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We conducted a study to analyse the effect of tablet named 'xab' that help smokers to stop smoking. 5500 of smokers are selected. half of them were given different doses of tablet while the other half were given a placebo. Their ages, weight, duration of smoking and the number of cigarettes smoked every day have been recorded for several months; the result of each group is compared

Identify dependent and independent variables?

For me, independent different doses and dependent is number of cigarettes, while age, weight and duration of smoking are confounding, why some colleagues tell me that age, weight and duration are independent, we do not manipulate them , they interfere with other variables and affect the experiment , is it my answer correct or no?

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    $\begingroup$ Please use the self-study tag for homework questions. $\endgroup$ – StatsStudent Jan 26 '19 at 17:36
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In causal inference terminology, if the study was randomized then age and weight (covariates not affected by your treatment) are not expected to be confounders by design.

When you successfully randomize, your treatment assignment is unconfounded, and you can measure the average treatment effect without adjusting for any other covariates. In experiments, you usually adjust for other covariates to (i) improve precision and/or (ii) estimate conditional effects or direct effects --- but not for control of confounding. As a matter of fact, regression adjustment in experiments might have unintended consequences if you are not careful, see for instance here.

In your case I just noticed that you also mention "duration of smoking", which seems to be something affected by your treatment. This is definitely not a confounder, it is either another outcome of interest or a mediator, so you should not mindlessly adjust for it in your regression before defining what your target effect of interest is and writing down your causal model.

To sum up, when you say certain variables are confounders this has a very specific meaning in causal inference: you are claiming that your randomization procedure was not successful and these variables not only affect your outcome, but somehow also influenced treatment uptake (also, you are claiming that these variables are not mediators). That is, you would be claiming that one needs to adjust for these covariates to get consistent estimates of your treatment.

Finally, if this is just a homework question and you do not fully understand causal inference yet, here is a simplified version --- for your case "duration of smoking" and the "number of cigarettes smoked" are either "dependent" variables or "outcomes" or "mediators", since they are affected by your treatment; whereas "age" and "weight" are independent variables (not confounders), they are not affected by your treatment nor they have affected your treatment (assuming randomization) but they may affect your "dependent variables" (your outcomes/mediators) of interest. None of the covariates are confounders under randomization.

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The labeling of the variables as independent variables, predictor variables, covariates, confounding variables, nuisance variables and other things is not completely uniform.

Some people (including me, sometimes) call everything on that side of the equation an "independent" variable. Some people (including me, sometimes) separate out covariates as variables that we aren't really interested in, but have to include. Other people divide them in different ways.

The math works out the same (as long as you don't get into moderation or mediation); a regression program just knows that there is a Y and a bunch of Xs (to use labels that do seem pretty universal).

TL:DR Neither of you is really right or wrong.

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    $\begingroup$ Not sure I agree that "the math works out the same" for confounders: sometimes conditioning on a confounder adds bias to estimates. Unless you mean something like "That math works out the same, correctly or incorrectly, no matter what you label the variables?" $\endgroup$ – Alexis Feb 10 '19 at 17:27
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    $\begingroup$ Yes, that's what I meant. That is, the computer program can't tell if the variables on the right side of the equation are IVs, covariates, moderators or whatever. $\endgroup$ – Peter Flom - Reinstate Monica Feb 11 '19 at 10:31

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