Sample Size Estimation Notes

Sample Size Estimation

Sample size estimation is a statistical process used to determine the minimum sample size required to detect an effect size of interest.
It helps justify the number of participants needed to form a representative sample, ensuring that sample-level differences reflect the population at large.
Understanding sample size estimation is crucial for interpreting research literature and the data collected.

Sample size estimation ensures that studies are appropriately powered, controlling error rates.
Type II error: Failing to reject the null hypothesis when it is false (i.e., concluding there is no population difference when a real difference exists).
Power is the probability of correctly rejecting the null hypothesis when it is false.
A study powered to 80% (0.8) means there is a 20% chance of Type II error.
If we want to detect a small effect size of 0.32 with a Type I error rate of 5% (alpha = 0.05) and a Type II error rate of 20% (power = 0.8), we might need 79 participants (observations).

Estimate the required sample size a priori (before data collection) to avoid bias.
Base estimations on the population effect, not just the observed sample statistic.
Sample size estimation depends on the statistical tests used (e.g., t-tests, ANOVA tests).

Sample size descriptions should be interpretable and replicable to ensure confidence in statistical outcomes.
Example: A study using GPaL software to estimate sample size for comparing strength levels in youth netball players.
Statistical power: 0.9 (10% chance of Type II error).
Effect size of 0.6 (moderate effect).
Required \ge 30 participants.
Inferences based on smaller effect sizes (less than 0.6) should be viewed cautiously due to potential lack of statistical power.

Appropriate sample recruitment informs the inferences you can make from the research results.
If studies report small effect sizes with inadequate sample sizes, be cautious about generalizing those findings to your own populations.