An example of the utility of the yearly chart occurs below. Every state must provide an annual report of specific data related to the education of students with disabilities to the United States Department of Education. The task of reporting special education data for Pennsylvania falls on the shoulders of PennData. PennData verifies and reports information about special education students who live in PA. Information collected includes counting students’ primary disability. As of 2014-15 the following disabilities appeared in the report: Autism, Deaf-Blindness, Hearing Impairment including Deafness, Intellectual Disability (MR), Multiple Disabilities, Orthopedic Impairment, Emotional Disturbance, Specific Learning Disability, Speech or Language Impairment, Traumatic Brain Injury, Visual Impairment including Blindness, and Other Health Impairment
Some of the previous disability categories have received a great deal of attention, namely autism. Even driving down a road you may have encountered a billboard raising awareness as to the prevalence of autism.
For people of a certain age, the number certainly seems incredible. I grew up a child of the 70s and the prevalence estimates came for autism came to about 1 per 20,000 (1 student in 20,000 had a diagnosis of autism). Today one can find prevalence figures at 1 in 88 and even 1 in 68. From my childhood to today, the proportion of children found to have autism has changed dramatically!
Why the prevalence has grown raises debate. Discussing why they have changed would require another blogpost (or three). But the data undeniably show a large increase in students receiving the diagnosis of autism. Now back to PennData.
The chart below shows the yearly counts of three different categories of students in the state of Pennsylvania: The total number of all reported disabilities, students with intellectual disabilities (previously reported as Mental Retardation), and students with Autism (previous category also included pervasive developmental disorder). As shown by the yearly chart, the data reflect the reality of changes for the disability category autism.
The celeration value covering 1995 to 2011 has accelerated by x2.5. A x2.5 celeration represents 150% increase across time! The bounce value of x1.3 speaks to variability. A x1.3 depicts stability. Therefore, we have two values on the yearly chart. Celeration and bounce illustrate a rapidly growing, stable acceleration of students diagnosed with autism.
Contrasting autism, students with intellectual disabilities has decelerated by ÷1.15. A ÷1.15 tells us the measured quantity decelerated 1.15 times every five years. A ÷1.15 comes to a 13% reduction. The bounce interestingly comes to x1.3, a remarkably stable pattern across time.
The last category shows the total students with disabilities for Pennsylvania. The celeration value displays a growth rate of x1.15. The bounce again comes to x1.3 and suggests stability across time. Variability would mean an influx of people or a dramatic lessening, for example by students leaving the state. But we see little variability.
Another beautiful feature of the yearly chart comes when we compare the three different data sets. Notice each data set starts off at different places on the chart. But the yearly Standard Celeration Chart (SCC) allows for a fair comparison of the statistical magnitude of three different data sets due to the proportional construction of the chart. Look at the linear graph below. Does it depict the same type of changes as the Yearly SCC?
A curious relation emerges when we view the yearly SCC (Figure 2). Students with intellectual disabilities started off much higher total number (approximately 28,000) than students with autism (about a 1,000) in 1994. A deceleration of ÷1.15, or a 13% reduction across time) for students with intellectual disabilities means in 2011 almost 10,000 fewer students falling under the specific disability category. The celeration value of x2.5 for autism reflects a 150% increase for the disability category across time. In 2011 about 19,000 more students had the disability of autism.
From the data, we cannot conclude the 10,000 fewer students with intellectual disabilities were categorized in the 19,000 students with autism. The PennData represent descriptive counts, not causal data. Still, the chart allows us to see relations between two sets of data and explore questions more vigorously. Why the deceleration in students with intellectual disabilities? Do the other disability categories show growth or decay across time? For example, one might also plausibly argue that students with intellectual disabilities now show up as students with multiple disabilities.
Many discoveries await you when you chart on the Standard Celeration Chart. And now that you have access to another chart, fire up those yearly data!