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Journal of Statistics Education
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Assessing Effectiveness of Mnemonics for Tertiary
Students in a Hybrid Introductory Statistics Course
Megan Mocko, Lawrence M. Lesser, Amy E. Wagler & Wendy S. Francis
To cite this article: Megan Mocko, Lawrence M. Lesser, Amy E. Wagler & Wendy
S. Francis (2017) Assessing Effectiveness of Mnemonics for Tertiary Students in a
Hybrid Introductory Statistics Course, Journal of Statistics Education, 25:1, 2-11, DOI:
10.1080/10691898.2017.1294879
To link to this article: https://doi.org/10.1080/10691898.2017.1294879
© 2017 The Author(s). Published with
license by American Statistical Association©
Megan Mocko, Lawrence M. Lesser, Amy E.
Wagler, and Wendy S. Francis
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Assessing Effectiveness of Mnemonics for Tertiary Students in a Hybrid Introductory
Statistics Course
Megan Mocko
a
, Lawrence M. Lesser
b
, Amy E. Wagler
b
, and Wendy S. Francis
c
a
Department of Statistics, University of Florida, Gainesville, FL;
b
Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX;
c
Department of Psychology, The University of Texas at El Paso, El Paso, TX
ABSTRACT
Mnemonics (memory aids) are often viewed as useful in helping students recall information, and thereby
possibly reducing stress and freeing up more cognitive resources for higher-order thinking.However,there
has been little research on statistics mnemonics, especially for large classes. This article reports on the
results of a study conducted during two consecutive fall semesters at a large U.S. university. In 2014, a large
sample (nD1487) of college students were asked about the usefulness of a set of 19 published statistics
mnemonics presented in class, and in 2015, the students (nD1468) were presented 12 mnemonics related
to inference and then asked whether or not they used mnemonics on that exam. This article discusses how
students assess the usefulness of mnemonics and evaluates the relationship between using mnemonics and
reducing anxiety. Additionally, the relationship between mnemonic usage and learning outcomes
achievement will be discussed, along with this study’s limitations and implications for teaching.
KEYWORDS
Anxiety; Hybrid; Mnemonic;
Memory; Online; Statistics
education; Study aids
1. Introduction
1.1. Potential Benefits of Mnemonics
Mnemonic, a word derived from the Greek word mnemonikos (“of
memory”), is a technique used to assist memory dating back to 477
BCE (Yates 1966). A mnemonic can be classified by its form (e.g.,
an acronym based on initial letters of the target material) and by
its function (e.g., recalling a fact versus recalling a process), and
Bellezza (1981) offers further refinements in classification. We
refer readers to Manalo (2002) and Bellezza (1981)forareviewof
mnemonics in educational settings in general.
In the field of cognitive psychology, mnemonic techniques
are considered to be strategies for encoding new information in
memory in such a way that they can be more easily retrieved.
Among the most studied techniques are those involving imag-
ery or verbal mnemonics (Cook 1989), such as using the first
letters of a set of words to form an acronym or phrase or using
the words to make up a story. The materials typically used in
controlled laboratory experiments are lists of words, but more
applied studies have been conducted with K–12 students using
classroom materials. It has long been known that memory per-
formance is best when information is encoded in a meaningful
or organized manner (Bower et al. 1969; Craik and Lockhart
1972), for example, by connecting it to pre-existing knowledge
structures. Some mnemonic techniques take advantage of the
benefits of meaningful and organized encoding and supplement
them by setting up an organized retrieval structure in which
each retrieval cue is stored with a specific piece of information
to be remembered. To be maximally effective, these cues must
be memorable and have a good probability of reminding the
individual of the target information.
The unprompted use of mnemonic techniques among college
students has been documented in both laboratory and classroom
settings. Immediately after learning a list of words for later recall,
the most commonly reported mnemonic techniques were first-
letter mnemonics and sentence mnemonics (Boltwood and Blick
1970). In a retrospective study of undergraduate psychology
students who had recently studied for final exams, 30% of students
reported using mnemonic techniques of some sort, with most
being verbal mnemonics (Gruneberg 1973).
The efficacy of first-letter based mnemonics depends on the
nature of the materials to be learned (Cook 1989). When sets of
unrelated words were learned, first-letter mnemonics did not
enhance performance relative to study with no particular
instruction; however, when learning sets of related words, first-
letter mnemonics did enhance performance. Sentence mne-
monics helped later recall and recognition of concrete nouns
(Bower and Winzenz 1970). Both ready-made and self-pro-
duced sentence mnemonics were helpful in several studies, but
the evidence is mixed with regard to which is more effective
(Cook 1989). Sentence mnemonics were particularly robust
across delays of several days or weeks (Boltwood and Blick
1970). In a more applied study, instruction of algebraic con-
cepts using ready-made sentence mnemonics involving rhymes
improved student performance over standard instruction both
in an immediate test and after a two-week delay (Machida and
Carlson 1984).
CONTACT Megan Mocko mmeece@stat.ufl.edu Department of Statistics, University of Florida, P.O. Box 118545, Gainesville, FL 32611-8545.
© Megan Mocko, Lawrence M. Lesser, Amy E. Wagler, and Wendy S. Francis
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommo ns.org/licenses/by/4.0/), which permits unrestricted use, distribu-
tion, and reproduction in any medium, provided the original work is properly cited. The moral rights of the named author(s) have been asserted.
