Table Of ContentThe impact of misunderstanding the
nature of statistics
Kai Ruggeri, Martin Dempster & Donncha Hanna
S
TATISTICSis one of the most common and vernaculars. However, at a very minimum,
topics across disciplines and levels of covering the general nature of statistics and
study (Blumberg, 2001). This is mainly its application to study is still fundamental.
due to a rise in need for students to apply In a much earlier paper on statistics edu-
analytical skills in almost any academic area cation, Caine et al. (1978) contest that how
(Garfield et al., 2001) or profession (Bakker statistics is taught must vary because stu-
et al., 2004). The statistical component of dents’ motivation may change based on their
academic programmes is considered critical, discipline. For students on a course where
and it is listed as one –if not the –focal point statistics is not considered requisite (e.g.
of higher education (Garfield et al., 2002). education, political science), the motivation
Lessons learned by researchers in the from the perspective of the student may be
teaching of statistics reveal much about the simply to demonstrate additional skills when
variety of obstacles faced by lecturers and applying for postgraduate courses and work.
students, such as statistics anxiety, negative Statistics is a vital portion of the psy-
attitudes, deficits in maths backgrounds, and chology programme both in the UK and glob-
expectations (Ruggeri, 2009). To this end, ally (Blumberg, 2001). Quantitative skills play
Batanero (2004) expressed the need for con- such a pivotal role in students succeeding in a
tinued work on identifying and addressing psychology degree and thus advancing into
these problems explicitly. This particularly skilled professions, that the way statistics is
included distinguishing statistics from maths taught and integrated into any course has
and learning more about the nature of issues been – and continues to be – a key area of
in statistics education across disciplines. research (Batanero, 2004). But, as Baloglu
Statistics is a unique subject in any cur- (2003) clearly shows, the extensive issues stu-
riculum and requires a distinct way of dents report in learning statistics suggests
thinking (Ben-Zvi & Garfield, 2004). While more than it merely being a difficult subject.
listing a variety of goals within a statistics Common goals from published work on
course, Blalock (1987) noted from experi- teaching statistics classes include over-
ence in teaching that learning statistics is not coming obstacles presented by anxieties,
merely being able to memorise and regurgi- beliefs, and negative attitudes toward statis-
tate formulae, but to truly be able to imple- tics (Schau, 2003). A limited but growing
ment critical quantitative skills to solve real amount of work has been done to confront
problems. From this first-person account, it is each of these (e.g. Baloglu, 2003; Onwueg-
apparent that this is not necessarily simple, as buzie, 2004) and characterise the affect on
statistics – like mathematics – is a language, learning and applying ways to address prob-
which means its vocabulary and rules must be lems in teaching statistics. The available lit-
applied to be useful (Conners et al., 1998). erature clearly indicates that this may be the
Because statistics is taught across many disci- most important aspect of statistics education
plines, there is not a single way of deter- on which research should focus but as this
mining exactly which concepts are most work will show, that idea –and all those listed
relevant in any classroom (Wilson, 1997), above –may perhaps overlook a central flaw
much like a language and its many dialects in even introducing students to statistics.
Psychology Teaching Review Vol. 17 No. 1 35
© The British Psychological Society 2011
Kai Ruggeri, Martin Dempster & Donncha Hanna
The following results were selected from included to explore assumptions made in
a comprehensive series of studies of statistics previous research. However, for the purpose
education in undergraduate psychology. The of this study, results relate only to three ques-
main focus of the overarching study was to tions on how students compared statistics to
determine the nature of statistics anxiety and other topics in psychology: ‘How useful/dif-
attitudes toward statistics by using multiple ficult/enjoyable, do you think, is the statis-
measurements and analyses. While there tics part of the psychology curriculum to
were considerable gains in understanding, it other topics in psychology?’ In the first
was perhaps the simplest questions that pro- instance, the question was worded ‘will be’
vided the best insight. and in the first two instances, cognitive psy-
chology, individual differences and percep-
Method tion were listed as examples of other topics.
Participants
All participants were first-year undergrad- Procedure
uate psychology students enrolled in an Questionnaires were distributed to first-year
undergraduate psychology course in students at the beginning of compulsory lab-
Northern Ireland. Only participants who oratory classes. Collection dates coincided
completed each collection were included in with specific aspects of the first year: before
the analysis (Table 1). any statistics had been undertaken, after the
first statistics assignment, at the beginning of
Instrument the new term, and before the final exam.
The full measure was comprised of the Sta- A detailed breakdown of what topics had
tistics Anxiety Rating Scale (Cruise & been taught previous to each collection, is
Wilkins, 1980) and the Survey of Attitudes provided in Table 2. Students were given no
Toward Statistics (Schau et al., 1995). Addi- time limit in which to complete the survey
tionally, various questions relating to student and it took on average between 12 and 15
backgrounds and expectations were minutes to finish.
Table 1: Participant demographics by collection.
Mean Age Male Female
Collection 1 19.97 33 113
Collection 2 20.2 34 114
Collection 3 20.46 27 97
Collection 4 20.66 29 96
Table 2: Topics covered before and during test collections.
Collection Term-Week (of 12) Subjects previously covered
1 1–4 None*
2 1–11 Central Tendency, Correlation, Chi-Square,
Group Comparison, Repeated Measures
3 2–1 Inference
4 2–11 T-tests, ANOVA, Experimental Design
*Specific previous experience was not collected.
