# Tutorial 2: Overlapping binaries.

Having previously demonstrated what two binary groupings look like when they are separated by six standard deviations, here I demonstrate what they look like when separated by 4 standard deviations. Such a binary has an overlapping coefficient of 4.55%, as seen from the code below, which computes from integration based on Weitzman’s overlapping distribution.

``## 0.04550026 with absolute error < 3.8e-05``
``## [1] "4.55%"``

This is what such data looks like graphed in a density curve.

The overlap range is now much larger, as can be seen in the scatterplot below.

Now let’s look at an overlap range of 2 standard deviations.

``## 0.3173105 with absolute error < 4.7e-05``
``## [1] "31.73%"``

The density plot now overlaps a lot.

And this is what the scatterplot looks like.

Now look at the scatterplot without color differences. At this point there is the barest of hints that there might be a binary in this system at all.

Let us compare that to the initial binary, separated by 6 standard deviations, now in grey.

With this data, the binary remains visible and obvious even when both samples are gray.

However, even if you cannot observe categories by directly looking, there are tools that can help identify N-nary categories in what looks to us like gradient data – the tools of unsupervised cluster analysis, which I will discuss in the next tutorial.

The RMarkdown file used to generate this post can be found here. Some of the code was modified from code on this site.

References:

Weitzman, M. S. (1970). Measures of overlap of income distributions of white and Negro families in the United States. Washington: U.S. Bureau of the Census.

# Tutorial 1: Gradient effects within binary systems

This post provides a visual example of gradient behaviour within a univariate binary system.

Here I demonstrate what two binary groupings look like when each binary is separated on a non-dimensional scale of 1 standard deviation for each binary, with a separation of 6 standard deviations. Such a binary has an overlapping coefficient of 0.27%, as seen from the code below, which was computed from integration based on Weitzman’s overlapping distribution.

``## [1] "0.27%"``

But the overlapping range hides the fact that in a group of, say, 10,000 for each binary, the outlier overlap is often enormous, and sometimes individual tokens look like they belong firmly in the other binary choice – like the one blue dot in the gold cloud. (Note that the y-axis is added to make the display easier to understand, but provides none of the data used in this analysis.)

In short, in a binary systems, individual tokens that exist thoroughly within the other binary range will exist due to simple random variation, yet they do not present evidence of constant gradient overlap or against the existence of the binary. Such things occur as long as the two binaries are close enough in relation to the number of examples – close enough being determined by simple probability, even in a univariate system (one without outside influences.)

The RMarkdown file used to generate this post can be found here. Some of the code was modified from code on this site.

References:

Weitzman, M. S. (1970). Measures of overlap of income distributions of white and Negro families in the United States. Washington: U.S. Bureau of the Census.

# Visual-tactile Speech Perception and the Autism Quotient

Katie Bicevskis, Bryan Gick, and I recently published “Visual-tactile Speech Perception and the Autism Quotient” in Frontiers in Communication: Language Sciences. In this article, we demonstrated that the more people self-describe as having autistic-spectrum traits, the more they tolerate a separation of time between air-flow hitting the skin and lip opening from a video of someone saying an ambiguous “ba” or “pa” when identifying the syllable they saw and felt, but did not hear.

First, in an earlier publication, we showed that visual-tactile speech integration depended on this alignment of lip opening and airflow, and that this is evidence of modality-neutral speech primitives. We use whatever information we have during speech perception regardless of whether we see, feel, or hear it.

This result is best illustrated with the image above. The image shows a kind of topographical map, where white represents the “mountaintop” of people saying the ambiguous audio-tactile syllable is a “pa”, and green represents the “valley” of people saying the ambiguous audio-tactile syllable is a “ba”. On the X-axis is the alignment of the onset of air-flow release and lip opening. On the Y-axis is the participants’ Autism-spectrum Quotient. Lower numbers represent people who describe themselves as having the least autistic-like traits; the most neurotypical. At the bottom of the scale, perceivers identify the ambiguous syllables as “pa” with as much as 70-75% likelihood when the air-flow arrived 100-150 milliseconds after lip opening – about when it would arrive if a speaker stood 30-45 cm away from the perceiver. Deviations led to steep dropoffs, where perceivers would identify the syllable as “pa” only 20-30% of the time if the air flow arrived 300 milliseconds before the lip opening. In contrast, at the top of the AQ scale, perceivers reported perceiving “pa” as little as only 5% more often when audio-tactile alignment was closer to that experienced in typical speech.

These results are very similar what happens with people who are on the autism spectrum with audio-visual speech. Autists listen to speech with their ears more than they look with their eyes, showing a weak multisensory coherence during perceptual tasks (Happé and Frith, 2006). Our results suggest such weak coherence extends into the neutoryipcal population, and can be measured in tasks where the sensory modalities are well-balanced (which is easier to do in speech when audio is removed.)

References:

Bicevskis, K., Derrick, D., and Gick, B. (2016). Visual-tactile integration in speech perception: Evidence for modality neutral speech primitives. Journal of the Acoustical Society of America, 140(5):3531–3539

Derrick, D., Bicevskis, K., and Gick, B. (2019). Visual-tactile speech perception and the autism quotient. Frontiers in Communication – Language Sciences, 3(61):1–11

Derrick, D., Anderson, P., Gick, B., and Green, S. (2009). Characteristics of air puffs produced in English ‘pa’: Experiments and simulations. Journal of the Acoustical Society of America, 125(4):2272–2281

Happé, F., and Frith, U. (2006). The Weak Coherence Account: Detail-focused Cognitive Style in Autism Spectrum Disorders. Journal of Autism and Developmental Disorders, 36(1):5-25