Scope of inference

 The scope of any inferences is constrained based on whether there is a random sample (RS) and/or random assignment (RA). 

Table 1-1 contains the four possible combinations of these two characteristics of a given study. 



Random assignment allows for causal inferences for differences that are observed - the different in treatment levels causes differences in the mean responses. 

Random sampling (or at least some sort of representative sample) allows inferences to be made to the population of interest. 

If we do not have RA, then causal inferences cannot be made. 

If we do not have a representative sample, then our inferences are limited to the sampled subjects.


Reference

Hypothesis testing (general) - Statistics with R (montana.edu)


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