36 Psychology Teaching Review Vol. 17 No. 1
The impact of misunderstanding the nature of statistics
Results First, to have such a dramatically consis-
Over the course of the first academic year, tent drop in the enjoyment level, it seems
there is some change in student perceptions unlikely that students had ever interacted
of statistics (see Figure 1). The most imme- with any discernable amount of statistics in
diately visible change is the decrease in sta- their education. Had this been the case, such
tistics enjoy-ability between the first and change would have been so improbable that,
second collections, and this lower score is unless some particular aspect (e.g. teaching)
maintained for the remainder of the year. was excessively poor, initial expectations
Friedman tests showed neither the per- would not have been so thoroughly unmet.
ception of statistics as being useful nor diffi- Also, to anticipate such a high level of enjoy-
cult changed significantly during the year. ment out of anything only to in turn have
Usefulness was rated generally at the median essentially the opposite experience indicates
of the one-to-five scale, while difficulty was students were not generally even aware of
consistently higher at all points. Enjoyment the real nature of the subject. These two con-
of statistics, compared to other parts of the cepts are not mutually exclusive and likely
psychology course, varied significantly are collectively responsible, though the
(χ2(3,84)=134.59, p<.001), especially when second is the more problematic.
comparing subsequent collections to the If students – who were presumably high
baseline results. performers in school and committed to their
studies enough to pursue tertiary degrees –
Discussion do not accurately understand even the pur-
A first impression of the results may be pose of statistics, it likely represents a larger
simply that students do not enjoy the actual obstacle. Potentially, that represents a false
learning of statistics in university. Whether perception most people have of not only the
that was related to the subject, the teaching, subject but the entire use of statistics.
the assessment, or a combination of those In that mainstream information is so
and other factors may be worth addressing heavily filled with so-called statistical infor-
but alone, it is hardly a surprising finding. mation in the form of means, percentages,
When considering these results more thor- and raw data, a distortion occurs with the
oughly, though, much more is gained. way real statistics are viewed. This may not be
Figure 1: Change in perceptions of statistics across year.
4.5
Statistics is difficult
4.0 Statistics is useful
se 3.5 Statistics is enjoyable
n
o
p 3.0
s
e
R
nt 2.5
e
d 2.0
u
n St 1.5
a
Me 1.0
0.5
0
1 2 3 4
New Student Collection
Psychology Teaching Review Vol. 17 No. 1 37
Kai Ruggeri, Martin Dempster & Donncha Hanna
a novel idea, but it strongly suggests that toward the subject. The result of these col-
better understanding of even simply the lectively then is seen in how well students are
theory behind statistics is something that all able to acquire statistical understanding,
students –not only those pursuing scientific apply related skills, and finish their course.
degrees in higher education – need to As assessment is highly subjective and likely
acquire when young. unable to capture long-term benefit, per-
Figure 2 represents the timeline and formance is not considered a critical aspect
influences on learning statistics (Ruggeri, (Ruggeri, 2009). Furthermore, the long-
2009). These were selected based on the term aspect has not been the focus of major
findings from the overall study. The general work and is thus difficult to consider.
concept is that the understanding students However, a major omission from this model
have about their course will impact their identified in the preceding results is under-
experiences in studying statistics. Their standing the nature of statistics. Given the
experiences, influenced heavily by the way arguments listed, this must come at some
the course is taught and structured, in turn point for these students, if not many others.
determine their disposition and emotions
Figure 2: Model for statistics education timeline.
Pre-course Factors Course Experiences Outcomes
Statistical Literacy/
Awareness Teaching
Critical Reasoning
Statistics Anxiety
Background Continue/Withdraw
and Attitudes
Expectations Course Structure Performance*
Long Term?
38 Psychology Teaching Review Vol. 17 No. 1
The impact of misunderstanding the nature of statistics
The impact of overlooking Conclusion
The decision to report the selected results Much about how students will experience
stemmed from essentially post hoc examina- the statistics aspect of their course can be
tion of the research. As it was being carried determined by their level of understanding
out, the intent had been to find the most about statistics before they begin. Further-
extensive explanations of statistics anxiety more, this concept applies not only to stu-
and negative attitudes. However, this was at dents but to the general population, as they
the expense of merely looking for the most are constantly impacted by information mis-
useful results. While such exclusion is not takenly identified as statistical. For teachers
uncommon, it raises questions about the of statistics, this should be treated as a crucial
benefit of learning large amounts of statis- element when developing the structure of
tical methods in place of more time spent on such courses.
basics.
This perspective teaches two main Acknowledgements
lessons. Thanks to a bursary provided by the DTRP,
1. The need to produce the most useful the core of this paper was presented in their
analysis must overcome the urge to produce symposium at the 2010 BPS Annual Confer-
the most complex, impressive one. ence. Many of the thoughts included in this
Without appeasing to the notion of more report came from suggestions and feedback
mainstreaming in statistical reporting, aca- from that symposium. Credit for the author’s
demics need to encourage students not to study goes to Queen’s University Belfast.
focus on impressive methodology and tech-
niques as much as producing an accurate Corespondence
report. Dr Kai Ruggeri
2. More time should be spent instructing stu- Research Associate,
dents on how to find appropriate result Department of Psychiatry,
instead of covering the most topics possible University of Cambridge.
in a short time. Email: [email protected]
If the basic nature of statistics is truly
having such a tremendous impact on stu-
dents, then there is clearly a need to focus
more on basics until they have acquired a
stable foundation of the discipline. Without
this, it is unlikely that they will be able to
progress beyond what has been taught to
them once out of their course.
Psychology Teaching Review Vol. 17 No. 1 39
Kai Ruggeri, Martin Dempster & Donncha Hanna
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