1) Simulate The Story
If a sampling idea feels abstract, simulate 1,000 samples and watch the means pile up. Seeing the stack is understanding the stack.
2) One Population… Many Samples
Teach your team to speak in plural: “Across many samples, we expect…” It shifts debates from certainty to reliability.
3) Standard Error On Every Slide
Whenever you show a sample mean, show its standard error. If you can’t, say why. Uncertainty belongs in the headline, not the footnote.
4) Finite Populations Need Respect
Sampling 40% of a small roster? Use the finite-population correction or at least note the shrinking variability. Context makes your standard error honest.
5) Batch Effects Are Bias In Costume
If one lab section, device, or grader dominates your sample, your independence is in trouble. Randomize the nuisance or stratify it.
6) Law Of Large Numbers ≠ Central Limit Theorem
Law of Large Numbers says the sample mean settles near μ. Central Limit Theorem says how the means are distributed along the way. Different promises… both useful.
7) Standardize The Process, Not The People
Before you standardize scores, standardize collection… instructions, timing, tools. Clean inputs make cleaner sampling distributions.
8) Intervals Need Verbs
A confidence interval isn’t decoration. Pair it with a verb: extend, target, adjust, delay. If it doesn’t change an action, it’s just scenery.