fortdefruitI

2021-07-05

When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether simultaneous or preceding sounds could reduce AB. Twenty subjects were presented a rapid visual stream of symbols and letters on a computer screen and asked to identify the first and second letters (the targets). After several trials, the subject's AB magnitude was measured as the difference between the percentages of first target and second target letters correctly identified. Each subject performed the task under each of three conditions. In the Simultaneous condition, a sound (tone) was presented simultaneously with the second target; in the Alert condition, a sound was presented prior to the coming of the second target; and in the No-Tone condition, no sound was presented with the second target. Scatterplots of AB magnitude for each possible pair of conditions are shown below as well as the least squares line for each.

a. Which pair of conditions produces the least squares line with the steepest estimated slope?

b. Which pair of conditions produces the least squares line with the largest SSE?

c. Which pair of conditions produces the least squares line with the smallest estimate of $\sigma$?

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(a) We note that all sketched lines in the scatterplots slope upwards.
The least-squares line has the steepest slope, when the line slopes upwards the strongest.
In this case, we note that the middle scatterplot of AB magnitude alert vs. AB magnitude No-Tone contains the steepest line and thus the pair of conditions Alert and No-Tone produce the steepest estimated slope.
(b) The least-squares line has the largest SSE when the vertical distance between the points and the least-squares line is greatest.
We note that the middle scatterplot of AB magnitude alert vs. AB magnitude No-‘Tone contains a single point at the bottom of the scatterplot that deviates much more from the least-squares line than all other points in the other scatterplots.
We would then expect the least-squares line in the middle scatterplot to have the largest SSE and thus the pair of conditions Alert and No-tone produce the largest SSE.
(c) he least-squares line has the smallest estimate of o when the vertical distance between the points and the least-squares line is greatest.
We note that the points in the right scatterplot of AB magnitude Sim vs. AB magnitude Alert appear to lie the closest to the least-squares line compared to the other scatterplots.
We would then expect the least-squares line in the right scatterplot to have the smallest estimate of o and thus the pair of conditions Sim and Alert produces the smallest estimate of σ

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