In parametric statistics, what is assumed about sample data?

In parametric statistics, it is assumed that sample data follows a specific probability distribution that is characterized by fixed parameters, such as the mean and standard deviation. This assumption is fundamental because many parametric tests, like t-tests and ANOVA, rely on the characteristics of this distribution to make inferences about the population from which the sample is drawn. For instance, the normal distribution is a common assumption, and knowing the parameters of this distribution allows researchers to apply statistical tests that can yield more powerful and accurate results.

The other options do not align with the foundational principles of parametric statistics. Data being solely nominal in nature does not apply, as parametric tests typically require interval or ratio data. The idea that dataset comparisons are impossible contradicts the very purpose of statistics, which is to compare groups and draw conclusions. Lastly, while larger sample sizes can often provide more reliable results, parametric tests do not strictly require large samples as long as the underlying assumptions about data distribution are met.