What is the problem with parametric statistic tests?

What is the problem with parametric statistic tests?

• A. If you violated an assumption it can invalidate the test. They make judgments of parameters (population) based on statistics (samples).
• B. They always provide exact p-values regardless of data.
• C. They require no assumptions about the population distribution.
• D. They are never affected by outliers.

Answer: (A)

Parametric tests hinge on assumptions about the population from which data come and use sample statistics to draw inferences about population parameters. When those assumptions are violated—such as the data not coming from the assumed distribution, variances not being equal, or observations not being independent—the test statistic and resulting p-values or confidence intervals can be biased or invalid. This is the core reason these tests have problems: their conclusions depend on those population assumptions holding true. Outliers can also distort means and variances, further skewing results. For contrast, the claim that they always yield exact p-values is not true; violations of assumptions or small samples can make p-values inaccurate. The idea that no assumptions about the population distribution are required is incorrect, as is the notion that parametric tests are never affected by outliers.

Parametric tests hinge on assumptions about the population from which data come and use sample statistics to draw inferences about population parameters. When those assumptions are violated—such as the data not coming from the assumed distribution, variances not being equal, or observations not being independent—the test statistic and resulting p-values or confidence intervals can be biased or invalid. This is the core reason these tests have problems: their conclusions depend on those population assumptions holding true. Outliers can also distort means and variances, further skewing results.

For contrast, the claim that they always yield exact p-values is not true; violations of assumptions or small samples can make p-values inaccurate. The idea that no assumptions about the population distribution are required is incorrect, as is the notion that parametric tests are never affected by outliers.