Published with license by American Statistical Association
JOURNAL OF STATISTICS EDUCATION
2017, VOL. 25, NO. 1, 2–11
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Statistics mnemonics are consistent with the Guidelines for
Assessment and Instruction in Statistics Education (GAISE)
College Report (ASA 2005; GAISE College Report ASA Revi-
sion Committee 2016) regarding reduced emphasis on mem-
orization because, as Lesser (2011a) noted, the mnemonics
are not “intended to replace higher-order thinking or concep-
tual understanding, but merely to stimulate students to take
into account more possibilities or to recall a low-level fact
more readily in order to have more cognitive resources avail-
able to apply to something more important and conceptual”
(p. 152). Lesser added that mnemonics might allow students
to “keep up better in real time with class discussion by being
able to apply to the conversation the mental energy or time
they would have had to spend trying to search their mind (or
book) to recall what a term meant”(p. 151). Mnemonics may
also help students perform better and/or with less anxiety on
exams. Also, as Stalder and Olson (2011)noted,mnemonics
are easily added to existing material and thus require less
instructor effort relative to other interventions. Stalder
(2005) also noted motivational effects for his introductory
psychology students: “Students generally reported that acro-
nyms increased their motivation to begin studying, that it was
helpful to solve review sheet acronyms [i.e., to review their
notes to fill in what each letter stood for] on their own, and
that they would try to use acronyms or other mnemonics on
their own in future courses”(p. 226).
That said, the value of mnemonics should not be over-
stated. Just as analogies can eventually hit limitations (see
Martin 2003, and its associated letters), so can mnemonics.
For example, there are many limitations of the famous PEM-
DAS (“Please Excuse My Dear Aunt Sally”) mnemonic used
to help mathematics students recall the correct order of
operations or procedure precedence in a mathematical
expression. For example, students may think multiplication
isofgreaterratherthanequalhierarchy than division and
incorrectly evaluate the expression 8 4£2. Also, Rogers
(2013) noted that parentheses do not always imply grouping,
and a vinculum, absolute value symbol, or square root sym-
bol can function as a grouping symbol without using paren-
theses. Lee and Messner (2000) noted that operations
involving additive inverses or towered exponents may not be
clear. And Urbina-Lilback (2016) noted that the particular
phrase “Please Excuse My Dear Aunt Sally”may be
completely unfamiliar or irrelevant in the culture of learners
from other countries. Another possible limitation is that
some mnemonics may not be easy to recall or implement,
although the latter may sometimes be addressed by the very
way a mnemonic is written (e.g., the modified representation
of SOHCAHTOA in Reilly 2014). The former may be
addressed by having the mnemonic be so explicitly tied to
the content that it cannot be forgotten, such as the acronym
mnemonics for mean, median, and mode that use those very
words (see Appendix A in the supplementary materials).
1.2. Prior Research
1.2.1. Identifying Statistics Mnemonics
Certain mnemonics in mathematics (e.g., FOIL, PEMDAS, and
SOHCAHTOA) seem to be far more widely known than any
mnemonics in statistics. It seems that until the current decade,
there was no attempt to compile (much less catalogue) a com-
prehensive collection of mnemonics that could be used in sta-
tistics courses. However, the papers of Hunt (2010) and Lesser
(2011a) collectively identify more than 30, with Lesser (2011b)
offering a couple of new ones and refinements for old ones.
These mnemonics serve a variety of roles, including helping
students recall facts, formulas, definitions, assumptions, or pro-
cesses. Lesser (2011a) gave a taxonomy for classifying mne-
monics by function (e.g., helping to recall a fact vs. helping to
implement a process) and by form (letter-based, image, and
rhyme/jingle). A subset of these mnemonics appears in Appen-
dix A and was used in the current study. The first two authors
subsequently encountered another 11 statistics mnemonics in
Table 1 of Stalder and Olson (2011), bringing the number of
published distinct statistics mnemonics to around 50.
1.2.2. Assessing Effectiveness of Statistics Mnemonics
There have been only a few studies on individual statistics-
related mnemonics, and these have generally had limitations.
For example, Lakin et al. (2007) found that students were better
at remembering and elaborating on the steps of the scientific
method if their instructor discussed the mnemonic acronym
HOMER more frequently—that is, as a structure for the entire
course rather than just when transitioning from one step of the
scientific method to the next. Those authors, however,
acknowledge the limitations that students were not randomly
assigned to sections of the course and there were two different
instructors as well. VanVoorhis (2002) sang mnemonic statis-
tics jingles in one section of psychology statistics and read defi-
nitions of the same terms in another section she also taught.
The section that was sung to performed significantly better
(t
69
D2.01, p<0.05) on test items related to the content of the
definitions/jingles and had a significant correlation (r
31
D.37,
pD0.04) between performance and self-rated familiarity with
the jingle. While the sections were shown to have statistically
equivalent grade point averages (GPAs), randomization was
not used to assign students to the sections, and it is possible
sections varied in some important way other than GPA.
Stalder and Olson (2011) gave anonymous semester-end
surveys to nD61 undergraduates from an introductory psy-
chology statistics course at a university in the midwestern
United States. The surveys assessed degree of recall and per-
ceived helpfulness for each of 11 listed mnemonics, finding sig-
nificant positive results (i.e., ratings significantly higher than
the midpoint of a 7-point scale) on both criteria for 8 of the 11
mnemonics.
Mocko (2012) discussed how and why her university took the
multi-section introductory statistics course and created a sepa-
rate section for students with learning disabilities, a population
for which mnemonics has been identified by researchers (e.g.,
Manalo et al. 2000) as often helpful for mathematics students.
During the Spring 2013 semester, she conducted a pilot study
(Mocko et al. 2013) at a large research university in the southern
United States on an (otherwise traditional) introductory statis-
tics class specifically designated for students with learning dis-
abilities (e.g., ADHD, reading comprehension, dyslexia, and
hearing impairment) registered with the campus’disability
resource center. During two class periods of the pilot study,
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students were given a 15-min pretest on statistical concepts
(spanning descriptive statistics, graphs, and inference), then
given a review sheet to study for 10 min, then given a memory
cleansing activity (e.g., a unrelated word search, maze, or crypto-
gram), and then a 15-min posttest on the same statistical con-
cepts. The randomized review sheets included mnemonics
drawn from Hunt (2010) and Lesser (2011a). The findings were
limited due to the small size of the class. The class had only 26
students, of which 21 consented to have their data in the study.
