Which type of statistical analysis is used when assumptions about the distribution or variance cannot be made?

The correct choice is nonparametric analysis. Nonparametric statistical methods are appropriate to use when the data do not meet the assumptions necessary for parametric tests, particularly regarding the distribution of the data or the equality of variances. These methods do not rely on any specific distributional assumptions, making them versatile and useful for analyzing ordinal data or data that do not follow a normal distribution.

In contrast, parametric analysis requires certain assumptions, such as normal distribution and homogeneity of variance. Descriptive analysis simply summarizes and describes the features of a dataset without making inferential assumptions. Inferential analysis, while it can use both parametric and nonparametric methods, typically involves assumptions about the data. Thus, nonparametric analysis is specifically designed for situations where these conventional assumptions cannot be met, making it the ideal choice for the given scenario.