How do I change logarithmic scaled data to linear scaled data? I am using decibels for my research, and I was told by someone that I cannot perform any statistical analyses on these measurements other than basic descriptive statistics because the data are logarithmic scale instead of linear scale. In my searches I mostly find articles about converting linear data to logarithmic data. 
How can I change my logarithmic data in to linear data so I can perform an ANOVA? I am using SPSS. Thank you! 
 A: First, don't transform out of the decibel scale, or at least do the analysis in both scales so that you can see if this person is foolish in insisting on the transformation.
Classic ANOVA is based on analyzing data in a scale where the magnitudes of error terms are independent of the values of the variables, and standard tests are most easily interpreted if the error terms have a normal distribution. In acoustic work you typically expect such independence between error magnitudes and variable values when you analyze data in the decibel scale, not in the scale of the underlying root-mean-square (RMS) sound pressure.
As others have noted, there is no prohibition against ANOVA on data in a log scale. If this person insists on a back tranformation to a linear scale, do the analysis in both scales and examine the residuals in your ANOVA. They will almost certainly be better behaved in the decibel scale, with the assumptions for interpretation of ANOVA significance tests met much better in the decibel scale. 
To transform back to RMS sound pressure from the decibel scale (which would be most consistent with the intent of the person who is trying to talk you out of the decibel scale), you need to take into account the reference sound pressure used for defining the scale. Abstracting from the Wikipedia page, the sound-pressure level or acoustic pressure level $L_p$ in decibels is related to the root-mean-square sound pressure $p$ by:

$$L_p =20 \log_{10}\!\left(\frac{p}{p_0}\right)\!,$$

where $p_0$ is a reference sound pressure, usually (but not necessarily) $20 \mu Pa$. So to get the root-mean-square sound pressure $p$ from the sound-pressure level $L_p$ in decibels, you use:

$$p = p_0 10^{L_P/20}.$$

A: Setting aside the false premise of your colleague's critique, which whuber and I discuss in the comments, the answer to your question is very straightforward: Exponentiation is the inverse of the logarithm function. If your data on the $\log_a$ scale are $x$, then on the linear scale they are $y$ such that $y=a^x$ for $a>0$.
