[MINI] Sample Sizes

Basics

Understanding sample sizes is crucial in data measurement and analysis. Kyle Polich and Linhda explain that sample sizes are essentially measurements that help develop models or understand underlying data. They highlight the importance of representativeness, especially in contexts like elections, where small sample sizes can lead to inaccurate predictions if not properly representative 1. Kyle notes, "If legitimately, you could sample in a way that's independent and identically distributed and have a good measurement of the general populace, then you can get by with small sample sizes in some cases." 2

   

Elections

The application of sample sizes in predicting electoral outcomes underscores the need for representative samples. Kyle uses the example of predicting election results to illustrate how small sample sizes can be misleading if they are not representative of the broader population 2. He explains that asking a small, non-diverse group about their voting intentions can skew results, as it may not reflect the actual voting population. Linhda adds, "If they're all part of the same family, they're probably all voting on the same side," highlighting the risk of bias in small, non-representative samples.

   

Tests

Statistical tests like the t-test and chi-square test are valuable tools for analyzing small sample sizes. Kyle mentions that the t-test is robust for datasets with limited independent degrees of freedom, making it suitable for small samples 3. He also discusses the chi-square test, which requires at least five observations per contingency cell to be effective. For situations where this isn't possible, exact tests can be used, though they may be computationally challenging. Kyle advises, "For a good data set that doesn't have too many independent degrees of freedom, the Ttest is pretty robust."