Independence
This is my proposed starting definition for independence:
Two samples are independent if changes to one will not lead to changes in the other. For example, if I give one class different lectures than a second class, if the two classes are independent, I wouldn't expect that change to impact the second class. This might not be the case if students from one class usually study with the other, if students attend lectures to which they aren't assigned, etc.
Note: Two samples can be independent even if they are not drawn from the same population. For example, if an 8:30 class consists entirely of engineering students and a 9:30 class consists of entirely of physics majors, the response of these students to instruction might be very different. This would be grounds to consider whether whatever differences between the classes I measure is do to some treatment I am giving or from the differences in the populations themselves. However, if changes I make to one class will not have a carry over effect on the other class, they can still be considered independent.
Please comment and revise!
Two samples are independent if changes to one will not lead to changes in the other. For example, if I give one class different lectures than a second class, if the two classes are independent, I wouldn't expect that change to impact the second class. This might not be the case if students from one class usually study with the other, if students attend lectures to which they aren't assigned, etc.
Note: Two samples can be independent even if they are not drawn from the same population. For example, if an 8:30 class consists entirely of engineering students and a 9:30 class consists of entirely of physics majors, the response of these students to instruction might be very different. This would be grounds to consider whether whatever differences between the classes I measure is do to some treatment I am giving or from the differences in the populations themselves. However, if changes I make to one class will not have a carry over effect on the other class, they can still be considered independent.
Please comment and revise!
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