# Increasing Photovoltaic Systems Efficiency Through the Implementation of Statistical Methods
## 3 Methodology
### ANOVA Method Regarding Operational and Structural Analysis  
The parametric statistical techniques begin with a series of conditions regarding the normality and homogeneity of the subjects' results distribution. Nonparametric techniques are also referred to as statistical techniques that are independent of data distribution when these assumptions are not met. The advantages of this technique lie in its ability to process a diverse range of data, both qualitatively and quantitatively. Nonparametric tests can be used when there are doubts about the normality of statistical data. The advantage of nonparametric tests is that they are more robust and use fewer assumptions than parametric tests. Nonparametric tests do not need a known a priori distribution of observed data or a large volume of data. The main disadvantage is the lower power to detect the falsity of a null hypothesis. There are several nonparametric methods, the most common being:  
* [PERSON]'s test technique--(\(\chi^{2}\));
* Mann-Whitney U test (equivalent to the independent parametric \(t\)-test);
* Wilcoxon test of paired ranks (ANOVA equivalent of repeated measurements or \(t\)-dependent);
* Kruskal-Wallis ANOVA test of ranks, equivalent to simple ANOVA (data are converted to ranks).
* Analysis of variance (ANOVA) is a statistical formula that compares variances across different groups' means (or averages). In this paper, we propose using the Kruskal-Wallis ANOVA test of ranks to determine the tilt angle of the panels based on geographical coordinates and season.  
The primary phenomenon that generates the application of statistical methods is data variability. The general notion of variability refers to the measurable deviations of individual values from a central value, known as the mean (\(\mu\)). By analysing statistical collectivity with the help of central tendency indicators, the manifestation of a particular phenomenon can be predicted. A collectivity has a specific internal organisation defined by how individual values are distributed around the central value. Thus, one central value may be credible, and another may not. For this reason, the central tendency analysis must be supplemented with indicators of variation and the form of distribution.  
In probability theory and statistics, variance is the mean of the squared deviations of a random variable from its mean. Informally speaking, it measures the distance of individual (random) values in a crowd from their average. Variance is a crucial concept in statistics, used in both descriptive and inferential statistics, as well as in hypothesis testing and Monte Carlo methods. Statistical methods are widely used throughout science.  
Analysis of variance (ANOVA) is a statistical method used to compare the means of three or more groups. Its purpose is to determine whether there are significant differences between groups and to identify which groups have these differences. ANOVA compares the variability between groups (intergroup variability) with the variability within groups (intragroup variability). If the intergroup variability is significantly greater than the intragroup variability, then we can conclude that there are significant differences between the groups.  
In the article, the Kruskal-Wallis \(H\) test will be applied using Relationship (1):  
\[H=\frac{12}{N\cdot(N+1)}\cdot\sum_{i=1}^{k}\frac{R_{i}^{2}}{n_{i}}+3(N+1) \tag{1}\]  
* \(N=\) the size of the sample analysed (total number of observations across all groups);
* \(k=\) number of groups;
* \(R=\) the sum of the ranks of a group; \(n_{i}=\) the number of elements in a group.