My experiment tests how frequently people in two different countries use different types of computers. Assume, that there are only three types of computers (desktop, laptop and tablet) . I am interested to see the difference of usage between types (within each country) as well as between two countries (for each type). I conducted the survey in which participants ranked how frequently they use each type (1 - low frequency, 10 - high frequency). I got the following avrage results (error bars are SEM):
For desktop there is almost no difference between countries, but there is quite a large one-side difference for laptops and desktops. But given that there are only three types of computers, how it can be that higher frequency for two types in country 1 is not compensated by higher values for other type for country 2? Am I right with my concern or there is a flow in my logic?
To resolve the issue, for each participant I calculated relative frequency by dividing the frequency value of each type by sum of frequencies. So, now the previous problem was solved (see the graph below). But: a) the applied normalization altered the relationship, so now the biggest difference between countries is for desktops; and b) how I can run now 2-way ANOVA for these data given that the values are not independent (in each country they summed up to 100).
What is the correct way to tackle my problem?