# Can I use anova on values in decibel (logaritmic)?

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:

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).

2: [

• By the way, could you share (a link to) the data? Commented Feb 20, 2020 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
Commented Feb 20, 2020 at 16:23

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)

• 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
Commented Feb 20, 2020 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 Commented Feb 20, 2020 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
Commented Feb 20, 2020 at 16:13
• Yes, but what does that have to do with the statistical distribution of the noise measurements? Commented Feb 20, 2020 at 16:14
• There's some nice discussion here: physics.stackexchange.com/questions/46228/averaging-decibels.
– Dave
Commented Feb 20, 2020 at 16:50