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

^{1}

^{2}

^{*}

## 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

## References

- Goldstein, E.B. Wahrnehmungspsychologie, 9th ed.; Springer: Berlin/Heidelberg, Germany, 2015; ISBN 978-38274018925. [Google Scholar]
- Engen, T. Psycohophysics. In Experimental Psychology, 3rd ed.; Kling, J.W., Ed.; Holt, Rinehart and Winston, Inc.: New York, NY, USA, 1972; pp. 1–46. ISBN 978-0030028069. [Google Scholar]
- Gescheider, G.A. Psychophysics: Method and Theory; Erlbaum, L., Ed.; Halsted Press: Hillsdale, NJ, USA, 1976. [Google Scholar]
- Pütter, A. Studien zur Theorie der Reizvorgänge. Pflügers Arch. Gesamte Physiol. Menschen Tiere
**1918**, 171, 201–261. [Google Scholar] [CrossRef] - Nuzzo, R. Scientific method: Statistical errors. Nature
**2014**, 506, 150–152. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bortz, J. Statistik Für Human- und Sozialwissenschaftler, 6th ed.; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar] [CrossRef]
- Jones, L.A.; Lederman, S.J. Human Hand Function; Oxford University Press (OUP): New, York, NY, USA, 2006. [Google Scholar]
- Goldstein, E.B. Wahrnehmungspsychologie, 4th ed.; Springer: Berlin/Heidelberg, Germany, 2015. [Google Scholar]
- Morioka, M.; Griffin, M. Difference thresholds for intensity perception of whole-body vertical vibration: Effect of frequency and magnitude. J. Acoust. Soc. Am.
**2000**, 107, 620–624. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bellmann, M.A. Perception of Whole-Body Vibrations: From Basic Experiments to Effects of Seat and Steering-Wheel Vibrations on the Passenger’s Comfort Inside Vehicles. Ph.D. Thesis, Uni Oldenburg, Shaker Verlag GmbH, Oldenburg, Germany, 2002. [Google Scholar]
- Bellmann, M.A.; Mellert, V.; Reckhardt, C.; Remmers, H. Basic Experiments on the Perception of vertical Whole-Body Vibrations; Fortschritte der Akustik, DAGA: Hamburg, Germany, 2001; pp. 494–495. [Google Scholar]
- Bellmann, M.A.; Remmers, H. Grundlegende Experimente Der Wahrnehmung Von Vertikalen Ganzkörperschwingungen; VDI-Berichte Nr. 1821; Tagungsband: Darmstadt, Germany, 2004; pp. 251–270. [Google Scholar]
- Baumann, I.; Bellmann, M.A.; Mellert, V.; Weber, H. Wahrnehmungs- und Unterschiedsschwellen Von Vibrationen Auf Einem Kraftfahrzeugsitz; Fortschritte der Akustik, DAGA: Hamburg, Germany, 2001; pp. 292–293. ISBN 3-9804568-9-7. [Google Scholar]
- Matsumoto, Y.; Maeda, S.; Oji, Y. Influence of Frequency on Difference Thresholds for Magnitude of Vertical Sinusoidal Whole-Body Vibration. Ind. Health
**2002**, 40, 313–319. [Google Scholar] [CrossRef] [PubMed][Green Version] - Forta, N.G.; Morioka, M.; Griffin, M. Difference thresholds for the perception of whole-body vertical vibration: Dependence on the frequency and magnitude of vibration. Ergonmics
**2009**, 52, 1305–1310. [Google Scholar] [CrossRef] [PubMed] - VDI 2057-1. Einwirkungen Mechanischer Schwingungen auf Den Menschen; Verein Deutscher Ingenieure, Beuth Verlag GmbH: Berlin, Germany, 2002.
- MTS. RPC Pro Software. Available online: http://www.mts.com (accessed on 1 February 2020).
- Levitt, H. Transformed Up-Down Methods in Psychoacoustics. J. Acoust. Soc. Am.
**1971**, 49, 467–477. [Google Scholar] [CrossRef] - Treutwein, B. Adaptive psychophysical procedures. Vis. Res.
**1995**, 35, 2503–2522. [Google Scholar] [CrossRef] - Cohen, J. Statistical Power Analysis for the Behavioral Sciences, 2nd ed.; Lawrence Erlbaum Associates: Hillsdale, NJ, USA, 1988. [Google Scholar]
- Bühner, M.; Ziegler, M. Statistik für Psychologen und Sozialwissenschaftler; Pearson Studium: München, Germany, 2009; Volume 1, ISBN 978-3-8273-7274-1. [Google Scholar]
- Stamm, M.; Altonsoy, E.; Merchel, S. Frequenzwahrnehmung von Ganzkörperschwingungen im Vergleich zur auditiven Wahrenhmung I. In Proceedings of the DAGA 2010—36th German Annual Conference on Acoustics, Berlin, Germany, 18 March 2010; pp. 868–876. [Google Scholar]
- Merchel, S.; Leppin, A.; Altinsoy, E. Multisensorische Interaktion im Fahrzeug: Audio-Taktile Intensitätswahrnehmung. In Proceedings of the DAGA 2010—36th German Annual Conference on Acoustics, Berlin, Germany, 18 March 2010; pp. 871–872. [Google Scholar]
- Valko, Y.; Lewis, R.F.; Priesol, A.J.; Merfeld, D.M. Vestibular labyrinth contributions to human whole-body motion discrimination. J. Neurosci.
**2012**, 32, 13537–13542. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gescheider, A.; Bolanowski, S.; Hardick, K. The frequency selectivity of information-processing channels in the tactile sensory system. Somatosens. Mot. Res.
**2001**, 18, 191–201. [Google Scholar] [CrossRef] [PubMed] - Gescheider, G.A.; Bolanowski, S.J.; Pope, J.V.; Verrillo, R.T. A four-channel analysis of the tactile sensitivity of the fingertip: Frequency selectivity, spatial summation, and temporal summation. Somatosens. Mot. Res.
**2002**, 19, 114–124. [Google Scholar] [CrossRef] [PubMed] - Lenhard, W.; Lenhard, A. Berechnung von Effektstärken. Psychometrica: Dettelbach, Germany, 2016. Available online: https://www.psychometrica.de (accessed on 1 February 2020). [CrossRef]
- Entrekin, R.; Suggs, C.W.; Abrams, C.F. Differential Vibration of the Feet and Trunk of Humans. Proc. Sixth Congr. Int. Ergon. Assoc.
**1976**, 20, 61–65. [Google Scholar] [CrossRef] - Schmidt, R.F.; Lang, F.; Heckmann, M. Physiologie des Menschen, 31st ed.; Springer: Berlin/Heidelberg, Germany, 2010. [Google Scholar] [CrossRef]

**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 | - | - |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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