# Underwater Communications for Video Surveillance Systems at 2.4 GHz
## 3 Scenario and Test Bench
### Analysis of Variance by Two-Way (ANOVA)  
The best way to check if there is any relationship between two parameters is analyzing the variance of these variables by an ANOVA. Our analysis will compare the data transfer rate and the working frequency used at each temperature and modulation. The working frequency and the data transfer rates modulation are the groups to be compared. The variable under study is the maximum distance between antennae at each temperature. As a summary, to perform this study, we have to take into account several things. Firstly, to avoid any bias during the measuring process, we have performed 100 sets of measurements with 30 repetitions per set. This kind of analysis requires several sets of measurements with several repetitions. The first step was checking if these sets of measurements followed a normal distribution. This step can be done using the descriptive analysis or checking if residuals follow the null hypothesis or the alternative hypothesis (as this section explains). From this moment, we can apply the ANOVA studies over the set of measurements [33]. For each ANOVA analysis, we consider two possibilities. This analysis compares individually the dependence of maximum distance between antennae and the data transfer rate (rows) and the dependence of the maximum distance between antennae and working frequency (columns). In both cases, the ANOVA poses a null hypothesis where there is non-dependence between parameters and an alternative hypothesis which express the dependence between them. Analysis of rows:  
We formulate two hypotheses:  
* H0 = maximum distance does not depend on the data transfer rate (null hypothesis). * H1 = maximum distance depends on the data transfer rate (alternative hypothesis). Analysis of columns:  
We formulate two hypotheses:  
* H0 = maximum distance does not depend on the working frequency (null hypothesis). * H1 = maximum distance depends on the working frequency (alternative hypothesis). To define, in each case, whether the alternative hypothesis should be rejected or not, we take as important parameters the statistical value of F, the critical value of F, which is calculated from the value of significance level \(\alpha\). In our case, we have fixed our value as \(\alpha\) = 0.05. The result of analysis of variances indicates the statistical value of \"F\" for each analyzed factor. In order to see if results present any significance (i.e., if the probability \"P\" has a value less than 0.05), the observed value of \"F\" needs to be, at least, equal to the critical value of F.  
This will mean that there is a significant relationship between the analyzed factors (working frequency and data transfer rate) and our results (maximum distance between antennae). In that case, the results show that both parameters are statistically significant. If this comparison is not met, we would conclude that the relationship between parameters is not significant and its variations are due to the randomness of the measures. Before performing ANOVAs, we have analyzed if measurements follow a normal distribution. To perform this task, we have checked the descriptive statistic of each set of measurements. In concrete, the kurtosis and skewness coefficients are analyzed. The results gave us that the coefficients were between \(\pm 2\), so it is possible to apply the ANOVA as a method of analysis of variance, because data follow a normal distribution. In addition to see if groups of measurements follow a normal distribution, we can also see if they have some influence over the analyzed variable. To do it, we can calculate the residuals of each group. The residuals are calculated as the difference between the average value of each group and each value (see Table 3). From the results, the null hypothesis and alternative hypothesis can also be presented:H0: \(X_{1}=X_{2}=\ldots=X_{I}=0\leftarrow\) Factor under study does not influence the parameter to be analyzed. H1: any \(X_{I}\
eq 0\leftarrow\) Factor under study shows some influence over parameter to be analyzed.