# Influence of Atmospheric Pollutants and Weather Conditions on Agricultural Productivity in Italy
## 2 Materials and Methods
### Analysis
The null hypothesis (\(H0\)) that the means of three or more components (in this case five) would be equal is compared with the alternative hypothesis (\(H1\)) that at least one mean would be different. The variables considered are five and the hypotheses are the following:  
\[H0:\ \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}\]  
\[H1:\ \mu_{1}\
eq\mu_{2}\
eq\mu_{3}\
eq\mu_{4}\
eq\mu_{5}\]  
In this scenario, the hypotheses consider five distinct datasets related to five environmental components: PM10, O\({}_{2}\), NO\({}_{2}\), SO\({}_{2}\), and rain. The objective is to determine whether there is a significant difference among the means of these datasets. The null hypothesis (\(H0\)) means that there are no significant differences between the means of these datasets while the alternative hypothesis (\(H1\)) allows that at least one of the five datasets' means is different from the others. This implies that there might be a significant variation in the average levels of one or more components compared to the others. Accepting the null hypothesis would mean concluding that the average conditions observed for the five components are essentially similar, and any observed differences could be due to chance or natural statistical variability. On the other side, accepting the null hypothesis could indicate that one of the environmental components behaves differently on average, possibly due to specific environmental factors, local emissions, climate variations, or other phenomena that affect that component more strongly. Data used in the ANOVA analysis were obtained as the absolute value of the difference between the measured and the estimated production using the quadratic relationship previously found. Fisher values between the 99% and 95% level of significance were used for statistical testing of cultures. Based on the analyses carried out, the ANOVA rejects the hypothesis \(H0\), indicating that the chosen variables (pollutants and rain) affect the crops, except for the analysis made for the city of Palermo, which accepts the hypothesis \(H0\), indicating that none of the variables taken into consideration affect the dependent variable (crop production). Having defined the statistical test of the ANOVA, it can be noted that among the dependent variables one has values that are high, in particular ozone. This indicates that the ozone is the variable that most affects the production. The corn production in Padua changes the incidence of variables on production according to the degree of importance. Using a 95% significance level will reject the \(H0\) hypothesis while using a 99% significance level will accept the \(H0\) hypothesis. In analyzing the variability according to the normalized IQR of the different sites, it becomes evident that Palermo exhibits the highest degree of variability, while Ferrara and Venice record the lowest values. Nevertheless, the IQR absolute values are low. In Palermo, no pollutant exceeds the set annual limit. The particulate matter concentration was constant during 2013-2019 and then decreased in 2020, when a minimum was recorded (probably due to the COVID-19 pandemic situation), and emissions increased again in 2021. The minimum for ozone concentration appears to be in 2019, but in subsequent years the concentration will return to or approach the level of 2015. Sulfur dioxide concentrations are very low and appear to be constant, except in 2020, when it reaches its weak peak (Figure 1). In Bari no pollutant exceeds the set annual limit. The PM10 concentration appears to constant with a slight decrease from 2017. The ozone concentration does not have a linear trend because it seems to have a decreasing and increasing trend depending on the year. The concentration of nitrogen dioxide, on the other hand, has a linear decline from 2017 (Figure 2). The city of Ferrara has no pollutants exceeding the established annual limits. Particulate matter concentrations are constant, except for a small peak in 2012 and 2020. Ozone concentration appears to have constant values in the considered period.