## Introduction

I started writing this file from scratch at 10:02 in the morning of the day I delivered this talk.

I felt there was a need to demonstrate that the claims I made in my paper were realistic.

I have started by writing an R markdown document, which is just a plain text file. I can therefore read or write this file on a braille display If I choose.

I have had no sighted assistance to prepare this document. The final version being used for the talk is an HTML file that is also very readable using standard tools.

I have used:

• the WriteR text editor Godfrey and Curtis (2016) which I use instead of the (currently) inaccessible RStudio IDE RStudio Team (2020) that my students use.
• A standard installation of R statistical software R Core Team (2020)
• The BrailleR add-on package Godfrey et al. (2020) which was first introduced in Godfrey (2012)
• and a selection of other R packages that we expect our undergraduate students to use, including ggplot2 Wickham et al. (2020), knitr Xie (2020), and rmarkdown Allaire et al. (2020)

## An Exploratory Data Analysis Task

A student completing one of our first year statistics courses should be able to complete the following task as part of an assignment.

“Use the diamonds data to highlight differences in the price of diamonds according to a selection of potential predictors of price.”

A sufficient solution is as follows:

library(ggplot2)
data(diamonds, package = "ggplot2")
Graph1 <- diamonds %>% ggplot(aes(x = carat, y = price)) + geom_point(alpha = 0.01) +
geom_smooth(color = "blue")
Graph1
geom_smooth() using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Graph2 <- diamonds %>% ggplot(aes(x = color, y = price)) + geom_boxplot()
Graph2

A blind person would add the following commands to know what those plots display:

library(BrailleR)
VI(Graph1)
This is an untitled chart with no subtitle or caption.
It has x-axis 'carat' with labels 0, 1, 2, 3, 4 and 5.
It has y-axis 'price' with labels 0, 5000, 10000, 15000 and 20000.
It has 2 layers.
Layer 1 is a set of 53940 points.
Layer 1 has alpha set to 0.01.
Layer 2 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
VI(Graph2)
This is an untitled chart with no subtitle or caption.
It has x-axis 'color' with labels D, E, F, G, H, I and J.
It has y-axis 'price' with labels 0, 5000, 10000 and 15000.
The chart is a boxplot comprised of 7 boxes with whiskers.
There is a box at x=D.
It has median 1838. The box goes from 911 to 4213.5, and the whiskers extend to 357 and 9138.
There are 482 outliers for this boxplot.
There is a box at x=E.
It has median 1739. The box goes from 882 to 4003, and the whiskers extend to 326 and 8674.
There are 760 outliers for this boxplot.
There is a box at x=F.
It has median 2343.5. The box goes from 982 to 4868.25, and the whiskers extend to 342 and 10693.
There are 694 outliers for this boxplot.
There is a box at x=G.
It has median 2242. The box goes from 931 to 6048, and the whiskers extend to 354 and 13721.
There are 473 outliers for this boxplot.
There is a box at x=H.
It has median 3460. The box goes from 984 to 5980.25, and the whiskers extend to 337 and 13460.
There are 456 outliers for this boxplot.
There is a box at x=I.
It has median 3730. The box goes from 1120.5 to 7201.75, and the whiskers extend to 334 and 16309.
There are 208 outliers for this boxplot.
There is a box at x=J.
It has median 4234. The box goes from 1860.5 to 7695, and the whiskers extend to 335 and 16427.
There are 66 outliers for this boxplot.