Due to absences and tardiness as well as the length of the in-class
activity, only 17 of the 21 students appeared to complete the
questions on the activity. Additionally, of those who consented
to have their data used, only 11 out of the 26 responded to the
online survey and only 8 consented for their data to be used.
From this pilot, we learned that some students did use mnemon-
ics that were provided by the instructor, found in the textbook,
created by themselves, or created by a classmate. Because this
population was small, the research team decided to try to survey
a larger, more general population of students.
1.3. Research Questions
This study aimed to explore benefits and usefulness of using
mnemonics in a hybrid college course in introductory statistics.
In particular, the research questions are as follows:
1. Do students use mnemonics and find them helpful in
introductory statistics?
2. Is there an association between student self-reported
usage of mnemonics and self-reported reduction in anxi-
ety from taking tests or learning statistics?
3. Is there a difference in the self-reported and measured
learning objectives as measured by exam questions,
among those with high versus low self-reported use of
mnemonics?
2. Methodology
2.1. Population/Sample
The study was conducted over two consecutive Fall semesters at
a large public research university in the southeastern United
States where roughly 55% of the undergraduate students are
White non-Hispanic, 18% Hispanic/Latino/a, 8% Black
non-Hispanic, and 8% Asian-American. Also, roughly 55% of
the undergraduate students are female, according to the univer-
sity website. For the Fall 2014 phase of the study, the sample
consisted of 1487 students, of whom 66% were female. Virtually
all students in the sample were in the traditional age group for
college students: 92% were between 18 and 20 years and 7%
were between 21 and 23 years. For the Fall 2015 phase, the sam-
ple consisted of 1468 students, of whom 67% were female. Once
again, virtually all of the students were in the traditional age
group with 93% between 18 and 20 years and 6% between 21
and 23 years. Since both semesters represented only tradition-
ally aged college students (by not exceeding age 24; see, e.g.,
https://nces.ed.gov/pubs/web/97578e.asp), these results are not
generalizable to nontraditional age college students.
During both semesters, new lectures were recorded. Within
each semester, students could attend each lecture in person or
watch its recording online. For the recorded lecture, the mean
number of views or partial views of videos per lecture for Fall
2014 was 1829 and for Fall 2015 was 1974. The students within
each term took essentially the same quizzes (questions of simi-
lar difficulty were drawn from a quiz bank) and the same
exams. These students were divided into sections of 40 stu-
dents. During the Fall 2014 semester, there were 45 sections
taught by 16 different teaching assistants (TAs), and during the
Fall 2015 semester there were 46 sections taught by 17 TAs.
The students met with a TA once a week to complete an activ-
ity. In the Fall of 2014, since the use of the mnemonics by the
teaching assistants could have added much variation in the
introduction of the mnemonic to the students, the TAs were
not taught or encouraged to use them. In 2015, the TAs used
the PHANTOM mnemonic (item #16 of Appendix A), to dis-
cuss the properties of the significance test. Because of the online
nature of the course, the impact of memory usage from the TAs
would be minimal.
The students attending the institution may represent higher
achieving students than typical college students. The university
website states that the middle 50% of entering freshman stu-
dents in 2014 have SAT scores between 1810 and 2060. The
mean SAT score for the Fall 2015 incoming class was 1899 at
the university. For the U.S., the median SAT score for the 2014
college-bound seniors was 1490. The students in this class out-
performed other college students on this standardized test.
2.2. Course
The study was conducted during a Fall 2014 and a Fall 2015
course offered in a hybrid format. The course has been taught in
this format for over a decade. The students could watch the lec-
tures online or in person, but had to attend a weekly on-campus
50-min lab meeting that entailed collecting data and working
with Minitab or statistical applets. The course emphasizes con-
cepts, but still covers calculation by hand. The students are pro-
vided a formula sheet during the exam. The students can see the
formula sheet before the exam, but they are given a fresh one
during the exam period. The material covered includes explor-
atory data analysis, regression, probability, sampling distribu-
tions, and one- and two-sample inference. During the Fall 2014
semester, randomization or bootstrap methods were not taught.
During the Fall 2015 semester, these topics were brieflyintro-
duced taking about 20 min of class time each. Each topic then
appeared as one question on a quiz. The course is run using the
Canvas course management system. This course is generally a
required course for business and social science majors.
2.3. Study Design
The study consisted of two phases, one that occurred in Fall 2014
and then another that occurred in Fall 2015. During the Fall 2014
semester, the instructor (the first author) introduced students to
the 19 mnemonics listed in the first part of Appendix A. During
the second week of November 2014, students were asked to com-
plete an extra credit survey (whose purpose had been explained in
the preceding lecture) about the use of mnemonics. Students were
asked to complete an informed consent form as a part of the survey
in Canvas. The survey mechanism allowed for anonymous
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responses, so the instructor would not know who consented to
their data being used. All students received extra credit for complet-
ing the survey, regardless of whether they gave consent for their
data to be used. Another benefitoftheuntimedonlinesurveyis
that students were able to give more thoughtful or complete
answers to certain questions. For example, in response to the ques-
tion asking students for any new mnemonics they may have
thought of, one student responded by giving the actual URL for a
YouTube music video (made by an AP statistics class about
hypothesis testing), a piece of information that would not have
been available if the survey had been pencil and paper without tech-
nology access. In the class, 178 students chose not to take the survey
or were already planning on dropping the course. Of those who
took the survey, less than 10% of the students did not give this con-
sent and there were only four students who gave consent who were
under 18 and therefore excluded by the IRB protocol.
