Chi-Square (χ2) Test

This is a non-parametric test, which is used for the purpose to check the significance of relationship between each precipitation variable at each low-resolution scale for the assigned weighted values. In this regard, the assumption is made to determine the association between precipitation variables and the low-resolution scales.

The null and alternative hypothesis will be:

*H*0: There is a significant relationship between precipitation variables and upscaled resolutions. *H*1: There is no significant relationship between precipitation variables and upscaled resolutions. The equation deriving chi-square statistic [56], is given by Equation (10):

$$\chi^2 = \left(\sum\_{i=1}^n (O\_i - E\_i)^2 \Big| E\_i\right) \tag{10}$$

where *Oi* represents the observed, and *Ei* represents the expected frequency.
