cumulative gaussian (normal) distribution function Search Results


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GraphPad Software Inc cumulative gaussian functions
Plots showing the mean proportion of time participants responded that the comparison rectangle was (a) wider or (b) taller than the standard rectangle for the seven comparison variants tested as function of which side the comparison was on (left/right) and the side that the pre-cue was tested on. Curves show the best fitting <t>cumulative</t> <t>Gaussian</t> function for the group means. Error bars show ±1 S.E.M.
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MathWorks Inc cumulative gaussian function
Plots showing the mean proportion of time participants responded that the comparison rectangle was (a) wider or (b) taller than the standard rectangle for the seven comparison variants tested as function of which side the comparison was on (left/right) and the side that the pre-cue was tested on. Curves show the best fitting <t>cumulative</t> <t>Gaussian</t> function for the group means. Error bars show ±1 S.E.M.
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MathWorks Inc gaussian cumulative density functions
Plots showing the mean proportion of time participants responded that the comparison rectangle was (a) wider or (b) taller than the standard rectangle for the seven comparison variants tested as function of which side the comparison was on (left/right) and the side that the pre-cue was tested on. Curves show the best fitting <t>cumulative</t> <t>Gaussian</t> function for the group means. Error bars show ±1 S.E.M.
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Plots showing the mean proportion of time participants responded that the comparison rectangle was (a) wider or (b) taller than the standard rectangle for the seven comparison variants tested as function of which side the comparison was on (left/right) and the side that the pre-cue was tested on. Curves show the best fitting <t>cumulative</t> <t>Gaussian</t> function for the group means. Error bars show ±1 S.E.M.
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MathWorks Inc fminsearch in matlab
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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MathWorks Inc cumulative gaussian psychometric function
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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SourceForge net cumulative gaussian function
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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MathWorks Inc matlab function norminv
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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MathWorks Inc maximum-likelihood method
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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MathWorks Inc sigmoid function
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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MathWorks Inc psignifit toolbox
Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a <t>Gaussian</t> probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).
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GraphPad Software Inc cumulative gaussian prism 4.0
Example stimuli are depicted as described in the text. Judgments were made regarding the center of rotation of the Glass pattern relative to the black outer <t>Gaussian</t> markers.
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Image Search Results


Plots showing the mean proportion of time participants responded that the comparison rectangle was (a) wider or (b) taller than the standard rectangle for the seven comparison variants tested as function of which side the comparison was on (left/right) and the side that the pre-cue was tested on. Curves show the best fitting cumulative Gaussian function for the group means. Error bars show ±1 S.E.M.

Journal: Attention, perception & psychophysics

Article Title: The Attentional Repulsion Effect and Relative Size Judgments

doi: 10.3758/s13414-018-1612-x

Figure Lengend Snippet: Plots showing the mean proportion of time participants responded that the comparison rectangle was (a) wider or (b) taller than the standard rectangle for the seven comparison variants tested as function of which side the comparison was on (left/right) and the side that the pre-cue was tested on. Curves show the best fitting cumulative Gaussian function for the group means. Error bars show ±1 S.E.M.

Article Snippet: Cumulative Gaussian functions were then fit to the data (GraphPad Prism; GraphPad Software, Inc) to determine the PSE.

Techniques: Comparison

(a) Plots show the mean proportion of time participants responded that the comparison rectangle was farther from fixation than the standard rectangle for the seven comparison offsets tested as a function of which side the comparison rectangle was on (left/right) and the location of the cue (foveal/center/peripheral). Curves show the best fitting cumulative Gaussian function for the group means. (b) Bar graph showing the mean PSE for the comparison rectangle as a function of cue location and the relative side of the comparison rectangle. The average PSE collapsed across comparison side is also shown. The solid horizontal line show the expected PSE if no distortion were present given that the standard rectangle was always offset from fixation by 5.0°. All error bars show ±1 S.E.M.

Journal: Attention, perception & psychophysics

Article Title: The Attentional Repulsion Effect and Relative Size Judgments

doi: 10.3758/s13414-018-1612-x

Figure Lengend Snippet: (a) Plots show the mean proportion of time participants responded that the comparison rectangle was farther from fixation than the standard rectangle for the seven comparison offsets tested as a function of which side the comparison rectangle was on (left/right) and the location of the cue (foveal/center/peripheral). Curves show the best fitting cumulative Gaussian function for the group means. (b) Bar graph showing the mean PSE for the comparison rectangle as a function of cue location and the relative side of the comparison rectangle. The average PSE collapsed across comparison side is also shown. The solid horizontal line show the expected PSE if no distortion were present given that the standard rectangle was always offset from fixation by 5.0°. All error bars show ±1 S.E.M.

Article Snippet: Cumulative Gaussian functions were then fit to the data (GraphPad Prism; GraphPad Software, Inc) to determine the PSE.

