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The main aim of this study is to point out the difficulties found when tryingto assess the statistical significance of the North-South asymmetry (hereafterSSNSA) of the most usually considered time series of solar activity. First ofall, we distinguish between solar activity time series composed by integer ornon-integer and dimensionless data, or composed by non-integer and dimensionaldata. For each of these cases, we discuss the most suitable statistical testswhich can be applied and highlight the difficulties to obtain valid informationabout the statistical significance of solar activity time series. Our resultssuggest that, apart from the need to apply the suitable statistical tests,other effects such as the data binning, the considered units and the need, insome tests, to consider groups of data, affect substantially the determinationof the statistical significance of the asymmetry. Our main conclusion is thatthe assessment of the statistical significance of the N-S asymmetry of solaractivity is a difficult matter and that an absolute answer cannot be given,since many different effects influence the results given by the statisticaltests. In summary, the quantitative results about the statistical significanceof the N-S asymmetry of solar activity provided by different authors, as wellas the studies about its behaviour, must be considered with care because theydepend from the chosen values of different parameters or from the consideredunits.

The statistical significance of the N-S asymmetry of solar activity revisited