Survey Sampling and Study Design

Any statistic computed from a sample is only useful if the sample represents the population it claims to describe. Simple random sampling gives every member of the population an equal chance of being selected, which avoids systematic bias but can by chance under-represent small subgroups. Stratified sampling fixes that by splitting the population into known subgroups (strata) — say, by sector or market cap — and sampling a fixed number from each, guaranteeing every subgroup is represented in proportion to its size. Cluster sampling instead samples entire pre-existing groups (say, whole trading days rather than individual trades) and includes every member of the chosen clusters, which is cheaper to collect but produces less precise estimates since observations within a cluster tend to be correlated rather than independent.

The design matters because it determines whether standard formulas for a sample's uncertainty even apply: a naively computed standard error assumes simple random sampling, and applying it to a cluster sample understates the true uncertainty, since clustered observations carry less independent information than the raw count of observations suggests.

For example, surveying "average daily volume across the market" by sampling only large-cap tickers would badly overstate typical volume — a stratified sample across cap-size buckets fixes that specific bias, since it forces the small-cap and mid-cap tiers into the sample in their true proportions rather than leaving their representation to chance.

Study design goes beyond sampling to how the data was generated in the first place: an observational study (just recording what happened) can only establish association, while a controlled experiment with random assignment to treatment and control groups is needed to claim causation, since randomization is what rules out confounding variables driving both the treatment and the outcome.