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if two variables are shown in a segmented bar graph, and the bars look very similar in their breakdown into segments, then the two variables are described as
having an association
related
explanatory
independent
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So, segmented bar graph basically show the same proportions. They are basically independent variable. And they are independent with respect to the variable they were segmented by.
For example you had distribution of people from Utah and Ohio by gender and found out same proportions of male and female in these 2 states, you would conclude population distribution is independent of gender in these 2 states.
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