" I have two varibalbe for friction that one of them is measured based on the mean value of the whole data set (discrete model) and the other one takes the distribution of the data set into account (probabilistic model) and the result as shown in the graph below where the blue line represent the result of the discrete model and the boxplot represent the result from the probabilistic model. "
One word of caution. The horizontal red lines in your box plots are median values. If you're going to compare the results between the two models, make sure you're not comparing apples to oranges. If you decide to stick with means (assuming your data are approximately normally distributed), then you'll need to calculate (and plot) the means of the boxplot data. I'd estimate that those data are not normally distrubuted based on the upper wiskers of the plot. If you decide to compare median values, you'll need the medians for the data from the blue line.
"My question is is there a certain type of statisticl tests such as t-test ANOVA...etc to determine if there is a significant difference between the two models in general and how can it be implemented in matlab. "
If you use median values (which I'm guessing is the better choice), you'll want to use a nonparametric test. If you're comparing the quality of two models, perhaps an AIC test is more appropriate.
