What type of statistical analysis would you apply when the assumption of normality is violated in a data set?

When the assumption of normality is violated in a data set, nonparametric tests are the appropriate choice. Nonparametric tests do not rely on the assumption that the data follows a normal distribution, making them ideal for analyzing data that is ordinal or skewed, or when sample sizes are small, where the normality assumption is hard to verify.

These tests focus on the ranks or signs of the data rather than the data's actual numerical values, which allows for a more flexible approach when the typical assumptions tied to parametric tests cannot be satisfied. This flexibility ensures that valid inferences can still be made even when the underlying distribution of the data deviates from normality.

In contrast, parametric tests assume normality and can yield unreliable results if this assumption is not met. Descriptive statistics summarize and describe the features of a data set but do not test hypotheses or make inferences about a population based on sample data. Inferential statistics encompass a range of statistical techniques, including both parametric and nonparametric methods, but in the context of a violated normality assumption, nonparametric tests would be specifically applied.