### Abstract

We introduce formula-based approaches for statistical tests regarding peri-stimulus time histograms (PSTHs) in cases when a conditioning stimulus was triggered by a motor-unit discharge with a constant delay time. The individual bin test and the cumulative sum test have recently been reported as methods for the quantitative analysis of PSTHs in the evaluation of human neural projections. These tests calculate confidence intervals using simulated point processes on the discharge of a motor unit, but require a significant amount of calculation time for the point process simulation. In order to overcome such a disadvantage in practical use, we provide a statistical formulization of the two above-mentioned tests using a combination theory. In general, the time required for calculating confidence intervals using these formula-based approaches was 2-13 times faster than when using the previous approaches. Unlike the previous ones, these formula-based approaches do not need to judge that a simulation process converges to the substationary state, and calculate an ideal distribution of statistical noise on the histogram, thereby providing high accuracy. We conclude that the formula-based approaches increase reliability and are sufficiently sophisticated for practical use.

Original language | English |
---|---|

Pages (from-to) | 1262-1267 |

Number of pages | 6 |

Journal | IEEE Transactions on Biomedical Engineering |

Volume | 50 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2003 Nov |

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### Keywords

- Cumulative sum
- Formulization
- Human
- Peri-stimulus time histograms
- Statistics

### ASJC Scopus subject areas

- Biomedical Engineering

### Cite this

*IEEE Transactions on Biomedical Engineering*,

*50*(11), 1262-1267. https://doi.org/10.1109/TBME.2003.818470

**Formula-Based Approach of Statistical Tests for Peri-Stimulus Time Histograms.** / Ushiba, Junichi; Onishi, Yoichi; Tomita, Yutaka; Masakado, Yoshihisa.

Research output: Contribution to journal › Article

*IEEE Transactions on Biomedical Engineering*, vol. 50, no. 11, pp. 1262-1267. https://doi.org/10.1109/TBME.2003.818470

}

TY - JOUR

T1 - Formula-Based Approach of Statistical Tests for Peri-Stimulus Time Histograms

AU - Ushiba, Junichi

AU - Onishi, Yoichi

AU - Tomita, Yutaka

AU - Masakado, Yoshihisa

PY - 2003/11

Y1 - 2003/11

N2 - We introduce formula-based approaches for statistical tests regarding peri-stimulus time histograms (PSTHs) in cases when a conditioning stimulus was triggered by a motor-unit discharge with a constant delay time. The individual bin test and the cumulative sum test have recently been reported as methods for the quantitative analysis of PSTHs in the evaluation of human neural projections. These tests calculate confidence intervals using simulated point processes on the discharge of a motor unit, but require a significant amount of calculation time for the point process simulation. In order to overcome such a disadvantage in practical use, we provide a statistical formulization of the two above-mentioned tests using a combination theory. In general, the time required for calculating confidence intervals using these formula-based approaches was 2-13 times faster than when using the previous approaches. Unlike the previous ones, these formula-based approaches do not need to judge that a simulation process converges to the substationary state, and calculate an ideal distribution of statistical noise on the histogram, thereby providing high accuracy. We conclude that the formula-based approaches increase reliability and are sufficiently sophisticated for practical use.

AB - We introduce formula-based approaches for statistical tests regarding peri-stimulus time histograms (PSTHs) in cases when a conditioning stimulus was triggered by a motor-unit discharge with a constant delay time. The individual bin test and the cumulative sum test have recently been reported as methods for the quantitative analysis of PSTHs in the evaluation of human neural projections. These tests calculate confidence intervals using simulated point processes on the discharge of a motor unit, but require a significant amount of calculation time for the point process simulation. In order to overcome such a disadvantage in practical use, we provide a statistical formulization of the two above-mentioned tests using a combination theory. In general, the time required for calculating confidence intervals using these formula-based approaches was 2-13 times faster than when using the previous approaches. Unlike the previous ones, these formula-based approaches do not need to judge that a simulation process converges to the substationary state, and calculate an ideal distribution of statistical noise on the histogram, thereby providing high accuracy. We conclude that the formula-based approaches increase reliability and are sufficiently sophisticated for practical use.

KW - Cumulative sum

KW - Formulization

KW - Human

KW - Peri-stimulus time histograms

KW - Statistics

UR - http://www.scopus.com/inward/record.url?scp=0141961005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141961005&partnerID=8YFLogxK

U2 - 10.1109/TBME.2003.818470

DO - 10.1109/TBME.2003.818470

M3 - Article

C2 - 14619996

AN - SCOPUS:0141961005

VL - 50

SP - 1262

EP - 1267

JO - IEEE Transactions on Biomedical Engineering

JF - IEEE Transactions on Biomedical Engineering

SN - 0018-9294

IS - 11

ER -