This web-based version of this paper is provided because the original was created in pdf only and was therefore of limited use to anyone reading it with screen reading software. It should not be referenced directly; please use:
Godfrey, A. J. R. (2009). “Are statistics courses accessible?” in Proceedings of the Workshop on E-Inclusion in Mathematics and Science 2009, Fukuoka, Japan, pp. 72–80.
Statistics courses in the modern era rely less and less on pen and paper
and more and more on the use of computers and specific software. This
paper considers the state of the accessibility of statistics courses for
vision impaired students.
There are four key elements contributing to this inaccessibility;
graphics, software, tables, and mathematical formulae. Each element is
addressed but greater emphasis is given to the accessibility issues for
statistical software. The author calls upon personal experiences as a
blind person using statistical software over the last fifteen years,
initially as a student and currently as a university lecturer.The idea of having to take a statistics course often induces expressions of fear and trepidation. Many of the first year students the author encounters hate the prospect of taking a statistics course and phrases like “I suck at math”, “I was useless in stats classes at school” and “I’m no good with numbers” are all too common. Anecdotal evidence suggests the blind students have fears too, but these are different, and in the author’s opinion, should be different. It is all too clear that the dominating problem for the blind student is “how am I going to do what they do?” The author argues that the very real concerns blind students face are not adequately countered by sufficient solutions and encouragement; resources are lacking; role models are few and far between; and the current way Statistics is taught is making things worse not better.
Introductory stats classes are of course taught to a very wide range of students. Subject areas at the author’s university that expect or encourage their majoring students to take an introductory statistics course include all business majors, all technology and engineering majors, psychology, geography, economics, biological sciences such as ecology and veterinary science, and in fact all science students are expected to take a course in statistics or calculus. In spite of its reputation, the statistics course is often viewed as preferable to calculus. Our chemistry and physics majors are notable as the mathematics course is recommended to meet the requirement for a numeracy component in their degree programme.
The timing of the introductory statistics course is far from consistent. It’s often hidden away and guised as something like “Research Methodology for …” or “…Analysis”. Sometimes these courses are left to postgraduate level but most are compulsory elements of the majoring requirements for the related discipline. The point here is that while death and taxes are inevitable, having to take a statistics course isn’t far off. In fact, to be sure of not having to take a statistics course means the intending university student probably needs to enrol in a law degree, the fine arts, or one of the Humanities subjects.
Aside from the challenges in actually dealing with numbers, statistics lecturers force students to create and interpret graphs, use a (usually new) software application, look up statistical tables, and the mathematical formulae with all that Greek. Most standard mathematics courses do not deal with all of these key elements of the standard introductory statistics course. The vision impaired student, be they blind or having some residual vision, must be ready to overcome the challenges that each of these four elements presents before the semester begins. We now address these four elements in turn.
There is no doubt that assessing, interpreting, and creating graphics has its challenges for the blind statistician. Working with graphs is also a challenge when assessment of knowledge is undertaken. How does the assessor know whether it is the student who knows that an outlier is highlighted in the histogram, or whether they were told it was there by their sighted reader/writer? Provision of tactile graphics is probably the only solution that will offer direct access to the graph to be examined. Work on producing tactile graphics is advancing satisfactorily, but the student must allocate time to become familiar with the use of tactical images.
Some people would say that screen reading software is an adequate substitute for tactile images. Even if screen reading software is developed sufficiently to cater for enough graph types, there will always be doubt over its ability to extract the necessary information without giving the blind student an advantage over their sighted peers through their reliance on the expert systems that contributed to the design of the screen reading software.
In many instances, the blind student will be faced with reliance on sighted individuals to be able to give them the knowledge they would be able to gain were they sighted or had direct access to the graphs through such media as tactile graphs. This remains a concern for the author when producing graphs to meet publishing standards. Ultimately, there is no problem with a blind student asking a sighted person if the graph is showing what was intended. The author has seen sighted students do this on many occasions usually when two or more students are working together a computer laboratory.
