Independant Sample or Dependant

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    Basically I have two sets of acid concentration data where the first set of data is taken when the acid is made, while the second set of data is taken after certain solution is added to the acid. I want to see if the solution has an effect on the acid concentration under certain temperature. Hence I need to do a t-test. Is those two samples considered as dependant or indenpendant data? So which t-test should I use? Thanks!


    Robert Butler

    As you describe your problem the question is not one of dependence or independence rather it is a comparison of some average response (measurement) made on two populations which may differ from one another because of the addition of a solution to one and not the other. 
      There are two possibilities here.  If you measured each sample prior to addition of the solution and then measured the solutions after the solution addition and you kept track of the measurements on a sample-by-sample basis then you can use the t-test to make a paired comparison.  If, on the other hand, you did not keep track of the measurements on a sample-by-sample basis but just simply recorded the before and after results then you will just use a two sample t-test to run your comparison. 
      Since the t-test assumes that your data is from a normal population and since it will usually assume equality of sample population variance (unless you have a program that allows/demands a decision concerning sample population variances) you will have to check to make sure that the sample variances are equivalent and you will also have to check the assumption of normality.  If the sample variances are not equivalent you will have to run a t-test with unequal variance. If the data is not from a normal distribution you will have to use another test such as the Mann-Whitney.
      You mentioned that you are going to check this difference at a specified temperature.  You need to understand that any conclusions that you draw from your analysis will only apply to the temperature that you chose.  For a different temperature you may get very different results.  If temperature is going to vary you may want to re-think your approach and consider revamping your investigation so that you could run a two way ANOVA in order to investigate both temperature and solution addition.

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