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I'm doing a project where I'm measuring outdoor sound in different spots. I've repeated the measurement 3 times at every spot on different days (with different weather etc). I measure every spot for 10 minutes and the sound level meter give me one value (in dBA, A-weighted decibels) every second. Now I want to do a statistical analysis on these values to compare and see if there's a statistical difference depending on the day/weather.

Can I do an anova-test on the decibel-values directly, do I need to convert them, or what do I do? I'm asking since decibel is made by a logaritmic function ... Hence you can't really add 1 dB + 1 dB, since it really become 3 dB ... So the mean value won't be 'correct'.

Hope someone understand what I mean ...

Adding a bit for one of the places I've measured at and the data comparison between the spots I've measured. These measurments are made the same day: enter image description here

As you can see spot 5 and 2 aren't significantly different while spot 2 and 3 are. The dBA-equivalent for spot 5 and 3 is 60,2 dBA and for spot 2 it's 58,4 dBA.

Shouldn't the anova/the tukey-kramer test show the same for the two comparisons?

Below is the measured values (dB) over time. I've measured for 10 minutes in each spot (point), that is located in different areas of a bigger area (school yard).

enter image description here

2: [enter image description here

Esme
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  • By the way, could you share (a link to) the data? – kjetil b halvorsen Feb 20 '20 at 16:10
  • Suppose you didn't know that a decibel was the logarithm of something: would that change your question? Indeed, it might be worth noting that whenever you have any numbers at all, representing anything whatsoever, they can always be considered logarithms, because every real number $x$ is the log of $e^x.$ – whuber Feb 20 '20 at 16:23

1 Answers1

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I would say you can use anova for analyzing noise level measurements, see this stored google search which links many papers using anova in the analysis of noise measurements.

As you say, noise measurements in decibel cannot really be added, say, if the problem is finding the resultant noise level from two simultaneous independent sources, like a jet taking off close the the noisy highway you're on.

But that is not your problem. You are making a statistical comparison of the noise levels under different conditions, comparing different distributions of noise levels. Your interest is in parameters of those noise level distributions, which is a very different problem from the technical problem of adding noise from independent, simultaneous sources. So, I guess it is more relevant to ask if the distribution of noise levels are sufficiently symmetrical/close to normal, so that the mean is a good statistical parameter.

For some related discussion see What is the terminology for data aggregated via summed totals versus data aggregated via means? 

EDIT

After you added the ANOVA example with data: I would suspect that the repeat measurements, the same day, same spot, are autocorrelated, so you should not treat them as independent observations, as you have done. Can you add some time series plot, or autocorrelations? (by site)

kjetil b halvorsen
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  • I want this to be true, but don't we run into issues with Jensen's inequality? The mean of the logs is not the same as the log of the mean. – Dave Feb 20 '20 at 15:50
  • @Dave: Can you explain why that should be a problem? Also, the logarithmic scale dB is used for noise because that is more relevant for human perception of n oise, I am told ... that seems to be another argument for my conclusion. But, I hope some others chime in on this interesting Q – kjetil b halvorsen Feb 20 '20 at 16:02
  • If I have pressure measurements of 10, 1, and 100, then their dB equivalents are 10, 0, and 20. The original measurements have a mean pressure of 37, equivalent to 15.7 dB. On the dB scale, the mean pressure is 10. If these values agreed, then there would be no problem, but they don't, leaving me wondering where I should be doing the arithmetic: in the original domain or the decibel domain. (Even taking the geometric mean in the dB domain doesn't result in equal means, and it's not just because of the 0 dB value.) – Dave Feb 20 '20 at 16:13
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    Yes, but what does that have to do with the statistical distribution of the noise measurements? – kjetil b halvorsen Feb 20 '20 at 16:14
  • It seems like transforming the measurements to the dB domain changes the distribution in a way that is very different from a linear transformation like converting miles to kilometers. – Dave Feb 20 '20 at 16:20
  • Yes, so it raises the same sort of questions as when analyzing log-transformed data , or the original scale. Often, if the log-transformed data is closer to a normal distribution, one would prefer anova on the log scale? – kjetil b halvorsen Feb 20 '20 at 16:23
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    There's some nice discussion here: https://physics.stackexchange.com/questions/46228/averaging-decibels. – Dave Feb 20 '20 at 16:50
  • The data is a bit skewed as expected, but not enough to not be able to perform an anova. So that shouldnt be the issue. But now I'm a bit conflicted between answers since @kjetilbhalvorsen says I CAN perform a statistical anayisis on my dB-data and Dave seems to disagree.. I've tried to perform anovas on the result and they do make sense. There's one thing though which are a bit weird. Between point 1 and 2 there's a significant difference (anova) and between 2 and 3 there's not a significant difference (also anova). But when I look at the dB-equivalents they are the same for point 1 and 3 – Esme Feb 24 '20 at 14:55
  • Can you please add this (as an edit) to the post? With some more detail, showing data, showing plots – kjetil b halvorsen Feb 24 '20 at 14:57
  • @kjetilbhalvorsen absolutely. I've added a bit. Hope it's enough to understand my issue. Otherwise; please ask for more info. – Esme Feb 24 '20 at 15:15
  • @kjetilbhalvorsen the data I've showed is for the same day and time pretty much. But the ANOVA result doesn't make sense since if you compare the results (dBA-euivalents) in the different spots (seeing how distance from a road affects measurments in dB). Because the dBA-equivalent for spot 5 and 3 is 60,2 dBA and for spot 2 it's 58,4 dBA. Hence the difference between spot 5 and 2 is the same as for between spot 3 and 2... Ugh. I just don't get it. – Esme Feb 24 '20 at 15:43
  • You need to tell us more about how you made the measurements. Still, I a afraid independence (or lack of) is an issue! – kjetil b halvorsen Feb 24 '20 at 15:46
  • I don't think that autocorrelation is the problem. But I've added some graphs showing the measurment over time (10 min period) in the different locations of the bigger area (a school yard). Hope it will help you to help me! @kjetilbhalvorsen – Esme Feb 25 '20 at 11:25