There are, however, alternatives to all graphics. Many graphs were designed to be used as highlights for quickly demonstrating a point discovered via analysis by other means. Calculation of the mean and the median as well as midpoints between quartiles would be used to gauge the skewness of a sample before graphs like histograms were so simply created by software. Now that software can create the graph so easily, we rely on this as the method for determining skewness. Exploratory data analysis techniques are prominent in introductory courses sometimes taking up as much of one quarter of the overall work. The old-fashioned ways are still relevant today but are less efficient for the sighted user. They are, of course, a better option for the blind user to consider, but seldom are they taught in the 21st century. Many of these numerical substitutes for graphs are not given as much prominence as in former times. Hypothesis tests exist for analyzing the existence of skewness, but hypothesis tests are usually taught well after exploratory data analysis through graphs.
As a further example, think about a simple two dimensional scatter plot. What is it for? First we look for relationships between the two variables in the graph, and if this relationship can be described as a trend. It is equally useful to look at Spearman’s rank correlation to see if any monotonic relationship exists, but this isn’t taught in many introductory courses. If we want to know if the trend is linear, we could then employ the Pearson’s coefficient which explicitly measures the strength of a linear relationship. As an aside, the author teaches Pearson’s correlation to introductory students but not Spearman’s correlation; this ought to change. Second, we look for outliers in the graph that are unusual because they have a combination of the two variables that is not in keeping with the relationship displayed by the other data. This can be achieved by just fitting the simple linear regression model, perhaps adding a quadratic term, and looking for points having large residuals.
In the modern approach to statistics, we are taught to look first and investigate afterwards. This encourages browsing. Like selecting food from a buffet, pouring (perhaps pawing) over graphs is not done easily. The message: Blind students need to learn how to do things differently to their sighted peers if they are to use statistical analyses in their ongoing study or careers. The standard introductory course may not actually provide the necessary content required by the blind student.
There are two sources of software issues. The first is in the classroom where demonstrations are becoming more dynamic and the second is when the student is tasked with producing statistical information from raw data.
In the past we used practical demonstrations using physical props like wooden blocks or the students themselves. Now we rely on software demonstrations to illustrate our ideas. These often come in the form of web enhancements and as video or multimedia presentations on CD-ROMs that accompany textbooks. Access to such demonstrations is over-rated and has serious limitations for the blind student. Alternatives do exist and the student’s lecturer needs to think carefully about how to explain material in words that these demonstrations display. Physical demonstration may well prove an invaluable approach even if it is seen as a retrograde step.
The second (and probably most concerning) source of software issues is the interaction of student and software to generate statistical analyses. The material taught in introductory courses is changing as we are able to rely more and more on statistical software. A natural consequence is that we can now observe some reduction in the mathematical content within courses, and the corresponding requirement to perform manual calculations. Tasks that were laborious before we had ready access to computers have become very easy. ANOVA and regression are just two examples where textbooks have used trivial and often fictitious small data sets to demonstrate the actual methodology. Once a real data set is used however, we turn to the computer to do the working for us, and can then use a real (and probably larger) data set. Of course, creation of graphics is much easier now too, and this might explain why we now have a greater focus on exploratory data analysis techniques in statistics courses.
Many subject areas will choose statistical software because it does everything that is wanted within a course. This in turn has an impact on what is taught within a course too. Some statistical software will do some tasks much better than others; there are features in Minitab that are not implemented well in SPSS, while some features in SPSS are not implemented in Minitab at all. There are, therefore, reasons why a lecturer could be strict on use of a single software choice. As a lecturer, it will be much easier to administer a course when all students are using the same application.
However, most statistical software is inaccessible to the blind user. Obviously students should not be restricted in their course selections on the basis of the software used in that course. Should allowances be made so that a blind student can use alternative software that is accessible? This author hopes so. If the student cannot access the chosen software for a course then they will need to ensure that whichever application they choose as a substitute can fulfil all the tasks of the course’s preferred software.
Most commercial software is produced in the United States. Given the U.S. has anti-discrimination legislation and is a comparatively litigious society, it is surprising that software developers continue to disregard the needs of blind users. In the author’s opinion, these laws should be used to protect the interests of blind people and their access to software but it is difficult to see that this will happen. It is certainly not a short to medium term solution.
