# Data normalization by using mean and standard deviation - Strange example

I read a paper which talks about two samples; the first one concerning data (e.g. resistance $$R_{ct}$$) from a biosensor1 (called module), the second one concerning data from biosensor2 (called CHI).

The author compares these data in a way which is difficult to grasp for me. In particular he said (from paper "Sun 2016 IEEE - A Multi-Technique Reconfigurable Electrochemical Biosensor"):

"The results, shown in Fig. 8, show the mean and standard deviation of the measurements normalized to the CHI data."

Could you explain me the normalization procedure please? Why did he calculate $$\frac{\mu_{biosensor1}}{\mu_{CHI}}$$ and $$\frac{\sigma_{biosensor1}}{\mu_{CHI}}$$?

• Let's look on the bright side: the author realised that starting the bars at 97 was a much better idea than starting at 0. How did this get published? Why won't people show the data too? Why does a bar appeal in any sense? The means and SD bars aren't enhanced in any way by the thicker bars. Aug 29, 2020 at 8:35

## 1 Answer

I'd say that the authors are not 'normalizing' to prepare a statistical elaboration, but just to show the results of their elaboration. Using their words: "While the variance in the data from the module is larger than that of the benchtop potentiostat ([...] $$0.630\Omega$$ versus $$0.186\Omega$$) each is still within acceptable bounds for that particular technique and matches well with the CHI measurements", i.e. the module measurements are very close to the CHI measurements: more than $$99.5\%$$ on average, within about $$99\%$$ and $$100.3\%$$.
Here 'normalizing' means "using CHI average measurement as a benchmark."
The figure is not perfect, but... what is the problem?

I'm not an engineer, so let me play with toy numbers.
The average CHI measurement is $$50$$, its confidence interval is $$(49,51)$$. The average module measurement is lower, $$49.2$$, its confidence interval is wider, $$(48.2,51.2)$$, because of a larger variance. Dividing by $$50$$, i.e. using $$50$$ as a benchmark, you have:

• CHI: $$100\%$$ on average, in $$(98\%,102\%)$$;
• module: $$98.4\%$$ on average, in $$(96.4\%,102.4\%)$$.

CHI is more precise, but module is still acceptable.

• Hello Sergio I noticed that the author calculated $(CHI \, mean / CHI \, mean)=1=100 \%$ and $(module \, mean / CHI \, mean)$...so maybe he normalized only the means, but not the standard deviations Aug 29, 2020 at 9:16
• They normalized the confidence interval bounds (which depend on the standard deviation). Aug 29, 2020 at 12:31