In the Fall 2015 semester, the students were introduced to the
original 19 mnemonics, but also 8 additional mnemonics that had
not been covered the previous semester. The new mnemonics were
either suggested during the Fall 2014 survey or were related to con-
tent (e.g., Type I and Type II errors) covered after the completion
of the Fall 2014 survey and so could not be included in that year’s
survey. For Fall 2015, the focus turned to the mnemonics related to
inference. The students were asked to complete an extra credit quiz
that included nine questions about memory use and an informed
consent form. The students were asked if their responses from the
survey could be used as well as their responses to select exam ques-
tions. The students received credit for completing the survey
regardless of their decision to participate in the study. In addition
to the survey, mnemonics were linked to 10 questions from the
exams –7 on the second exam and 3 on the last exam. The students
were then asked how confidenttheyfeltaboutthatsetofexam
questions. Because the exam questions would later be linked to sur-
vey questions, the survey results were not anonymous, but tracked
by a university assigned student identification number. These num-
bers were then deleted once the linkage was made. For the Fall 2015
semester, students who were under 18 or did not consent to have
their data used in the study were removed from the study as per
IRB protocol. Additionally, students who did not take the survey,
did not take the exams at the regularly scheduled times, dropped
the course or entered their school identification number incorrectly
on their Scantron form during one of the exams were also not
included in the study. After all of this was taken into consideration,
1468 students’responses were studied (the starting enrollment for
the course was 1911).
2.4. Mnemonics Assessed
For the Fall 2014 phase of the study, all known mnemonics that
corresponded to content covered in the particular course were
chosen. All chosen mnemonics corresponded to examples from
Lesser (2011a), except for three (#2, #11, and #13) that were
provided by the first author. The mnemonics that were not
used were mnemonics for terms or concepts not discussed in
the course. For the Fall 2015 phase of the study, although the
first author continued to introduce mnemonics to the class
from the previous study, the study concentrated only on the
mnemonics that dealt with inference. The mnemonics used for
inference included the mnemonics listed in Appendix A (#16,
#17, #18, and #19). Additionally, eight other mnemonics were
added (listed in Appendix B in the supplementary materials).
Some (#20, #21, #22, #23, and #24) of these were suggested by
students in the Fall 2014 semester, one (#25) came from Stalder
and Olson (2011), another (#26) came from Lesser (2011a),
and one (#27) came from the first author.
2.5. Construction of the Surveys
The Fall 2014 survey included 2 demographic questions about age
and gender, and 17 questions about their previous/current mne-
monic usage, preferences for mnemonics, use of mnemonics to
help reduce anxiety, and use to help prepare for exams. Included in
these questions were also questions about the students’perceived
memory ability. The students werealsoaskedtoprovideanymne-
monics that they had thought of that could be used in an Introduc-
tion to Statistics course. The remaining 19 questions asked
students about their usage and perceived helpfulness of that partic-
ular mnemonic. An earlier version of the survey had been used in a
pilot study in Spring 2013 (Mocko et al. 2013). This survey was
adapted and improved upon, mainly in terms of how the questions
were organized. In the older version, students were asked “Which
mnemonic (mnemonics) did you remember during the exam
(even if you don’t remember them now)? Please write down the
actual mnemonics, if possible, or at least the name or topic of each
mnemonic that you remembered.”This question required that the
respondent write the mnemonic(s) into a short answer survey box,
and it did not get any responses during the pilot. This question was
revised in the new survey to improve response rate. This one ques-
tion was divided into 19 questions that asked specifically about
each mnemonic’s usage. The other main change on the survey was
that the students were also asked how many mnemonic aids they
felt helped them get a correct answer on the first exam or on the
second exam, rather than just lumping those two separate items
together by referring to “the exam.”The survey questions can be
found in Appendix C in the supplementary materials.
The Fall 2015 data collection, just like the Fall 2014 data collec-
tion, included two demographic questions about age and gender,
but it also included an additional question about the students’lan-
guage spoken outside of school and nine other survey questions.
The same survey questions were not used because the authors
wanted to focus the students’responses to questions related to how
difficult the students felt that the course was and around issues of
confidence. In order to assess whether the students had any previ-
ous statistical training, the students were also asked if they had
been in a course that discussed the p-value. This was done because
some courses in K–12 may cover statistical concepts, but the course
name might not be “Introduction to Statistics”or a similar title. The
survey questions for the Fall 2015 semester can be found in Appen-
dix D in the supplementary materials.
3. Results
On the survey, the students sometimes skipped a question or
two, but this was a relatively minor occurrence. For each ques-
tion, there were 0–5 missing values in the responses. In the fol-
lowing analyses, it is of primary interest to detect any
association between items in the survey. Hence, chi-squared
association tests are reported for detecting statistical
JOURNAL OF STATISTICS EDUCATION 5
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significance and Cram
er’sVeffect size measures are reported to
assess the practical significance. Reliabilities were computed for
the scale assuming a particular item is dropped. Small variation
in these item-deleted reliabilities (computed using Cronbach’s
a) is desirable since that indicates that no one item significantly
affects the scale’s internal consistency. For the Fall 2014 survey,
the item-deleted reliabilities are all either 0.84 or 0.85 when
considering all items in the survey asking about mnemonics
and for the Fall 2015 survey, they ranged from 0.62 to 0.69.
3.1. Usage and Helpfulness of Mnemonics
In this subsection, we will address the first research question
about usage and helpfulness of mnemonics by first looking at
past usage of mnemonics in previous courses and then usage in
the statistics course. First, students were asked to state their
level of agreement with the statement that they had used a
mnemonic in a previous course (Q5) or a mathematics/statis-
tics course (Q6). The students were asked to state if they
strongly agreed, somewhat agreed, agreed, neither agreed nor
disagreed, disagreed, somewhat disagreed, or strongly dis-
agreed. Out of 1486 students, 69.2% had some level of agree-
ment (includes agree, somewhat agree, and strongly agree) with
the statement for both types of previous courses, whereas only
7.5% had some level of disagreement (includes disagree, some-
what disagree, and strongly disagree) about usage in any course
and mathematics/statistics courses.
