  The main aim of this study is to point out the difficulties found when trying
to assess the statistical significance of the North-South asymmetry (hereafter
SSNSA) of the most usually considered time series of solar activity. First of
all, we distinguish between solar activity time series composed by integer or
non-integer and dimensionless data, or composed by non-integer and dimensional
data. For each of these cases, we discuss the most suitable statistical tests
which can be applied and highlight the difficulties to obtain valid information
about the statistical significance of solar activity time series. Our results
suggest that, apart from the need to apply the suitable statistical tests,
other effects such as the data binning, the considered units and the need, in
some tests, to consider groups of data, affect substantially the determination
of the statistical significance of the asymmetry. Our main conclusion is that
the assessment of the statistical significance of the N-S asymmetry of solar
activity is a difficult matter and that an absolute answer cannot be given,
since many different effects influence the results given by the statistical
tests. In summary, the quantitative results about the statistical significance
of the N-S asymmetry of solar activity provided by different authors, as well
as the studies about its behaviour, must be considered with care because they
depend from the chosen values of different parameters or from the considered
units.
