I’d say sample size is more important if any experiment can get any statistical significance with the right sample size but not any sample size can get any statistical significance with the right experiment.
Thanks for listening. I still think that this is a misleading statement.
If we are considering empirical experiments, then our approximation of samples as being iid and sampled with replacement may break down at relatively small sample sizes, invalidating fundamental assumptions of common statistical significance tests.
If we are considering a mathematical model of a random experiment, then when the null hypothesis is true, the probability of a Type I error remains fixed at the chosen level of alpha no matter the sample size.
Thanks for listening. I still think that this is a misleading statement.
If we are considering empirical experiments, then our approximation of samples as being iid and sampled with replacement may break down at relatively small sample sizes, invalidating fundamental assumptions of common statistical significance tests.
If we are considering a mathematical model of a random experiment, then when the null hypothesis is true, the probability of a Type I error remains fixed at the chosen level of alpha no matter the sample size.