Parametric tests require which of the following?

• A. They require non-normal data
• B. They assume ordinal data
• C. They assume equal variances only for two-sample tests
• D. They require random sampling, interval data, normal distribution, and equal variances

Answer: (D)

Parametric tests rely on a specific set of assumptions about the data and how they were collected, because these conditions ensure the test statistic has the expected distribution under the null hypothesis. The essential requirements are that the observations come from a random sample (to represent the population and provide independence), the data are measured on an interval (or ratio) scale (so differences and means are meaningful), the underlying population distribution is normal (or the residuals are approximately normal for the model in use), and the variances are equal across groups being compared (homoscedasticity) when that model calls for it. Together, these conditions allow the test to use its theoretical sampling distribution to determine p-values and confidence intervals.

Non-normal data is not a requirement for parametric tests; in fact, they rely on normality, but they can be robust to mild deviations or with large samples where the central limit theorem helps. Ordinal data isn’t appropriate for standard parametric tests because the distances between categories aren’t guaranteed to be equal, which undermines the meaning of means and variances. And while equal variances matter for many parametric procedures, that assumption isn’t exclusive to two-sample tests—it's also central in other contexts (like ANOVA); when variances are unequal, there are adjusted or alternative methods, such as Welch’s tests.