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I have this data set that contains information on the group (control or treatment) and the initial weight and final weight of the test subjects (fish). And I want to compare the effect of treatment on fish's weight gain. However, this data set is not paired; there is no identification and it's just a list of observed weight. I am planning to use mixed anova to analyse this, but mixed anova assumes the observations are paired.

Since all the fish did gain weight, is it ok for me to just pair up the data based on the observation order? Or should I assume that there are four groups (control fish weight before, control fish weight after, treatment fish weight before, and treatment fish weight after) and just run a regular anova test on the four groups.

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    $\begingroup$ Do you mean that the data are paired, but that you don't have the ID information needed to account for the pairing in the model, or that the data never were paired in the first place? $\endgroup$ – gung - Reinstate Monica Sep 20 '15 at 2:24
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    $\begingroup$ Sorry I should've better explained that. The data are not paired. So whoever was recording the data was not able to record the initial and final weight of the same fish. The person just randomly picked 20 fish at the beginning and recorded their weight, and at the end, randomly picked another 20 fish from the same tank, and recorded the final weight. $\endgroup$ – chrism Sep 20 '15 at 2:32
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    $\begingroup$ Looks like you'd have to do some sort of independent t-test. $\endgroup$ – StatsStudent Sep 20 '15 at 7:07
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Since there is no pairing, and no reason to believe the 20 fish weighted at both time points are the same, some independent groups analysis should be used.

You have two time points, and two groups, treatment and control. Since it is reasonable to believe that all the fish will gain weight with time, it is of no interest to test a hypothesis only about weight gain alone. The research hypothesis must be that growth is higher in treatment group than in control group. In the following linear model (expressed here in R) that is expressed by the interaction term, so that is what you should test:

mod <- lm(weight ~ time + treatment + time*treatment, data =your_data_frame)
summary(mod)
anova(mod)   
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