Statistics assignments that require the use of a z-table can be challenging for students with low vision who often receive copies of z-tables that are not optimized with visual impairment access in mind. Honestly, I had so much trouble finding accessible z-tables for visual impairment and print disabilities that I decided to create my own templates that I could use in my Statistics classes. I was looking for something that could be downloaded for offline access, used clear fonts that could be easily enlarged with screen magnification or browser zoom, and that matched the formula sheets used in high school and college classrooms, and have shared these files below that anyone can use. Here are my favorite tips and free resources for adapting accessible z-tables for low vision and large print formats, part of my Math Problems for Low Vision series that covers topics related to math accessibility.
Also known as a standard normal table, the z-table is a common fixture in many statistics classes, providing information on the percentage of values that are less than a given z-score. A typical z-table consists of 11 columns and anywhere between 35 and 70 rows containing long decimal values placed in close proximity and in small print sizes to fit on a single page.
Another barrier to access for z-tables is that they are often shared as PDF documents in a low-resolution format that contains scanned images or blurry/pixelated text, which can be difficult to read even without a visual impairment- highlighting text as an anchor tool is not possible on a scanned image that does not contain actual text. The non-responsive nature of a PDF makes it even more difficult for students to enlarge the font size or adjust the spacing of numbers within the table, not to mention keep track of specific rows or columns. If a physical copy is created from a low-resolution digital file, attempting to enlarge the text will only intensify the pixelated or blurred appearance, making text even more difficult to access.
Attempting to create an accessible copy by enlarging a physical copy or low-resolution file to increase the font size also creates a frustrating experience, as the resulting table will likely take up several dozen pages or have information cut off at the edge due to the sheer amount of numbers involved.
One option for customizing how a z-table is viewed is to export the values as a CSV file, which is a plain text file that contains a list of data separated by commas. This can be converted into a spreadsheet in Microsoft Excel or Google Sheets, used with statistical programming languages like Python or R to locate values, imported into database software, or used to create a table. Most z-tables display values rounded to five decimal places, though formula sheets for AP Statistics or other statistics classes often display values rounded to four decimal places.
For convenience, I have created two csv files for z-tables, one rounded to five decimal places with a range of -.3.9 to +3.9, and a second table rounded to four decimal points with a range of -3.4 to +3.4, which is the same as the Standard Normal Probabilities table listed on the AP Statistics formula sheet. Both csv files have headers and are 100% free to download.
A focus window or line guide blocks out surrounding text on a page or displays a certain number of lines at a time so the reader can focus on one section at a time. There are a few different ways to use this strategy for reading a z-table, including:
In a traditional z-table with the example value of 1.44, the first part of the z-score is displayed in the leftmost column (1.4), while the top row of the table corresponds to the second part of the z-score (0.04). One option for making a z-table easier to read for students with low vision is to transpose the rows and columns sot that the first part of the z-score is shown in the top row (1.4), while the second part of the z-score is displayed in the leftmost column (0.04), creating a table with fewer rows but more columns.
This layout would be helpful for students who want to use a line guide or typoscope to block out surrounding text, as this would block out nonessential visual information and provide the student with an option to use a second line guide to block out surrounding text to focus on a single line. This would also work out better for creating a large print booklet or accessible physical copy, since it is easier to fit the vertical columns on one page when printing in a portrait layout.
For convenience, I have transposed the layout of the csv files shared in an earlier section, one for AP Statistics with four decimal places and one with five decimal places. Both csv files have headers and are 100% free to download.
HTML formats are designed to be read in the web browser and offer a responsive layout with options for using browser zoom, enlarging the text size, adjusting line spacing and other digital text preferences. This can be easier than reading a PDF document, which has fewer options for magnification or adjusting the size or appearance of text. Another bonus is that the user can search for specific rows using the Ctrl + F keyboard shortcut, which can help with locating values.
I created a basic HTML table for both z-tables, which can be customized using the Developer Tools menu in a web browser (keyboard shortcut Ctrl + Shift + I). Once the Developer Tools menu is open, select the text box for the body section of the page to customize characteristics such as:
To use this HTML table efficiently with a screen reader, use the Ctrl + F keyboard shortcut to search for the first part of the z-score, including the negative sign. This will bring the cursor to the row of interest, which makes it easier to locate the desired value.
For students that want a z-table more suitable for printing or for navigating using an eReading software, an EPUB file format or Word document may be preferred. Alternatively, users may prefer to sideload a HTML document into a reading application like the Amazon Kindle app.
In my personal experience, the z-table in the back of the EPUB version for my college statistics textbook was easy to enlarge on the computer, but I didn’t like the way it looked on my iPad very much. To create a version that looked better on my iPad, I edited the HTML documents (linked above) in Microsoft Word to show fewer columns on each page, cutting and pasting columns underneath the table in the document. The headers were displayed on each page of the document, so it was easier to keep track of numbers, and I could also customize the display further with color coding, additional line spacing and custom fonts.
If internet access is allowed, one option for viewing an accessible z-table for students with low vision is to browse the free online z-table at ztable.io (link below). This website offers several features for learning to use a standard normal table, including:
When hovering over values in a z-table, the corresponding row and column will be highlighted in purple to serve as a visual landmarking tool. Because it is a website, it is highly unlikely that this would be approved as a testing accommodation, but it is a helpful tool for instructors or for homework practice and provides clearer font display compared to a PDF.
By Veronica Lewis/Veronica With Four Eyes, www.veroniiiica.com
Published October 2024.
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