Convenience sample

A convenience sample is chosen by accessibility: the researcher takes the individuals who are easiest to reach, and no chance mechanism decides who is in. Nobody has a known probability of selection, and the parts of the population that were never within reach have probability zero, so the sample is not random in the sense the inference formulas require.

Suppose a reporter stands outside a gym at 6 a.m., interviews the first 60 people who leave, and finds that 41 of them, or $41/60 \approx 0.68$, exercise daily. A calculator will produce a 95 percent confidence interval for that: $0.68 \pm 1.96\sqrt{\frac{0.68 \times 0.32}{60}}$, which is $0.68 \pm 0.118$, or 0.562 to 0.798. The arithmetic is correct and the interval is worthless, because the randomness condition behind it was never met. It describes 60 people leaving one gym at 6 a.m. and nothing wider.

The sentence that keeps convenience sampling alive is "I did not pick them for any particular reason, so the sample is basically random." Not choosing on purpose is not the same as choosing by chance. Randomness means a mechanism that hands every member of the population a known probability, and standing where people happen to be gives everyone else a probability of zero while the people who are there share whatever put them there.

A convenience sample is not a voluntary response sample, where the subjects put themselves in by answering. Here the researcher does the reaching. Both are nonrandom, and topic 1.12 Potential Problems with Sampling is where the course puts the damage they do.

One thing convenience recruiting does not wreck is an experiment. Randomly assigning treatments to volunteers who were easy to find still supports a cause-and-effect claim about people like those volunteers. What it cannot do is generalize to a wider population, because that right comes from random selection.