A city offers a daily walking program and asks whether it lowers resting heart rate. Here we are allowed to cheat: you set the program's real effect, so you always know the right answer. Then run the study two ways — let people choose whether to walk, or let a coin decide — and watch which design can actually find the truth you planted.
Who ended up in each group
already fitless fit
Where the studies land
one study’s reported benefitthe truth you setwhat this design is aimed at
What a bigger study buys you
Each band covers the middle of what that design would report at a given size. Growing the study narrows a band — it never moves one.
Set up the citythen run a study
0.0 bpm
10 bpm
80/20
200
True benefit0.0
This study said—
Average of 0—
Built-in bias0.0
The one question that classifies a study: did the researcher impose the treatment and decide who got it? Yes → experiment. If the subjects, their doctors, or nature decided → observational, no matter how large or careful it is.