confidence intervals

confidence interval

a range of values around a sample estimate that is likely to contain the true population parameter if the study were repeated many times

capture percentage

the percentage of times your current confidence interval would contain a new sample estimate from future replications, it is used to understand the stability of your result

prediction interval

a range that estimates where a future individual observation is likely to fall, given your current data.

2 main approaches to sample size planning

• power analysis: ensures you can detect a meaningful effect.

• precision planning: ensures your estimate has a narrow confidence interval

sample size planning

the process of determining how many participants or observations are needed in a study to ensure that your statistical analysis will be informative, reliable and accurate.

CI around a Standard Deviation

Rarely reported, but useful when planning future studies or comparing variability.

Chi-Square Distribution

The distribution used to calculate confidence intervals around standard deviations.

Narrower CI

Happens with larger sample sizes and lower variability, indicates more precision.

Wider Ci

Happens when sample size is small or data is more variable — indicates less precision.

CI Overlap Misconception

The incorrect belief that overlapping CIs always mean non-significant differences real tests require CIs on differences.

Confidence Level

The percentage of intervals (e.g., 95%) that would contain the true parameter if the study were repeated many times.