Are support resources suitable for the blind student? Generally they are not. Modern guides to software are aimed at using the graphical user interface (GUI) and dialogue box approach that is pervasive in most commercial packages. Some effort needs to be made to ensure that resources suitable for the blind user are kept up to date and available. This would include scripts written for screen readers so that we can work with statistical software.
Can educators be expected to know how to use their software in different ways? Can they be expected to have resources that tell the student how to use Minitab or SPSS by typing commands rather than using the GUI for example? From my own experience, typing commands is painful in some software packages. Modern versions of software such as Minitab allow the user to at least re-issue commands previously typed into the command window. Other systems such as SAS mostly rely on commands but have recently added menus to aid the user in developing the code required for many simple analyses.
The message: Find software that suits both student and lecturer alike. This will not always be a simple task so the student must be prepared to have the discussion well before the semester begins.
You might think this is simply a matter of getting tables printed in Braille or large print, but in the modern era many sighted students are using scientific calculators that have ready access to the distributions we use in introductory courses. The basic model used in New Zealand high schools has an impressive array of features. As a consequence of the capacity of students to use these features, assessment techniques are changing. The student who does not have ready access to the simple tools will become comparatively inefficient.
The message: Be ready to use tables before the course starts. It is unlikely that a software solution will be appropriate for use in assessment exercises such as tests or exams without prior negotiation.
Unfortunately there is no escaping horrible formulae, although the reliance on doing all the substitutions and integral calculus that was part and parcel of the introductory course in the 20th century is reducing. There is no way of avoiding the various symbols that arise in a statistics course. The intending statistics student needs to know how they will present work in a format the lecturer can handle.
There are some very good sources of formulae nowadays in forms that are fairly easy to learn. Wikipedia’s pages with formulae are using simple LaTeX commands and structures as the alt tags for the graphics read by the sighted user. Some free online texts are also available but the intending student needs to make sure the level of the material is pitched appropriately. Getting the source documents as well as the printable version is possible.
Many lecturers will also present their work in documents prepared using LaTeX. Being able to read such documents from source code may make life a lot easier. Documents written in Microsoft Word and using MathType can be converted to readable LaTeX, but these documents can become messy and rather cumbersome. Other solutions using html and supporting mathematical mark up language is another option for reading formulae, but this is not a practical solution for the creation of documents by the blind student.
The message: The blind student must be prepared to write in Greek. This may mean gaining some basic familiarity with LaTeX or some other system for presenting student work.
Aside from the fact that it is possible to meet the challenges of the four key elements as described above, there are reasons why blind students can succeed where their sighted peers may not. Statistics is all about the ability to predict the future with knowledge of the past; to apply probability; to deal with randomness and understand variability to name just a few points.
Blind people live life encountering things unexpectedly even if they have some vague idea of where something should be (estimation) there is always some amount of inaccuracy (error).
Part of any successful teacher-student relationship is the ability to connect the theory in a course to real life examples that resonate with the students. The experiences of the blind student may not match those of their sighted peers. In the author’s experiences, this mismatch exists in many different ways. For example, international students do not understand any examples based on events in New Zealand’s history without some serious explanation, but all students relate to world news events. Finding examples that match a blind student’s experiences will be difficult for the lecturer who has little knowledge of the blind person’s world. This can be overcome through developing rapport, but this requires some proactive effort by the student.
This author firmly believes that some statistical ideas are best learnt from one’s blind peers. Some notions are so easy to frame up for blind students if only the right scenario can be found to help its explanation. Generally speaking, blind people have been able to form networks where they can pick up information from one another. This is especially true for assistance with our specific software just to name one example. In the author’s opinion, those of us at the forefront of new endeavour by blind people must expect to support those that come along behind us. Thankfully, many blind people do this all the time.
The inaccessibility of software needs to be recorded so that improvements can be made. The experiences listed here are based on varying amounts of experience and will need updating and checking for currency. The commercial packages are presented in chronological order of the author’s interaction with them. In all cases, no specialized scripting for the screen reader software was available. Only in recent times has a second screen reader option been available to trial so comments are appropriate for the situation a new student would find themselves in. No Braille displays have been used with the software.