A talented (perhaps blind) student would perhaps improve the first graph using the following:

Graph1a <- diamonds %>% ggplot(aes(x = carat, y = price)) + geom_point(alpha = 0.01) +
geom_smooth(color = "blue") + facet_wrap(~color)
Graph1a
geom_smooth() using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
VI(Graph1a)
This is an untitled chart with no subtitle or caption.
The chart is comprised of 7 panels containing sub-charts, arranged horizontally.
The panels represent different values of color.
Each sub-chart has x-axis 'carat' with labels 0, 1, 2, 3, 4 and 5.
Each sub-chart has y-axis 'price' with labels 0, 5000, 10000, 15000 and 20000.
Each sub-chart has 2 layers.
Panel 1 represents data for color = D.
Layer 1 of panel 1 is a set of 6775 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 1 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
Panel 2 represents data for color = E.
Layer 1 of panel 2 is a set of 9797 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 2 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
Panel 3 represents data for color = F.
Layer 1 of panel 3 is a set of 9542 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 3 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
Panel 4 represents data for color = G.
Layer 1 of panel 4 is a set of 11292 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 4 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
Panel 5 represents data for color = H.
Layer 1 of panel 5 is a set of 8304 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 5 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
Panel 6 represents data for color = I.
Layer 1 of panel 6 is a set of 5422 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 6 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.
Panel 7 represents data for color = J.
Layer 1 of panel 7 is a set of 2808 points.
Layer 1 has alpha set to 0.01.
Layer 2 of panel 7 is a 'lowess' smoothed curve with 95% confidence intervals.Layer 2 has colour set to vivid violet.

The VI() command has extracted quite alot of information from the created graph objects. It produces exact details when these are easily obtained, but only structural information for some plot elements.

The BrailleR package is undergoing improvements, with special attention being given to the plots generted using the ggplot2 package. There is definite need for ongoing effort in this regard.

## The Four Elements of a Statistics Course

At the first workshop in this series, now eleven years ago, I said there were four main concerns for anyone undertaking a course in statistics Godfrey (2009).

They haven’t changed in number, but the emphasis in today’s environment are very definitely different, and I suggest that blind students are considerably better off today than a student from ten years ago.

## Element 1: Graphs

Aside from the dramatic improvements in the ability to know what has been produced, little has changed in the tools being used by blind students today.

We have seen improvements in tactile graphic creation and development of interactive tools for exploration of graphs.

The range of tools has increased, but interactions with students suggest to me that the way these students expect to engage in theri statistics courses has not changed. Students rely more on human support than is truly necessary.

## Element 2: Statistical Software

Godfrey (2009) unashamedly promoted use of R (R Core Team 2020) for offering the best access to software for blind people.

The last ten years has seen little change in the accessibility of statistical software. While personal preference plays a role in making this proclamation, I still believe R is the best option for any blind person, with only two other options offering anything close to what I consider access.

Ten years of attempting to gain any traction with statistical software developers has been almost fruitless. The advances in R are courtesy of a large and extremely active open source community. The only other options that offer the blind user any hope of equivalent access as enjoyed by their sighted peers remains SAS and Stata. Rather unfortunately, neither of these options has much traction in the teaching of undergraduates in any discipline nowadays, and only SAS can claim to take access for blind users seriously.

## Element 3: Tables

Looking up tables to perform manual calculations ought to be a thing of hte past, but due to the inability to successfully modernise assessment procedures, their use remains.

Even if a student must use tabulated information, there is no need for them to rely on the printed version of the tables. We can use software as a calculator; sighted students using modern calculators don’t have to look at printed tables either.

The critical point that seperates 75% of the standard normal distribution from the other 25% is found using:

qnorm(0.75)
[1] 0.6744898

OK, the printed tables are rounded to four decimal places for proportions and two for z values, so the student might need to use:

round(qnorm(0.75), digits = 2)
[1] 0.67

## Element 4: Mathematical Formulae

Tools to embed mathematical content in HTML pages have dramatically improved over the last ten years. Tools to help blind users read that content have also improved significantly.

It is now realistic to expect a sighted student to include the proper symbols in their work. We want to see $$\mu$$ used for the population mean.

In markdown, this is created using standard LaTeX notation and served to the reader using either MathML or MathJax.

Today’s blind authors cannot rely on pdf to create mathematical content independently.

## BrailleR in Action

In order to support blind people wishing to make use of the range of tools I’ve found most useful, and those that I’ve created over the last ten years, I have compiled my work into an online book called “BrailleR in Action”

It uses the same tools as do many other authors in the R community and is based on R markdown. We now use this format for