Volatile organic compounds, such as formaldehyde, can be used as biomarkers in human exhaled breath in order to non-invasively detect various diseases, and the same compounds are of much interest also in the context of environmental monitoring and protection. Here, we report on a recently-developed gas sensor, based on surface-functionalized gold nanoparticles, which is able to generate voltage noise with a distinctly non-Gaussian component upon exposure to formaldehyde with concentrations on the ppm level, whereas this component is absent, or at least much weaker, when the sensor is exposed to ethanol or to pure air. We survey four different statistical methods to elucidate a non-Gaussian component and assess their pros and cons with regard to efficient gas detection. Specifically, the non-Gaussian component was clearly exposed in analysis using level-crossing parameters, which require nothing but a modest computational effort and simple electronic circuitry, and analogous results could be reached through the bispectrum function, albeit with more intense computation. Useful information could be obtained also via the Lévy-stable distribution and, possibly, the second spectrum.