The following information is relevant to each application’s version and the author must point out that change in software over the years has proven that the comments below are unlikely to remain relevant for new versions of the software. Experimentation is therefore required and recommended; fortunately, most statistical software has a demo version that can be downloaded for a free trial and even the most rudimentary internet search will find the relevant home page. There are of course a large number of software applications that are not described here. Again, experimentation is the only way to determine the usefulness of a particular software tool. In either case, keeping abreast of the experiences of others is always advisable.
The author’s first experiences with Minitab were using it on a DOS PC. This meant typing commands out and mistakes in the syntax meant re-typing the entire command over. Accessibility was good but there was a great deal of pain. Menus in the DOS versions of Minitab were basically non-existent so were not an accessibility issue.
With the move to Windows came a menu-driven approach to using Minitab. Versions 10 to 12 were accessible in terms of menus and dialogue boxes although some detailed dialogue boxes did need some serious guidance to see how the cursor was behaving. The data worksheet was also accessible and behaved as would common spreadsheets.
As with many software developments, Minitab became inaccessible with a new version (Version 14 in this case). The menus were still accessible, but more dialogue boxes were being developed or modified to do a much wider range of tasks than in previous versions. Accessibility was becoming a problem, but the knowledge gained from working in Version 12 meant accessibility was not dramatically diminished.
Version 15 has become even more inaccessible. Menus and dialogue boxes do not function well with screen reader software and without the author’s prior experience, he believes this software would be almost unintelligible for the blind student studying independently.
For most of its history, SAS has relied on the user writing small programs for even the most basic of tasks. These programs are typed in plain text and the output files are plain text also. This makes SAS quite accessible in many respects, but SAS is changing. In Version 8, a GUI was overlaid to generate default code for the user. It is still possible to use the text approach as this is what is required for the more complicated analyses anyway.
The drawback for all SAS users is the large quantity of output that it generates. This might change as we concern ourselves with over-generation of paper as time progresses but in the meantime this software is difficult to work with due to the massive quantity of information generated. It is very difficult to control the amount of output given by SAS.
Some modern statistical techniques are using extra features on top of SAS that are not part of the base distribution. Data mining is done using software that is entirely mouse driven for example. It is therefore not accessible.
SAS is seldom used in first-year courses as it has a steep learning curve. It is often used for postgraduate work however, but this is often just a historical hangover. Another factor worth considering is that SAS licences are often quite attractive for universities.
SPlus was originally a command-line operated application, as it is built on top of the S language. The “Plus” is for the front end that has been commercialized, and this added value is almost entirely based on the GUI and some other modifications for Windows users. The GUI was not useful from 1998 to 2004, but the command line approach worked well for the author during his Doctoral research. SPlus can pull in text files of commands and route all text output to a text file, making it as accessible as statistical software gets.
SPlus does not have as much functionality built in as do some other packages, but SPlus users share their added work freely so a very wide range of statistical analyses are possible even if not using the base distribution.
SPlus users would not use a data worksheet often so accessibility to the data window was seldom used. Displaying data was done via commands and viewed using alternate spreadsheet software.
SPlus is (or was) seldom used for teaching introductory courses because it was thought to have a steep learning curve. A criticism that has been inherited by its freeware successor (described below).
SPSS is the only statistical software to have been subjected to attempts to write scripts for JAWS screen reading software that were bundled with JAWS. These scripts were useful for the version of SPSS they were for, but they failed with the release of the following version of SPSS.
SPSS is not as accessible as the most useful versions of Minitab. It is currently more accessible than the current version of Minitab. It is possible to write code but resources for doing this are quite limited, and seldom used by academics.
In the last few years, the author has moved to one statistical software application for almost everything he does. While other software has increased its inaccessibility to the extent that he cannot use it independently, one system leaves all others far behind. This software is known as “R” and was originally developed in Auckland, New Zealand. It is freely available for all operating systems and is spreading to more languages all the time. R operates in the same way as S, the language used to underpin SPlus described above.
The core development team is now a worldwide group, nominally based in Austria. There are also hundreds of statisticians all over the world creating additional packages for use within R who make them available for download at any time. Many former users of SPlus have moved to R as their programs are easily transferred.
R installs and uninstalls cleanly in that all necessary files are placed in one directory structure on the hard drive. This includes the help files which are plain html. Many of the documentation files are available as LaTeX files too so are again, quite accessible.
