- Classify a study as observational or experimental, and determine whether the study’s results can be generalized to the population and whether they suggest correlation or causation.
- If random sampling has been employed in data collection, the results should be generalizable to the target population.
- If random assignment has been employed in study design, the results suggest causality.
- Stratifying and blocking both allow for controlling for potential confounders, but at different stages of the study design. We stratify when we sample (divide population into strata and sample from within each stratum), and block in the process of random assignment (divide sample into blocks and randomly assign from within each block to treatment groups).
Foundations of probability
Must read: https://plato.stanford.edu/entries/probability-interpret/
One should just know that, besides the Kolmogorov definition of classical probability as a probability measure, another classical probability theory was developed by von Mises: probability was defined as the limit of relative frequencies.
What is Measure Theory?
A simple answer is that it is a theory about the distribution of mass over a set S. If the mass is uniformly distributed and S is an Euclidean space Rk, it is the theory of Lebesgue measure on Rk (i.e., length in R, area in R2, volume in R3, etc.). Probability theory is concerned with the case when
S is the sample space of a random experiment and the total mass is one.
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