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Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it is violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity. Espaio The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities x (in decibels), the Weber fraction y (in decibels) is shown. Figure 1 is a scatter plot of the data. Also given is the product of the stimulus intensity and the Weber fraction for each of the ten stimuli. (These products, written in the column labelled "xy", may aid in calculations.) Stimulus Weber intensity, x fraction, y xy (in decibels) (in decibels) 35 -0.45 -15.75 40 -0.43 -17.2 45 -1.39 -62.55 14 50 -1.07 -53.5 -24 55 -2.15 -118.25 60 -2.76 -165.6 65 -3.2 -208 70 -3 -210 75 -4.27 -320.25 Stimulus intensity (in decibels) 80 -4.48 -358.4 Figure 1 Send data to calculator Send data to Excel What is the sample correlation.coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places. (If necessary, consult a list of formulas.) Weber fraction (in decibels) 回 日 B回回

Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it is violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity. Espaio The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities x (in decibels), the Weber fraction y (in decibels) is shown. Figure 1 is a scatter plot of the data. Also given is the product of the stimulus intensity and the Weber fraction for each of the ten stimuli. (These products, written in the column labelled "xy", may aid in calculations.) Stimulus Weber intensity, x fraction, y xy (in decibels) (in decibels) 35 -0.45 -15.75 40 -0.43 -17.2 45 -1.39 -62.55 14 50 -1.07 -53.5 -24 55 -2.15 -118.25 60 -2.76 -165.6 65 -3.2 -208 70 -3 -210 75 -4.27 -320.25 Stimulus intensity (in decibels) 80 -4.48 -358.4 Figure 1 Send data to calculator Send data to Excel What is the sample correlation.coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places. (If necessary, consult a list of formulas.) Weber fraction (in decibels) 回 日 B回回

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Data Table and Correlation Analysis** The table presents data regarding stimulus intensity (in decibels) and corresponding weights: | Stimulus Intensity (dB) | Weight | |-------------------------|--------| | 60 | -2.76 | | 65 | -3.2 | | 70 | -3 | | 75 | -4.27 | | 80 | -4.48 | ### Figure 1: Scatter Plot The scatter plot features stimulus intensity on the x-axis and weight on the y-axis. Each data point is represented by an "x" marking the correlation between these two variables. ### Task Calculate the sample correlation coefficient for the above data. Ensure that intermediate calculations are carried to at least four decimal places, with the final answer rounded to three decimal places if necessary. For assistance, refer to a list of formulas. **Interactive Tools:** - Options to send the data to a calculator or Excel are provided. - Icons are visible for quick actions such as new calculations or help (indicated by symbols for input, reset, and help).
Transcribed Image Text:**Data Table and Correlation Analysis** The table presents data regarding stimulus intensity (in decibels) and corresponding weights: | Stimulus Intensity (dB) | Weight | |-------------------------|--------| | 60 | -2.76 | | 65 | -3.2 | | 70 | -3 | | 75 | -4.27 | | 80 | -4.48 | ### Figure 1: Scatter Plot The scatter plot features stimulus intensity on the x-axis and weight on the y-axis. Each data point is represented by an "x" marking the correlation between these two variables. ### Task Calculate the sample correlation coefficient for the above data. Ensure that intermediate calculations are carried to at least four decimal places, with the final answer rounded to three decimal places if necessary. For assistance, refer to a list of formulas. **Interactive Tools:** - Options to send the data to a calculator or Excel are provided. - Icons are visible for quick actions such as new calculations or help (indicated by symbols for input, reset, and help).
**Weber's Law and Auditory Intensity Discrimination** Weber's law, commonly introduced in psychology courses, posits that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant. This ratio, known as the "Weber fraction," implies that the perception of changes in stimulus intensity is consistent regardless of the base intensity. While Weber's law often holds as a useful rule of thumb, there are exceptions, particularly with certain auditory stimuli where the Weber fraction varies systematically with stimulus intensity. **Experimental Data and Analysis** The table below presents data from an auditory intensity discrimination task. It includes the stimulus intensity \(x\) (in decibels), the Weber fraction \(y\) (in decibels), and the product of the stimulus intensity and the Weber fraction (\(xy\)) for ten different stimuli. These products may facilitate calculations related to Weber's law. | Stimulus Intensity \(x\) (in decibels) | Weber Fraction \(y\) (in decibels) | \(xy\) | |----------------------------------------|-----------------------------------|-------| | 35 | -0.45 | -15.75| | 40 | -0.43 | -17.2 | | 45 | -1.39 | -62.55| | 50 | -1.07 | -53.5 | | 55 | -2.15 | -118.25| | 60 | -2.76 | -165.6| | 65 | -3.2 | -208 | | 70 | -3.0 | -210 | | 75 | -4.27 | -320.25| | 80 | -4.48 | -358.4| **Figure 1: Scatter Plot of Experimental Data** The scatter plot in Figure 1 visualizes the relationship between stimulus intensity \(x\) and Weber fraction \(y\). The x-axis represents the stimulus intensity in decibels, while the y-axis represents the Weber fraction in decibels. The plot illustrates a decreasing trend, suggesting that as the stimulus intensity increases, the Weber fraction becomes more negative. **Further Analysis** For those interested in exploring the correlation of these data, the sample correlation coefficient can be calculated. Ensure all intermediate computations are carried to at
Transcribed Image Text:**Weber's Law and Auditory Intensity Discrimination** Weber's law, commonly introduced in psychology courses, posits that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant. This ratio, known as the "Weber fraction," implies that the perception of changes in stimulus intensity is consistent regardless of the base intensity. While Weber's law often holds as a useful rule of thumb, there are exceptions, particularly with certain auditory stimuli where the Weber fraction varies systematically with stimulus intensity. **Experimental Data and Analysis** The table below presents data from an auditory intensity discrimination task. It includes the stimulus intensity \(x\) (in decibels), the Weber fraction \(y\) (in decibels), and the product of the stimulus intensity and the Weber fraction (\(xy\)) for ten different stimuli. These products may facilitate calculations related to Weber's law. | Stimulus Intensity \(x\) (in decibels) | Weber Fraction \(y\) (in decibels) | \(xy\) | |----------------------------------------|-----------------------------------|-------| | 35 | -0.45 | -15.75| | 40 | -0.43 | -17.2 | | 45 | -1.39 | -62.55| | 50 | -1.07 | -53.5 | | 55 | -2.15 | -118.25| | 60 | -2.76 | -165.6| | 65 | -3.2 | -208 | | 70 | -3.0 | -210 | | 75 | -4.27 | -320.25| | 80 | -4.48 | -358.4| **Figure 1: Scatter Plot of Experimental Data** The scatter plot in Figure 1 visualizes the relationship between stimulus intensity \(x\) and Weber fraction \(y\). The x-axis represents the stimulus intensity in decibels, while the y-axis represents the Weber fraction in decibels. The plot illustrates a decreasing trend, suggesting that as the stimulus intensity increases, the Weber fraction becomes more negative. **Further Analysis** For those interested in exploring the correlation of these data, the sample correlation coefficient can be calculated. Ensure all intermediate computations are carried to at
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