Averaging across dB versus intensity units changes the computed mean

Evidence

Because the results of the same person in different trials (intraindividual differences) as well as the results from different subjects (interindividual differences) can vary substantially, it is advisable to perform several runs of the same type of experiment and to average the data. This means that after an experiment a large number of data points are available for which an average value has to be calculated. The choice of the unit for the averaging procedure among the stimulus magnitude measures (i.e. among level, sound pressure, or sound intensity) plays a crucial role. An example is given in Fig. 1.10 which shows values of absolute thresholds for 8 subjects. In the upper part, the individual threshold values are given as dots along a scale of relative sound intensity 1/10 . For these 8 data points the arithmetic mean, the geometric mean, and the median are indicated by arrows. … For example a relative intensity of 100 corresponds to a level of 20 dB, a relative intensity of 2 to a level of 3 dB and so forth. Because of the transformation of the scales, the arrangement of the dots in the upper versus the lower panel of Fig. 1.10 is completely different. … In the upper part, the arithmetic mean lies between the sixth and the seventh data point, in the lower part however between the fifth and the sixth data point. As concerns the geometric mean, in the upper part it is situated between the fifth and the sixth data point whereas in the lower part between the third and the fourth data point. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 139

Categorization

Category: Factual Claims

• XREF: Connects to Stevens’ power law and the general log-scale averaging problem in psychophysics encountered elsewhere.
• QUESTION: Which averaging unit is psychoacoustically correct for threshold data — intensity, pressure, or level?

Related

• The measurement scale chosen for averaging radically affects psychoacoustic data summaries (similarity 0.91)
• The choice of averaging unit among level, pressure, or intensity critically shapes threshold data. (similarity 0.90)
• The median resists stimulus-scale transformations, unlike arithmetic and geometric means (similarity 0.81)
• Hearing-impaired listeners vary more than normal hearers in quiet threshold, complicating averaging (similarity 0.80)
• Sound level meters need time averaging to estimate varying pressure levels (similarity 0.79)
• Median and interquartile range stay scale-invariant where means fail (similarity 0.79)
• Standard loudness analysis discards response variability that probabilistic models can exploit (similarity 0.78)
• Spatial averaging of measurements suppresses interference artifacts while preserving spectral information (similarity 0.78)

Broader Connections

• Total information requires averaging over all symbols, not single ones #exemplifies (0.78) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2618
• Spatial averaging of room curves reveals boundary effects hidden in individual measurements #epitomizes (0.75) — Toole, Floyd E, Sound reproduction- the acoustics and…, 1467