Why should I calculate sample size BEFORE collecting data, not after?+β
Deciding your required precision in advance and calculating the sample size that achieves it is the statistically sound approach. Collecting a convenient amount of data and hoping the resulting margin of error is narrow enough leaves your study's precision to chance rather than design.
What if I donβt know the population standard deviation for a mean-based calculation?+β
Use a reasonable estimate from prior research, a pilot study, or a conservative (larger) guess if genuinely uncertain β overestimating Ο leads to a larger, safer sample size; underestimating it risks an underpowered study.
Why does a 99% confidence level require a larger sample than 95%?+β
Higher confidence requires a wider margin of safety, which the formula achieves partly through a larger critical z-value (2.576 vs 1.96) β for the same target margin of error, more data is needed to narrow the interval enough to still hit that higher confidence level.
Why do quadrupling the sample size only halve the margin of error?+β
Because margin of error scales with 1/βn, not 1/n β this square-root relationship is why survey sample sizes hit diminishing returns: doubling precision requires roughly four times the data, not twice.