Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.

Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing mean blood sugar levels between patients receiving different treatments becomes statistically reliable using parametric statistical methods.

On the other hand, nonparametric statistics do not make any assumptions about the data's underlying distribution. They come into play when data fail to meet the prerequisites of parametric tests or when handling ordinal or categorical data. These methods offer several advantages, including robustness to outliers and no specific distributional assumptions. However, they are generally less powerful than parametric tests when all the parametric assumptions are met.

Nonparametric statistical methods find use in various biostatistical applications. The Wilcoxon rank-sum test, which compares median survival times between two groups of lab animals, is one example. Another is the Kruskal-Wallis test, a nonparametric alternative to ANOVA for comparing medians of multiple groups.

Parametric and nonparametric statistics have unique significance and applications in biostatistics, with their use determined by the nature of the data and the statistical assumptions that can be made.