# Difference Thresholds for the Perception of Sinusoidal Vertical Stimuli of Whole-Body Vibrations in Ranges of Amplitude and Frequency Relevant to Ride Comfort

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## Abstract

**:**

## 1. Introduction

#### 1.1. Basic Principles

_{0}, and the alternative hypothesis, H

_{1}. Later definition of a hypothesis is always associated with the risk of a wrong decision. As a matter of principle, type I errors (α-risk), which lead to a wrong decision favouring H

_{1}, and type II errors (β-risk), which favour H

_{0}in a wrong decision, are distinguished in this case (schematic overview, see Table A4). The significance level, α, indicates the probability of a formulated alternative hypothesis, H

_{1}, being wrongly assumed. The statistical power (1-β) indicates the probability of a binary hypothesis test deciding the feasibility of an alternative hypothesis, H

_{1}. In research, defined limits of 0.05 for α and 0.80 for 1-β have become established. Information about practical significance, however, cannot be derived from the α/β-constellation [5]; thus, an explanation of the practical importance of statistically significant results makes additional calculation of the effect size for existing data sets meaningful. The effect size in this case refers to the calculation of the degree of difference, i.e., the magnitude and direction of a difference between two distributions. More information on this point is contained in [6].

#### 1.2. Previous Studies

#### 1.3. Motivation

## 2. Test Environment and Methodology

_{i}and R

_{i}are the measured accelerations of the test and reference stimuli at the reversals, respectively. Reversal point p defines the peaks or troughs in subject responses (Figure 2).

## 3. Results

_{adj}= p × 6, number of paired comparisons = 6) in such a way that it was compared with the established significance level of α = 0.05. The approach according to Cohen [20] was taken into account in interpreting the effect size. For further information, see [21] (Bühner and Ziegler).

#### 3.1. Effect of Amplitude

#### 3.2. Effect of Frequency

## 4. Discussion

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Diagrams and Tables

**Table A1.**List of vibration receptors and their classification [8].

Sensory Cells | Response to | Optimum Frequency Range | Occurring in Skin Layer |
---|---|---|---|

Merkel cell | pressure | 0.3–5 Hz | Upper skin layer |

Meissner cell | Slight contact (speed) | 3–40 Hz | Middle skin layer |

Ruffini cell | Stretching of skin (speed) | 14–400 Hz | Middle skin layer |

Paccini cell | Fast vibrations (acceleration) | 40–500 Hz | Lower skin layer |

Frequency | 1.3 Hz | 1.3 Hz | 6 Hz | 6 Hz | 6 Hz |
---|---|---|---|---|---|

Amplitude | 0.2 m/s² | 0.5 m/s² | 0.2 m/s² | 0.5 m/s² | 1.2 m/s² |

Mean | 10.7 | 6.2 | 8.4 | 7.6 | 6.5 |

Standard deviation | 1.5 | 1.9 | 2.2 | 1.9 | 1.9 |

Median value | 11.0 | 6.7 | 8.4 | 7.9 | 7.3 |

Upper quartile | 10.0 | 4.4 | 7.7 | 5.9 | 5.0 |

Lower quartile | 11.3 | 7.3 | 9.8 | 8.7 | 7.6 |

IQR | 1.2 | 2.9 | 2.1 | 2.8 | 2.7 |

d | Interpretation acc. to Cohen [20] |
---|---|

<0 | Negative effect |

0.0 | No effect |

0.1 | |

0.2 | Minor effect |

0.3 | |

0.4 | |

0.5 | Average effect |

0.6 | |

0.7 | |

0.8 | Major effect |

0.9 | |

≥1.0 |

**Table A4.**Type I and type II errors in statistical decisions [6].

Statistical Decision | Applicable to the Population: | |
---|---|---|

Null Hypothesis H_{0} | Alternative Hypothesis H_{1} | |

Decision in favour of H_{0} | Correct decision | Wrong decision (type II error) |

Decision in favour of H_{1} | Wrong decision (type I error) | Correct decision |

## Appendix B

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**Figure 1.**Test apparatus with two z-axis vibrating platforms at the comfort interfaces of seat (

**right**) and footwell (

**left**).

**Figure 2.**Typical curve for determining a relative difference threshold associated with a reference stimulus by means of the transformed 3-down/1-up method.