R is considered by many to have a steep learning curve. This author disagrees. For many of our students, and in particular when it comes time to consider the needs of the blind user, R is easier to learn than SAS for example. For the sighted world, R is harder to learn and teach than the GUI based applications such as Minitab or SPSS. Part of the problem is that the GUI approach feels familiar to the vast majority of students and there is instant gratification when students see results print out.
R is fundamentally different in that it is an object oriented system. It has similarities to such software as Matlab for example. The author takes advantage of this fact when teaching his second year technology and engineering students during the last quarter of a course dominated by use of Matlab.
In object oriented systems we are more purposeful when we act. We take steps because we know what we want. Blind students need to know what they want before they ask for it. This author’s experience dealing with many blind people suggests that blind people are good at knowing what they want; knowing how to get it often poses some difficulty. Creation of adequate resources is a task being undertaken by the author to meet the needs of blind students as an added bonus of creating material for the sighted students he teaches.
By choosing to run R in a terminal window instead of the default GUI operation, accessibility to all text information is assured. This claim has been tested using JAWS, NVDA and Window Eyes screen readers. Output can be saved as plain text files and is therefore readable by all vision impaired students using their normal mode of operation, whether this be using screen reading software, text enlargement, or a Braille display. No scripts are required to assist screen readers, and therefore Braille displays, with access to the statistical output from R. An initial attempt to write scripts for the GUI operation of R proved successful but short-lived; these were not simple to write and did not survive the next version change in the software. This author firmly believes that a solution that works straight out of the box must be viewed as preferable to the massive undertaking required to create and maintain suitable scripts for any screen reading solution.
In many professions chosen by blind and vision impaired students it is obvious that there is a career that will result from completing a tertiary qualification. Role models are well-known in such disciplines as counselling, physiotherapy and the law. There are not so many to find in statistical careers, although there are a number to be found if you look hard enough. There are a number of practising actuaries for example.
Postgraduate study in statistics is possible. Aside from his own experiences, the author knows of one blind person currently undertaking doctoral research today, and knows of yet another that has completed their PhD in applied probability.
If role models are to be sought then the author must point out that the current World Blind Union President (Marianne Diamond from Australia) was trained as a mathematical statistician; although her career path did not involve practising as a statistician, it is not unusual for a graduate to use their knowledge in a different field after leaving university.
The author must (slightly reluctantly) also consider himself among the role models, but an old saying remains prominent in the author’s mind since first hearing it many years ago: “Those who can, do; those who can’t, teach.” Without question it has proven easier to teach stats than to do stats, but why is it so? Teaching means this author does not need to do the interpretation of graphs and the like himself. He does not have to mark the students’ work himself and now that assignment questions can be set with different data sets for each student, it is the senior students who mark the students’ work need to have the students’ data in mind. Any interpretation-type statements made by the student must be logical and suit their data. Because the author has worked using a programming approach, he can generate the basic requirements for every student’s data set when the data is created.
It is easier to guide research than to do it. Working as the statistician, rather than the researcher using the stats, means relying on knowledge of the theory and the ability to communicate ideas worth investigating. A necessary task for the modern academic statistician is to pick up consulting work within, and external to, the university environment. Research collaborations are the natural consequence of consulting work. Many practising statisticians are doing this as their primary task. The author is, therefore, confident that he or any other blind person who chooses to do so can work as a statistician outside the comfort of a university environment.
In the 20th century, access to printed information was the primary limitation on the blind student. In the author’s opinion, it is the modern ways of teaching statistics that are driving the inaccessibility in the 21st century. The ability of the blind student to take courses in qualitative disciplines and succeed is increasing with the improvements in technology. In many sciences, the opposite is true as we lose ground due to advancements in software and other technologies that are not created with the blind user in mind.
It is possible for the blind student to succeed in a statistics course. It will take some serious preparation before the course starts, some additional work during the course, and some reasonable accommodations being made by the course staff. As much as the blind student is afraid of failing statistics, most academic staff are afraid of failing capable students.
Funding in support of the author’s participation at WEIMS’09 was obtained from the Cyril White Memorial Fund.