I have to verify the presence or the the absence of a phenomenon in 3 different cases (A,B,C) and then representing the results in a single bar graph in order to compare the the results of the three cases together. The phenomenon to detect is constituted by four indicators ($I_1$, $I_2$, $I_3$, $I_4$) and in order to verify if and in which levels this phenomenon is present in each case, I have to calculate if and how much this indicators are present in every single case. In order to fulfill my aims (the verification of the presence of the phenomenon and the comparison) I thought to proceed as following:
calculating (separately for each indicator) in which percentage the $I_1, I_2, I_3, I_4$ are present in the cases A, B, C. For example, in the case A: $I_1=70%$, $I_2=20%$, $I_3=10%$, $I_4=20%$.
considering that the indicators have not the same weight in the determination of the phenomenon, I have used the operation of "pondering" by giving to each indicator the correct weight and then multiply the "weight" for all indicators' values of each case. For example, $I_1= 3$; $I_2=1$; $I_3=1$; $I_4=5$. So, in the case A: $I_1=70*3$; $I_2=20*1.....$
at this point I though that it seemed right to do the operation of "normalization" in order to make possible the comparison of all the resulting of the three cases in a single bar graph. The operation that I have do is the following: *$I_1(A)-X_m$(possible minimum value of $I_1A$)$/XM$(possible maximum value of $I_1$A)$-X_m$ . In this case $X_1=$ each value that each indicator takes in the single cases.
after having gathered all the resulting data normalized, I have have summed them for each case ($I_1A+I_2A+I_3A+I_4A$) and then convert them in a bar graph where the y-axis represent the levels in which the phenomenon is present in the case, and the x-axis represent every case.
I would to know if, by doing the normalization, I can make comparable all the three cases in a graph which act like an "index" of the presence of the phenomenon or if I made something wrong.