**Figure 3.**(

**a**) Relative difference thresholds at 1.3 Hz: effect of amplitude, (

**b**) Relative difference thresholds at 6.0 Hz: effect of amplitude. The line in the box shows the median value of the distribution additionally indicated as a numerical value. The outliers were defined as larger than 1.5 times the interquartile range (IQR).

**Figure 4.**(

**a**) Relative difference thresholds at 0.2 m/s²: effect of frequency, (

**b**) Relative difference thresholds at 0.5 m/s²: effect of frequency. The line in the box shows the median value of the distribution additionally indicated as a numerical value. The outliers were defined as larger than 1.5 times the interquartile range (IQR).

**Figure 5.**Comparison of results (median relative difference thresholds) previously studied (extract up to 20 Hz) and currently study.

**Table 1.**Overview of relevant studies contributing to the objective evaluation of just-noticeable differences of sinusoidal whole-body vibrations (AFC: alternative forced choice, IFC: interval forced choice)

Publication | [9] | [10,11,12] | [13] | [14] | [15] |
---|---|---|---|---|---|

Year | 2000 | from 2001 | 2001 | 2003 | 2010 |

Frequency | 5, 20 Hz | 4–80 Hz | 12.5–80 Hz | 4–80 Hz | 2.5–315 Hz |

Amplitude | 0.1, 0.5 m/s² | 0.063 m/s² (96 dB) | 0.1 m/s² (100 dB) | 0.7 m/s² | 0.05, 0.2, 0.8 m/s² |

Inquiry technique | 2 AFC 1 up–3 down | 3 AFC 1 up–2 down | 3 AFC 1 up–2 down | method of limits | 2 IFC 1 up–3 down |

Convergence | 79.4% | 70.7% | 70.7% | 50.0% | 79.4% |

Increment step | 2.9% 0.25 dB | 5.9% 0.5 dB | 5.9% 0.5 dB | 2.9% 0.25 dB | 2.9% 0.25 dB |

Test subjects | 12 | 8–16 | 10 | 16 | 12 |

Result | 8.1–12.3% | ~19% | ~20% | 5.2–6.5% | 9.5–20.3% |

No. | f Hz | Paired Comparison m/s² | Statistical Power | Significance p _{adj} | Effect Size d | Interpretation acc. to Cohen [20] |
---|---|---|---|---|---|---|

1 | 1.3 | 0.2 ↔ 0.5 | >0.8 | <0.01 | >1.0 | Large |

2 | 6.0 | 0.2 ↔ 0.5 | <0.8 | >0.05 | - | - |

3 | 6.0 | 0.5 ↔ 1.2 | <0.8 | >0.05 | - | - |

4 | 6.0 | 0.2 ↔ 1.2 | <0.8 | <0.05 | >0.8 | Large |

No. | a m/s² | Paired Comparison Hz | Statistical Power | Significance p _{adj} | Effect Size d | Interpretation acc. to Cohen [20] |
---|---|---|---|---|---|---|

5 | 0.2 | 1.3 ↔ 6.0 | <0.8 | <0.05 | >1.0 | Large |

6 | 0.5 | 1.3 ↔ 6.0 | <0.8 | >0.05 | - | - |

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**MDPI and ACS Style**

Festa, M.; Durm, T.; Lünebach, M.; Gauterin, F.
Difference Thresholds for the Perception of Sinusoidal Vertical Stimuli of Whole-Body Vibrations in Ranges of Amplitude and Frequency Relevant to Ride Comfort. *Vibration* **2020**, *3*, 116-131.
https://doi.org/10.3390/vibration3020010

**AMA Style**

Festa M, Durm T, Lünebach M, Gauterin F.
Difference Thresholds for the Perception of Sinusoidal Vertical Stimuli of Whole-Body Vibrations in Ranges of Amplitude and Frequency Relevant to Ride Comfort. *Vibration*. 2020; 3(2):116-131.
https://doi.org/10.3390/vibration3020010

**Chicago/Turabian Style**

Festa, Maurizio, Tiemo Durm, Mark Lünebach, and Frank Gauterin.
2020. "Difference Thresholds for the Perception of Sinusoidal Vertical Stimuli of Whole-Body Vibrations in Ranges of Amplitude and Frequency Relevant to Ride Comfort" *Vibration* 3, no. 2: 116-131.
https://doi.org/10.3390/vibration3020010