Techniques: Comparison

(a) Plot shows the mean proportion of time participants responded that the comparison rectangle was wider than the standard rectangle at the seven comparison widths. Width means were tested as a function of which side the comparison rectangle was located (left/right) and the trial stimulus array offset position (foveal/peripheral). Curves show the best fitting cumulative Gaussian function for the group means. (b) Bar graph showing the mean PSE for the comparison rectangle width as a function of comparison rectangle location and the stimulus array offset position (i.e., position of the standard rectangle at fixation or periphery). The solid horizontal line show the expected PSE if no distortion were present given that the standard rectangle always had a width of 3.0°. All error bars show ± 1 S.E.M.

Journal: Attention, perception & psychophysics

Article Title: The Attentional Repulsion Effect and Relative Size Judgments

doi: 10.3758/s13414-018-1612-x

Figure Lengend Snippet: (a) Plot shows the mean proportion of time participants responded that the comparison rectangle was wider than the standard rectangle at the seven comparison widths. Width means were tested as a function of which side the comparison rectangle was located (left/right) and the trial stimulus array offset position (foveal/peripheral). Curves show the best fitting cumulative Gaussian function for the group means. (b) Bar graph showing the mean PSE for the comparison rectangle width as a function of comparison rectangle location and the stimulus array offset position (i.e., position of the standard rectangle at fixation or periphery). The solid horizontal line show the expected PSE if no distortion were present given that the standard rectangle always had a width of 3.0°. All error bars show ± 1 S.E.M.

Article Snippet: Cumulative Gaussian functions were then fit to the data (GraphPad Prism; GraphPad Software, Inc) to determine the PSE.

Techniques: Comparison

Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a Gaussian probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).

Journal: Proceedings of the Royal Society B: Biological Sciences

Article Title: Do perceptual biases emerge early or late in visual processing? Decision-biases in motion perception

doi: 10.1098/rspb.2016.0263

Figure Lengend Snippet: Sensory re-weighting and late, decision-related bias models. (a) Outline of the sensory re-weighting model. The sensory representation of the moving stimulus is modelled as a Gaussian probability density function (𝒩) centred on the true direction of motion (μ) and variance σd, a free parameter for both models. The weighting function w is modelled as a gamma probability function (Γ) governed by two parameters: a shape parameter (A) and a scale parameter (B). Both s and w are derived in the same way for both the sensory re-weighting and late, decision-related bias models. The sensory representation of the motion stimulus is multiplied by the weighting profile, resulting in the weighted sensory representation (wsr). To fit these models to the data, we obtained the (Gaussian) maximum-likelihood estimates for σd, A, B (and δ, for the modified model). (b) Model predictions for sensory re-weighting model. For both situations in our Experiment 1, reference present or absent during the estimation task, the model predicts the same biased responses, as the re-weighting of sensory information is tied to discrimination boundary which is unchanged in both situations. For the same reason, the original model predicts the same responses for Experiment 2, where the position of the reference is systematically changed at the time of the estimation task. (c) Outline of the late, decision-related bias model. The early sensory representation s remains unchanged. The re-weighting of the sensory information by a weighting function w is dependent on the presence of an explicit reference during the estimation task. In addition, the re-weighting is relative to the position of one or more references at the time of estimation. The parameter δ can absorb differences between the position of the discrimination boundary (during stimulus presentation) and the reference during the manual estimation task and correctly predicts shifts in the responses (from r to r'). (d) Model predictions for the late, decision-related bias model. In the situations where a reference is present during the estimation task (and not shifted with respect to the discrimination boundary), the original and modified models make the same predictions (light grey lines, left panel). However, if no reference is present at the estimation stage, the model predicts veridical responses (dark grey line, left panel). Additionally, if the reference present during estimation is displaced relative to the decision boundary, the modified model predicts concomitant changes in the responses (dashed and solid light grey lines, right panel).

Article Snippet: We used nonlinear least-squares ( fminsearch in Matlab; Nelder–Mead algorithm [ 9 ]) to estimate the two parameters ( μ , σ ) of the best-fitting cumulative Gaussian distribution.

Techniques: Derivative Assay, Modification

Example stimuli are depicted as described in the text. Judgments were made regarding the center of rotation of the Glass pattern relative to the black outer Gaussian markers.

Journal: Frontiers in Computational Neuroscience

Article Title: Detecting global form: separate processes required for Glass and radial frequency patterns

doi: 10.3389/fncom.2013.00053

Figure Lengend Snippet: Example stimuli are depicted as described in the text. Judgments were made regarding the center of rotation of the Glass pattern relative to the black outer Gaussian markers.

Article Snippet: The data was fit with a cumulative Gaussian (Prism 4.0, Graphpad Software Inc., 2005) using the following variant of Equation 3: (4) Y = 0.5 { 1 + e r f [ x − P S A σ 2 ] } where Y = proportion of responses to the right, erf = error function, x = amount of displacement, PSA = point of subjective alignment, and σ = the standard deviation of the fitted cumulative Gaussian.

Techniques: