It is identified in some pieces of text I have read that paired t test is used to compare between cases and matched controls with regard to a continuous variable. Is this correct and how is this justified?
If you mean that the main exposure of interest is a continuous variable, why would you not use some form of logistic regression model (with case vs control as the outcome variable)? This 2016 BMJ article may be of interest.
- https://www.bmj.com/content/352/bmj.i969
HTH.
If participants were first placed into pairs based on a shared, common variable and then one individual in the pair was randomly assigned to either the treatment or control condition (and the remaining individual to the other condition) - then a paired samples t-test would be appropriate.
In an independent samples t-test, which group an individual is assigned to (treatment or control) is independent of the assignment of all other participants. Hence, the name. The paired samples t-test also goes by the name "dependent samples t-test". It is called this because individual assignment is not independent. For example, in a matched pair - if one individual in the pair is assigned to the treatment condition, the other individual in the matched pair is assigned to the control condition (and vice versa). The assignment of one individual is dependent on the assignment of the other.
A paired samples t-test is "justified" in this situation because the assortment into matched pairs removes the variability associated with the variable of interest. For instance, if we grouped participants into pairs based on age prior to assignment any differences found between individuals in the treatment and control conditions is not likely due to age. The caveat is that individuals in the matched pair could differ in other ways that we didn't control for.
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