Such problems can be of various kinds: Statistical models, once specified, can be tested to see whether they provide useful inferences for new data sets.
[4] Statistical theory provides a guide to comparing methods of data collection, where the problem is to generate informative data using optimization and randomization while measuring and controlling for observational error.
Some of these tasks are: When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the randomization used to generate the data.
Statistical theory provides the basis for a number of data-analytic approaches that are common across scientific and social research.
In addition it provides a range of robust statistical techniques that are less dependent on assumptions, and it provides methods checking whether particular assumptions are reasonable for a given data set.