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I'm trying to get a better understanding of how the independence assumption can be violated in ANOVA. To this end, I've come up with an example using one factor with 3 levels:

Say we're doing an experiment related to cancer treatment. The subjects are divided amongst 3 groups: A = new drug being investigated, B = placebo, C = drug currently on the market.

My question is this: if the participants in all 3 groups come from the same population (people with whatever type of cancer we're investigating), does this mean the independence assumption is violated?

Once certain people are assigned to group A, this should change the probability distribution representing the possible responses we can get for groups B and C. Or do people usually operate under the assumption that the population is so large and proportionally allocated that removing group A's responses won't noticeably change the response distribution for groups B and C?

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If the participants in all 3 groups come from the same population, it only resticts the scope of your generalization: results of your analyses would only be meaningful for this population.

As long as subjects assigned to each group were chosen randomly, the distribution of the remaining population should be a non-issue, or at least a random factor beyond your ability to control. A stratified random approach is sometimes used to ensure that a priori important predictors (eg age, sex) are consistently represented in each treatment group.

But an example of a truly violated independence assumption would be e.g. a) if the same person was assigned to group A, then B, then C, in non-random order, then all the 3 responses were analysed as independent; b) if a response taken from the same subject, say weight, was recorded on day 1, 5, 10, then these datapoints were analyzed as independent responses.

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