Which statistical analysis requires the assumption of a normal distribution of the sample data?

The assumption of a normal distribution of the sample data is a foundational characteristic of parametric statistical analyses. Parametric tests, such as t-tests or ANOVA, rely on certain assumptions about the parameters of the population from which the sample is drawn, including the normality of the data. This means that the underlying data should follow a bell-shaped curve, which allows for the application of these statistical methods that estimate population parameters based on sample statistics.

Using a parametric approach when the data violates the assumption of normality can lead to inaccurate results, as these tests may not account for the inherent variability in data that doesn't conform to the normal distribution. Therefore, it is critical to check for normality, especially when dealing with smaller sample sizes.

Nonparametric tests, in contrast, do not rely on normal distribution assumptions and can be used with ordinal data or non-normally distributed interval data. Inferential statistics is a broad category that includes both parametric and nonparametric methods, while descriptive statistics refers to methods that summarize data but do not make predictions or inferences about a population, thus not requiring any distribution assumptions.