Students were also asked to give their past frequency of use
of mnemonics (frequently, occasionally, or not at all). The stu-
dents reported that they had used mnemonics frequently
(22.2%) or occasionally (69.6%) in any of their previous
courses, but only 11.4% used frequently or 67.0% occasionally
in other mathematics/statistics courses. In Fall 2014, students
were asked to describe to what extent they agreed that mne-
monics were helpful. Table 1 shows that 71.2% of the students
surveyed somewhat agreed, agreed, or strongly agreed that
mnemonics in the course were helpful.
3.2. Self-Reported Anxiety and Use of Mnemonics to
Reduce Anxiety
The second research question was about the frequency with
which students used mnemonics to reduce test anxiety as
well as the anxiety of learning statistics. To address this
question, the research team examined questions that related
to mnemonic usage and anxiety in learning statistics (Q10)
as well as mnemonic usage and anxiety in test taking (Q8).
Table 2 reports these results. In summary, 43.8% of students
agreed (somewhat agree, agree and strongly agree combined)
that test anxiety was reduced, and 41.2% reported that gen-
eral anxiety about learning statistics was reduced.
Additionally, the relationship between test anxiety and
the anxiety about learning statistics is reported in Table 3.
The expected cell count was less than 5 in multiple cells, so
the three levels of agree responses were combined and the
three levels of disagree responses were combined. The asso-
ciation was significant: X
2
(4) D1046.2, p<0.0001, with
1485 respondents. Cram
er’sVwas equal to 0.594, and this
indicates a very strong effect (Cohen 1988,p.49).Thissig-
nificant association indicates that students who found the
mnemonics more helpful in reducing test anxiety also found
mnemonics more helpful in reducing anxiety about learning
statistics.
3.3. Learning Objectives and Use of Mnemonics
To answer research question 3, first the Fall 2014 survey results
were used to explore the students’self-reported use of mne-
monics on the exam, and then the results of the Fall 2015 were
used to explore the students’self-reported usage of mnemonics
while answering specific test items. On the Fall 2014 survey, a
question asked the students whether they remembered any of
the mnemonics while they were taking the test. The distribution
of responses to this question can be found in Table 4. In short,
only 14.3% of students said that they did not use any mnemon-
ics to help during the exam.
Students were also asked whether they felt that the mne-
monics helped them to get any of the questions correct on the
two exams that had already occurred during the semester. The
results for this can be found in Table 5. From these self-
reported results, about 80% used a mnemonic on each exam.
In Fall 2015, students were asked whether they had used a
mnemonic while working out problems during the exam
period. Appendix E in the supplementary materials lists the
exam questions. Some questions (Exam 2 question #1, Exam 2
question #3, Exam 3 question #1) were adapted from the
Table 2. Survey responses to questions about mnemonics and anxiety.
Strongly
disagree Disagree
Somewhat
disagree
Neither agree
nor disagree
Somewhat
agree Agree
Strongly
agree
I have found mnemonics (memory aids) helped reduce my test
anxiety in this course. (nD1487, reliability D0.85)
79 (0.53%) 186 (12.5%) 117 (7.9%) 453 (30.5%) 350 (23.5%) 235 (15.8%) 67 (4.5%)
Ifind that using mnemonics (memory aids) helped reduce my
anxiety learning statistics in this course. (nD1487,
reliability D0.85)
104 (7.0%) 227 (15.3%) 145 (9.7%) 396 (26.7%) 380 (25.6%) 188 (12.7%) 45 (3.0%)
Table 1. Question related to mnemonics and helpfulness.
Strongly
disagree Disagree
Somewhat
disagree
Neither agree nor
disagree
Somewhat
agree Agree
Strongly
agree
“The Memory Aids in this course were helpful.”
Responses (nD1485)
28 (1.9%) 72 (4.8%) 49 (3.3%) 278 (18.7%) 476 (32.1%) 427 (28.8%) 155 (10.4%)
6M. MOCKO ET AL.
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ARTIST database (https://apps3.cehd.umn.edu/artist/), while
others were written by the authors. After each question that
was linked to a mnemonic, the student was asked the following
question:
For the above question, which statement best describes your
experience?
(a) I used a mnemonic and it was very helpful.
(b) I used a mnemonic and it was somewhat helpful.
(c) I remembered a mnemonic, but I did not use it.
(d) I did not remember a mnemonic, but I would have used
it had I remembered it.
(e) I did not remember a mnemonic, and I would not have
used it even if I had remembered it.
The student was considered to have used a mnemonic if they
chose answer aor b. For each of the 10 questions (7 from Exam
2 and 3 from Exam 3), the percentage of students who used a
mnemonic is given as a function of whether their answer was
correct or incorrect in Appendix E.
Two of the ten exam questions stand out. Question #1 on
Exam 3 asked students about the definitions of Type I and
Type II error. For this question, 79.3% of the students who
used a mnemonic got it correct, compared to 73.1% of students
who did not use a mnemonic.
The other question was question #11 on Exam 2. This ques-
tion was asking for the students to apply the p-value rule. For
this question, 93.2% of the students who used a mnemonic got
it correct, compared to 88.5% of students who did not use a
mnemonic.
The question that had the lowest reported mnemonic usage
was question #5 on Exam 3 (i.e., Ex3 Q5). This question asked
about the concept of a significance test. For this question, only
66 students self-reported use of a mnemonic.
A chi-squared test was used to examine the association
between mnemonic usage and correctness for each question.
False discovery rate adjusted p-values (Benjamini and
Hochberg 1995) are included in Table 6. These adjusted values
can be compared to a 5% significance level to assess evidence
for association between mnemonic usage and correctness. Note
that the association between mnemonic usage and correctness
was significant for all items except the first two.
The first two questions from Exam 2 do not show a differ-
ence in mnemonic use for students who answered correctly and
those who answered incorrectly. All but two of the remaining
questions showed that students who answered correctly were
more likely to report having used a mnemonic. The two excep-
tions were questions Ex2 Q7 and Ex3 Q5. For question Ex2 Q7,
there was only a small (3.2%) difference. For question Ex3 Q5,
there was a much larger difference of 22.2%, but, for this ques-
tion, the percentage of students who used a mnemonic was
quite small (only 4.5%). Cram
er’sVis also included in the table;
this measure reflects a small to moderate level of association
(Cohen 1988) for the questions showing statistical significance.
