EXPERIMENT 01
Law of Large Numbers
Compare the running average after 10, 50, and 200 random observations. Does it generally move toward the population mean? Save a screenshot and explain why individual paths still fluctuate.
The science of what we cannot fully observe
Sampling, seen.
From one population of observations to the sampling distribution of its mean. Change the sample size, repeat the draw, and watch uncertainty take shape.
Ready to experiment
StudentsOne population · one color · each square is an observation unless marked as a sample mean.
Sampling distribution of the mean
Each square = one sample meanRepeated random samples produce different estimates. A smooth curve traces their emerging distribution.
The most recent sample
5 observations, one sample meanThe entire population
One populationWhat are we comparing? Every teal square below is one individual in the population. The small panel above shows one random sample; the top panel accumulates the means of many such samples. We are measuring sampling variation, not a causal effect.
Explore the three laws
Use the same population to see why statistical inference works. Choose a principle, then change Sample Size or Sampling Method and try again.
A running average finds its center
One long sequence of observationsThree experiments to try
EXPERIMENT 02
Central Limit Theorem
Keep the number of repeated samples high. Compare samples of size 2 with much larger samples. How does the shape of the distribution of means change?
EXPERIMENT 03
Standard Error
Compare the spread of sample means for sample sizes n and 4n. Then choose the biased convenience sample: does increasing n eliminate selection bias?