# A Probabilistic Classification Procedure Based on Response Time Analysis Towards a Quick Pre-Diagnosis of Student’s Attention Deficit

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Experiments with DMDX

#### 2.3. Procedure for the Data Analysis

## 3. Results and Discussions

#### 3.1. Ex-Gaussian Analysis

_{C}, σ = ω y τ = t

_{0}, that is, in terms of the Gaussian and exponential functions parameters,

^{2}= σ

^{2}+ τ

^{2}, and the skewness 2τ

^{3}/S

^{3}[38]. In fact, one can characterize this distribution f(x) through its moments. One can consider moments of this distribution centered either at the origin (raw moments), or centered at the corresponding average (central moments). Thus,

#### 3.2. Classification Methodology

#### 3.3. Vector Criterion Based on the Ex-Gaussian Parameters

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The age distribution of the sample is shown in panel (

**a**) and a fragment of a *.azk output file in panel (

**b**). In order to protect the privacy of the child who performed the experiment, the characters “TTTTT” have been used as a pseudonym for the actual name.

**Figure 2.**In panel (

**a**), a visual example of the attention network task (ANT) carried out in this work is shown whereas in panel (

**b**), the four cue conditions are included.

**Figure 5.**Probability distributions of the mode (

**a**) and of μ parameter in an ex-Gaussian representation of the data (

**b**).

**Figure 6.**Probability distributions of σ (

**a**) and τ (

**b**) parameters in an ex-Gaussian representation of the data.

**Figure 7.**Probability distributions of the candidates resulting from the probability distribution of the mode in panel (

**a**) and of the candidates resulting from the probability distribution of the parameter μ in panel (

**b**). The average curve has also been included.

**Figure 8.**Probability distributions of the candidates resulting from the probability distribution of σ (

**a**) and τ (

**b**) parameters of the ex-Gaussian probability density. The average curve has also been included.

**Figure 9.**Euclidean norm and the norm of the maximum applied to the vector defined in Equation (8) as a function of the student label. In the upper panel, students from 1 to 100 are shown, and in the lower panel, students from 101 to 200. The students labeled as 110 (M), 131 (F), 137 (M), 169 (F), 185 (M), and 189 (F) appear in this classification only. The letter “M” between parentheses stands for male and the letter “F” for female.

**Table 1.**Results of the classification for the distribution of the mode, $\mathsf{\mu}$, $\mathsf{\sigma}$ and $\mathsf{\tau}$ (columns from second to fifth) taking into account a 7% of world prevalence of ADHD in school-aged children. The rows show the mode, the probability percentages at both sides of the mode (%-PD), the splitting of the prevalence percentage (%-Prev.), corresponding number of children (No. Ch.), and the selected children in terms of labels.

Mode | $\mathsf{\mu}$ | $\mathsf{\sigma}$ | $\mathsf{\tau}$ | |||||
---|---|---|---|---|---|---|---|---|

Mode (ms) | 525.5 | 545.5 | 87.5 | 112.5 | ||||

L | R | L | R | L | R | L | R | |

%-PD | 44.4 | 55.6 | 45.0 | 55.0 | 16.5 | 83.5 | 14.9 | 85.1 |

%-Prev. | 3.1 | 3.9 | 3.2 | 3.8 | 1.2 | 5.8 | 2.0 | 5.0 |

No. Ch. | 6 | 7 | 6 | 7 | 2 | 11 | 2 | 11 |

Selected children (labels) | 2, 28, 34, 55, 77, 75, 130, 85, 102, 107, 134, 142, 159 | 28, 34, 55, 58, 75, 77, 80, 102, 106, 130, 163, 167, 184 | 5, 39, 41, 58, 71, 80, 85, 109, 130, 136, 141, 183, 184 | 5, 28, 34, 55, 58, 80, 109, 113, 133, 136, 163, 183, 187 |

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**MDPI and ACS Style**

Hernaiz-Guijarro, M.; Castro-Palacio, J.C.; Navarro-Pardo, E.; Isidro, J.M.; Fernández-de-Córdoba, P.
A Probabilistic Classification Procedure Based on Response Time Analysis Towards a Quick Pre-Diagnosis of Student’s Attention Deficit. *Mathematics* **2019**, *7*, 473.
https://doi.org/10.3390/math7050473

**AMA Style**

Hernaiz-Guijarro M, Castro-Palacio JC, Navarro-Pardo E, Isidro JM, Fernández-de-Córdoba P.
A Probabilistic Classification Procedure Based on Response Time Analysis Towards a Quick Pre-Diagnosis of Student’s Attention Deficit. *Mathematics*. 2019; 7(5):473.
https://doi.org/10.3390/math7050473

**Chicago/Turabian Style**

Hernaiz-Guijarro, M., J. C. Castro-Palacio, E. Navarro-Pardo, J. M. Isidro, and P. Fernández-de-Córdoba.
2019. "A Probabilistic Classification Procedure Based on Response Time Analysis Towards a Quick Pre-Diagnosis of Student’s Attention Deficit" *Mathematics* 7, no. 5: 473.
https://doi.org/10.3390/math7050473