4. Discussion
4.1. Summary/Interpretations
4.1.1. Usage and Helpfulness of Mnemonics
For the sample, 91.8% of the students had used mnemonics fre-
quently or often in any past courses, but only 78.4% had used
mnemonics frequently or often in a past mathematics/statistics
course. The analysis suggests that there is a practical difference
in the use of mnemonics between the different types of courses.
Since nearly three-quarters (71.3%) of those surveyed expressed
some level of agreement that the mnemonics in the course were
helpful, there seems to be compelling evidence that there is a
demand or opportunity for mnemonics to be used more widely
in mathematics/statistics courses.
4.1.1.1. Why might mnemonics be considered useful? The stu-
dents were asked about the amount of memorization required
in the course. Out of the class, 44.5% agreed at some level that
they had trouble remembering symbols or notations in mathe-
matics/statistics courses.
When the students were asked to choose a completion for
the fill-in-the-blank sentence “Statistics/math involves ____
memorization,”531 (35.7%) chose “a large amount,”795
(53.5%) chose “a medium amount of,”153 (10.3%) chose “a
small amount of,”and 7 (0.47%) chose “no.”So, a majority of
students still felt that there was a large amount of memorization
Table 4. Number of mnemonics that students reported remembering when they took the test.
None
Parts of a
mnemonic
1 or 2 complete
mnemonics
Bits and pieces of a few
mnemonics
3 or 4 complete
mnemonics
More than 4 complete
mnemonics
Number of mnemonics during exam,
Responses (nD1486)
212 (14.3%) 217 (14.6%) 542 (36.5%) 295 (19.9%) 173 (11.6%) 47 (3.2%)
Table 5. Number of questions students reported answering correctly due to a
mnemonic.
0
questions
1
question
2
questions
3
questions
4 or more
questions
Correct for
first exam
(nD1487)
281
(18.9%)
348
(23.4%)
504
(33.9%)
205
(13.8%)
149
(10.0%)
Correct for
second
exam (nD
1483)
335
(22.6%)
361
(24.3%)
401
(27.0%)
197
(13.3%)
189
(12.7%)
Table 3. Test anxiety (row) versus anxiety learning statistics (column).
Anxiety learning statistics
Test anxiety
Agree (that it
reduced anxiety
learning statistics)
Neither
agree nor
disagree
Disagree (that it
reduced anxiety
learning statistics)
Agree (that it reduced
test anxiety)
507 101 43
Neither agree nor
disagree
70 261 121
Disagree (that it
reduced test anxiety)
36 34 312
JOURNAL OF STATISTICS EDUCATION 7
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needed in the course even for a course that tried to emphasize
concepts.
These responses suggest that mnemonics could be used to
help recall information or procedures. For example, when the
students were asked whether they found that the mnemonics
provided in the course helped them with definitions of a term,
steps of a procedure or aspects of a concept, 70.7% agreed
(somewhat agreed, agreed, or strongly agreed combined).
When the students were asked whether they agreed with the
statement that they had specifically spent time studying mne-
monics to help with the exam, only 34.5% agreed (somewhat
agreed, agreed, or strongly agreed combined).
4.1.1.2. What qualities may lead to a mnemonic being consid-
ered helpful? One of the questions asked the students why they
remembered the mnemonic(s) that they did. Students were
allowed to mark any or all of the choices that applied. The
most endorsed reasons were “Mnemonic was brief”(57.8%)
and “Mnemonic was well connected to the content”(43.9%).
The mnemonics that had rhyme (37.1%), humor (35.6%), or a
visual representation (33.4%) also received support. The rea-
sons with the fewest endorsements were mnemonic was
“strange/bizarre”(24.3%) or “the time that I spent studying or
reviewing the mnemonics”(13.5%). For students who are
already having trouble remembering concepts, remembering a
long mnemonic may not be helpful when they might as readily
memorize the full statistical concept. As for the second most
common reason, if a mnemonic was well connected to the
material, it was more obvious why learning that mnemonic
would be beneficial—essentially, it was not yet another con-
struct to memorize but more of a tool to remember what they
needed to know. This finding was consistent with the notion
that the mnemonic itself must be memorable to be useful and
the notion that it must provide a strong cue to the target
information.
Surprisingly, the option of “Mnemonic was visual”was fur-
ther down the list—at about 33.4%. Students do not rank visual
mnemonics as helpful as a word or phrase. Note, however, that
in cognitive studies, imagery-based mnemonics were more
effective than verbal mnemonics (Bower and Winzenz 1970).
The other least common choices were “The piece of content
was something that I was already familiar with,”“Mnemonic
was strange/bizarre”and “The time that I spent studying or
reviewing mnemonics.”
4.1.1.3. Which mnemonics were perceived as the most use-
ful? The students were asked to mark the answer choice that
best reflected their reported use and usefulness of the mne-
monic. The distribution of responses for each of the 19 mne-
monics appear in Appendix A. No more than five students
skipped any particular item. The mnemonic with the highest
rate of reported usage and usefulness (63.7%) was the mne-
monic “Population and Parameters both start with p. Sample
and Statistics both start with s.”This mnemonic illustrates the
attributes of brevity and being well connected to the context.
This result is consistent with responses to the survey question
that asked about qualities preferred in a mnemonic. The mne-
monic with the second highest rate of reported usage and use-
fulness was “Explanatory variable on the xaxis.”Once again,
this memory aid has the qualities of brevity and being well con-
nected. Also, notice that both of these mnemonics are of the
same type; both leverage the “first letter of a word”to recall a
fact. This finding is consistent with the finding that first-letter
based mnemonics have frequent spontaneous use relative to
other types of mnemonics and that they are effective for learn-
ing inter-related pieces of information (Boltwood and Blick
1970; Cook 1989).
