0,277*
(0,065)
-0,475**
(-0,177)
-0,244
(-0,109)
a
-0,274
(-0,136)
a
-0,205
(-0,085)
1,969***
1,252***
2,745***
1,468***
0,425
0,555***
0,383***
645
0,338***
0,451***
0,520***
155
2,840
***
0,367***
a
2,586***
0,340***
p < 0,10; * p < 0,05; ** p < 0,01; *** p < 0,001
1
for first and second bachelor students perception of mathematical skills were assessed; for third Bachelor and Master students
perception of statistical skills were assessed
4.2
Statistics anxiety and learning statistics
Table 3 shows the results of the regression analyses that test the effect of attitudes on both learning
statistics (model 1) and the long-term retention of quantitative methods (model 2), controlled for the
antecedents shown above.
CONFERENCE PAPER: Presented at the 4th International Conference on Education and
New Learning Technologies (EDULEARN12), Barcelona (Spain)
Table 3: Results of regressions analyses with the ‘grades on
statistics course’ as dependent variable for the first bachelor
students and the ‘long-term retention of quantitative methods’ as
dependent variable for third bachelor and master students.
Statistics:
Unstandardized
regression
coefficients
(b),
2
standardized coefficients (B) and coefficient of determination (R )
2
and adjusted R .
Model 1:
Statistics
course grades
b
(B)
-0,759**
Interest
(-0,160)
0,133
Cognitive competence
(0,026)
1,099***
Value
(0,194)
-0,057
Difficulty
(-0,012)
-0,083
Age
(0,042)
Perception of mathematics/statistics
0,770***
1
skills
(0,209)
-0,005
Perception of use statistics in future job
(-0,001)
0,058
Self-confident of ability to learn statistics
(0,017)
-0,062
Subjective experience with statistics
(-0,018)
0,504
Women (reference: Men)
(0,051)
1,173***
Mathematic classes in High School
(0,335)
0,100
Expected grades for statistics
(0,042)
Quantitative material in nonmethodological courses
Constant
-0,654
2
R
0,232***
2
Adjusted R
0,211
n
434
a
1
Model 2:
Long-term
Retention
b
(B)
a
2,618
(0,215)
0,980
(0,069)
0,617
(0,037)
3,739**
(0,288)
0,049
(0,012)
-2,699*
(-0,260)
-0,625
(-0,051)
a
1,758
(0,174)
-3,436
(-0,122)
5,599***
(0,279)
1,241
0,298***
0,241
136
p < 0,10; * p < 0,05; ** p < 0,01; *** p < 0,001
Mathematical skills for the first model; statistics skills for the second model
Model 1, estimated for first year students, shows that, contrary to the expectation, students with
positive attitudes with regards to interest have lower grades (b= -0,759). Value, on the other hand, is
positively related with obtained grades (b = 1,099). Of the anxiety inducing factors, we find a positive
effect of mathematical self-concept and the number of mathematic classes taken in high school. With
regards to gender, we see that there is no difference in grades between men and women, suggesting
that the difference in attitudes do not translate to grades.
If we take a look at the long-term retention of quantitative methods (model 2), the relation between the
attitudes and the acquiring of quantitative skills is somewhat different. Whereas there was no relation
between difficulty and the grades for statistics, the ‘difficulty’ scale is positively related with the longterm retention. Better attitudes concerning the difficulty of statistics are related with a better long-term
CONFERENCE PAPER: Presented at the 4th International Conference on Education and
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retention of quantitative methods (b= 3,739). The perceived statistics skills, on the other hand, have a
negative effect, whereas it had a positive effect on the grades in the first year. Concerning experience
with statistics, we find that the degree of use of quantitative material in non-methodological courses is
positively related with the long-term retention of quantitative methods. Finally, there are indications
(significance level: p<0,10) that interest and subjective experience with statistics are positively related
with the long-term retention of quantitative methods (b= 2,618 and b= 1,758, respectively).
5
CONCLUSION
The aims of this paper are twofold. First, it explores the different antecedents of statistics anxiety in
one model, making a distinction between students in the beginning of their higher education career
and students at the end of their career. Next, the main goal of this paper is to study the relation
between attitudes toward statistics and the learning of statistics and the long-term retention of
quantitative skills. This study makes use of the survey conducted, as part of the EPOS-project, with all
political science students of our university. By means of OLS regressions the relations between the
dispositional, course-related, and person-related anxiety inducing factors are assessed. The results
show us that all three types of antecedents have their influence on the attitudes toward statistics.
However, we see some differences between students from the first two years of the programme and
students from the last two years. For example, whereas the effect of subjective experience with
statistics is positively related with the valuing of statistics for the first group, it is negatively related with
both interest and difficulty for the graduating students. In addition, the analyses show that the number
of statistics courses taken has no influence at all on the attitudes toward statistics; it is the extent to
which quantitative material is used in non-methodological (substantive) courses that triggers students’
interest in statistics. This can be seen as a strengthening of Markham’s [26] call for the use of
statistics in substantive courses. Furthermore, this latter result suggests that one should introduce
statistics not in one course, but in as many as possible, preferably throughout the whole curriculum.
With regards to the second aim of this study, the attitudes towards statistics have an effect on the
learning of statistics and on the long-term retention of quantitative methods. However, the negative
effect of interest in statistics for the first year students shows that negative attitudes toward statistics
are not always a barrier for learning. This is in line with the possible facilitative component of statistics
anxiety, i.e. a “certain amount of statistics anxiety may prevent students from being too complacent in
preparing for an upcoming examination” [5, p. 200]. Students with less interest in statistics might study
harder to make sure they do not fail for the examination and have to take the exam twice. The valuing
of statistics is positively related with students’ grades, suggesting that making students see the value
of statistics for their future career can be an effective way of facilitating the learning process. On longterm retention, we find negative attitudes about both interest and difficulty a barrier for retention of
quantitative methods. The extent in which quantitative methods are used in substantive courses on the
other hand is a facilitating factor for the long-term retention. Next, the results show that the perception
of one’s experience with statistics is positively related with the long-term retention of quantitative
methods, however, students should not become too over-confident about their own statistics skills, as
the perception of statistics skills is negatively related with long-term retention.
What can be learned from this study for the practice of teaching statistics? For learning statistics in an
introductory course, the main thing one should focus on, is that students see the value of statistics for
their future career. A possible tactic to do this, can be by using examples from the sphere of interest of
the students and/or real life examples [7]. For the long-term retention of quantitative methods,
students should practice statistics more often, so they feel/are more experienced with the subject,
without being too confident of their skills. The analysis shows that introducing statistics in substantive
courses is a helpful tactic. This is in line with Markham’s [26] call for introducing statistics in
introductory courses, and in line with Adeney and Carey’s [27], [28] view on contextualising
quantitative methods. Last, this result can be seen as a support for the approach of the EPOS project,
which aims to integrate quantitative methods in a structured way throughout the whole curriculum [2].
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CONFERENCE PAPER: Presented at the 4th International Conference on Education and
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