The two mnemonics that received the lowest rankings were
the graphical image of the mean and the song about the p-
value. In the case of the graphical mean, it could be that to
make the visual image more helpful, it needed to be better con-
nected by the instructor. However, this result is consistent with
the finding that the quality of the mnemonic being visual was
not as highly endorsed as brevity and connectedness. As for the
p-value song, the instructor played the song for the students
over the classroom audio system. During the Fall 2014 semes-
ter, the p-value song was heard in both the recorded and live
lectures. During the Fall 2015 semester, the instructor played
the audio file again, but explained that some people learn more
easily with music. The instructor reported that the students
seemed more receptive and even clapped after hearing the p-
value jingle. The p-value song has more words than the two
more highly ranked mnemonic items, so it lacked the brevity
that the students seemed to prefer.
It is also of interest to observe whether students created their
own mnemonics. Students were encouraged to create and sub-
mit their own mnemonics to be shared with the class and asked
on the survey to report any that they had used as well. For this
question, 114 students (7.7% of those that took the survey) sub-
mitted a mnemonic in response to the request. Some of the
mnemonics provided by the students were only slight varia-
tions of the provided mnemonics in the course. For example,
the student submission “RAMP”(residual equals actual minus
predicted) is very similar to the mnemonic called “ROMP”
(residual equals observed minus predicted) from the list pro-
vided to the class.
The first two authors independently reviewed the student-
suggested mnemonics and after discussion came to 100% con-
sensus on a list of mnemonics that showed the most promise in
helping students remember key concepts and ideas in an intro-
ductory statistics course. The most common responses were
about a method to describe a histogram and for hypothesis test-
ing based on a p-value, with eight and seven suggestions,
respectively. There were also four suggestions for assumptions,
Table 6. Multiplicity adjusted p-values for chi-squared test of association between
mnemonic usage and correctness.
Exam Question
% Correct with
mnemonic
% Correct without
mnemonic
p-value
(adjusted)
Cram
er’s
V
2 1 83.3% 77.1% 0.1500 0.07
2 3 20.6% 20.0% 0.1500 0.07
2 5 73.9% 69.0% 0.0003 0.12
2 7 63.1% 66.3% 0.0050 0.10
2 9 79.6% 68.1% 0.0000 0.16
2 11 93.2% 88.5% 0.0003 0.13
2 13 92.9% 89.0% 0.0000 0.15
3 1 79.3% 73.1% 0.0000 0.14
3 3 99.3% 99.1% 0.0116 0.10
3 5 48.5% 70.4% 0.0005 0.12
8M. MOCKO ET AL.
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confidence intervals, scatterplots or regression as well as the test
statistic format. There were also six other areas (remembering
symbols, distinguishing Ho and Ha,p-value, mean/median,
parameter/population/sample/statistic, and sample size) that
received three or fewer suggestions. There were also mnemon-
ics suggested that were unclear (8), inappropriate for class use
(5), already on the list provided (5), or not really a mnemonic
(3). The mnemonics that showed the most promise and related
to inference were included in the Fall 2015 semester and are in
Appendix B.
4.1.2. Self-Reported Anxiety and Use of Mnemonics to
Reduce Anxiety
Almost half of the class agreed that using mnemonics helped
reduce test anxiety (43.8%) or anxiety over learning the mate-
rial (41.2%). The cross tabulation (Table 3) suggests that there
is an association between these two variables. Students who
reported that they agreed that mnemonics helped in one area
were more inclined to say that they helped in the other area.
This is consistent with Stalder and Olson’s(2011)finding that
students who remembered a high number of the mnemonics
had a higher reduction in anxiety ratings. This research finding
supports the use of mnemonics to relieve anxiety, particularly
for high-stakes assessments.
4.1.3. Learning Objectives and Use of Mnemonics
In the first exam of Fall 2014, 35% of students indicated some
level of agreement that they studied mnemonics for the exam,
but this figure likely underestimates the true proportion of stu-
dents who studied the mnemonics. This is because students
might have recalled the mnemonic while looking over their
notes, but they might not have felt that this was explicitly
studying the mnemonics for the exam. Also, only 14.3% of stu-
dents reported that they had not used any part of a mnemonic
during the exams and only about 20% (18.9% for Exam 1 and
22.6% for Exam 2) could not credit any mnemonic for helping
them get to a correct answer on the exam. This shows that
mnemonics in this study did provide at least a little aid to most
students during the exam periods.
In Fall 2015, the students were asked at the time that they
completed the question whether they used the mnemonic. The
results showed that students did use mnemonics on the exam
to answer questions. The question with the highest mnemonic
usage was the question that utilized the Type I/Type II error
mnemonic(s). There are two mnemonics associated with this
concept that were presented to the students. These mnemonics
are “A Type I error is a false Positive; and P has one vertical
line. A Type II error is a false Negative; and N has two vertical
lines”and “For a Type II error, you Fail to Reject Ho when Ho
is False—a description with 2 Fs. For a Type I error, you Reject
Ho when Ho is True.“
Additionally, out of the 10 questions included on the exam,
8 questions showed statistically significant association between
use of a mnemonic and question correctness, although only 6
of these showed higher mnemonic usage for those who
answered the question correctly. This gives further evidence
that teaching students about mnemonics can help them better
answer exam questions and hopefully better understand con-
cepts presented in an introductory statistics course.
4.2. Implications for Instruction
Based on what we observed in this study, we can say that stu-
dents have probably used mnemonics in their previous courses
and even in their mathematics/statistics courses, to a lesser
degree. Therefore, when teaching, the instructor can assume
that most students have experienced mnemonics positively in
another course. This may make some teachers less anxious
about trying mnemonics.
Additionally, the most commonly selected response to
where the students learned about the mnemonic was the
teacher (79.0%). The other sources were selected as follows:
themselves (54.2%), other students (36.5%), something online
but not on the course management system (22.5%), textbook
(14.3%), or other book (6.0%). Therefore, it does appear to be
worthwhile to spend valuable class time to present and practice
mnemonics. The students are less likely to get this helpful
information elsewhere, even in the age of the internet.
Additionally, when considering which mnemonics to pres-
ent to the class, it may be important to remember that in our
study, students preferred mnemonics that were brief and
directly related to the content. Moreover, these mnemonics
should be repeated in class in order to help students “practice”
their use. The students demonstrated their preference for these
qualities when they remarked about mnemonics they found the
most helpful as well as when asked to identify desirable quali-
ties for mnemonics.
When a student reveals to an instructor extreme test
anxiety, or even if the instructor is just discussing anxiety
with the entire class, perhaps the instructor can discuss the
use of mnemonics as an addition to the student’s toolbox
of possible resources and approaches. Encouraging students
to study some mnemonics for the exam may give the stu-
dents the edge that they need to help fight the anxiety that
they experience when working on a problem. Remembering
a mnemonic to help the student begin the problem may be
enough to get them started toward successful completion.
The instructor can also tell students that there is some evi-
dence that using mnemonics might help them with anxiety
during the exam and help them do well on the exam.
Instructors are encouraged to apply and fine-tune the find-
ings from this study by facilitating conversation with and
among their own students about memory and mnemonics in
order to get a direct sense of what aspects of the content seem
hard to remember and why. This local knowledge, together
with the suggestion of criteria for classification of mnemonics
(e.g., Lesser 2011a), can yield best practices for identifying
effective mnemonics for one’s student population. To help stu-
dents with their studying, the instructor can offer access to a
list of mnemonics, and let students collectively add to it, per-
haps on a wiki page. On the list used in this study, there is
sometimes (but not always) a sentence that visually or verbally
connects each mnemonic to its topic, and this is a recommen-
dation by Stalder (2005) that the authors support.
4.3. Limitations
While the sample size was quite large, the survey data was
collected from the students of only one instructor at one
JOURNAL OF STATISTICS EDUCATION 9
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research institution in the southeastern United States. Since
the class size was so large, with around 1800 students ini-
tially enrolled in the course both semesters, there was lim-
ited opportunity for one-on-one interactions between
students and teachers. Students do not often get a lot of
personal attention from the instructor. Perhaps this charac-
teristic mitigates some of the instructor effect on the results.
Additionally, the list of mnemonics was posted on the
course website so that even students who may not have
watched or attended a lecture still had access to the mne-
monics. Because the instruction about mnemonics occurred
largely in the online lectures and not in the face-to-face lec-
tures, results from the hybrid course should reasonably
translate to an online course. However, the impact of mne-
monics in a smaller face-to-face course may be different,
due to the increased face-to-face dialogue with the instruc-
tor. Additionally, because there were very few students over
the age of 24 in the study, generalizations from this study
to nontraditional age students should be avoided.
It is possible that asking students about the use of mnemon-
ics could have increased the students’overall use of mnemonics
on the exam. However, because these questions did not make
reference to any specific mnemonic, it seems unlikely that it
provided a strong cue to use the mnemonic that would be most
helpful for the particular question, especially considering that
so many different mnemonics were presented to the students.
5. Directions for Future Research
In light of the aforementioned limitations, it would be useful to
see how the mnemonics would be rated by students at addi-
tional institutions, including institutions that have students
with different cultural and linguistic backgrounds as well as
greater age diversity. Additionally, a study that compared the
progress on student learning outcomes between students who
were exposed to mnemonics and those who were not would
add to the discussion.
It would also be helpful to gather data that goes beyond self-
report and directly tracks student performance on items whose
content relates to the mnemonics, including information on
which mnemonic they used. This information could be helpful
in determining whether students are using and remembering
the mnemonic correctly. When tracking actual student perfor-
mance, it would be helpful to know what characteristics of the
mnemonics help students reach a further level of statistical rea-
soning than mnemonics with other characteristics. For students
with high anxiety, can mnemonics reduce the level of anxiety to
help them reach further success? In the future it would be help-
ful to also obtain a report of anxiety prior to instruction.
Additionally, we should consider how many and how often
mnemonics need to be presented in order to be helpful as well
as the appropriate distribution of these presentations. Do mne-
monics need to be presented every time that the material
related to that content is presented or is there an optimal tim-
ing and frequency? Additionally, how should the mnemonic
terms be presented—read out loud or as part of a problem solv-
ing experience? Jacoby (1978) stated that requiring problem
solving rather than just remembering a solution enhances the
impact of spaced repetition of tasks on memory. In studies
where only one mnemonic is being studied, there is often more
flexibility to control and measure this variable. For example,
Lakin et al. (2007) explored the effectiveness of the HOMER
mnemonic (for the scientific method) in three sections of a
course: in one section, it was used as a structure for the course
and presented on 71.4% of the course meeting days, while in
the other two sections it was used only on “transition days”
(23.8%). On the last day of class, the students were asked to
state the steps of the scientific method. The group that had seen
the topic as the structure of the course performed better than
those who only used it on “transition days”(p<0.01).
Another consideration is the way in which the mnemonic is
presented. Mnemonics can be presented by being read out loud
by another person, read silently, displayed on a projector,
handed out on a worksheet, or connected with an in-class or
out of class activity. Additionally, the mnemonic could just be
words or a picture. Mnemonics can be used to remember a
term or a process. For more examination of taxonomy matters,
see Lesser (2011a).
In future work, it would be good to explore further how best
to incorporate mnemonics into a beginning statistics course.
This research may include how many, how frequently, and
what types of mnemonics, as well as the effect of mnemonics
on understanding and anxiety. There seems to be some promis-
ing evidence that using mnemonics helps students in introduc-
tory statistics courses, but there remains much room to
investigate how best to implement this resource.
Acknowledgments
The authors express appreciation to the JSE Editors and anonymous refer-
ees for their very helpful feedback.
Supplementary Materials
Supplemental data for this article can be accessed on the publisher’s
website.
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