Which statement best describes the assumptions of parametric tests?

Which statement best describes the assumptions of parametric tests?

• A. They require homogeneity of variance, interval-level data, and a normally shaped sampling distribution.
• B. They require non-normal distributions and ordinal data.
• C. They are used only for large samples.
• D. They do not rely on any data assumptions.

Answer: (A)

Parametric tests rely on certain population assumptions to produce valid results: the data should be measured at an interval level so arithmetic operations like means and variances are meaningful; the groups being compared should have roughly equal variances (homogeneity of variance) so the test statistic isn’t biased by differing spread; and the sampling distribution of the statistic (for example, the distribution of the mean difference) should be approximately normal. When these conditions hold, the test statistics, p-values, and confidence intervals are accurate and the tests generally have good statistical power. The other statements miss important points: non-normal distributions and ordinal data violate the normality and scale requirements, especially with smaller samples; parametric tests are not restricted to large samples—their use depends on meeting assumptions rather than sample size alone; and parametric tests do rely on data assumptions rather than being assumption-free.

Parametric tests rely on certain population assumptions to produce valid results: the data should be measured at an interval level so arithmetic operations like means and variances are meaningful; the groups being compared should have roughly equal variances (homogeneity of variance) so the test statistic isn’t biased by differing spread; and the sampling distribution of the statistic (for example, the distribution of the mean difference) should be approximately normal. When these conditions hold, the test statistics, p-values, and confidence intervals are accurate and the tests generally have good statistical power.

The other statements miss important points: non-normal distributions and ordinal data violate the normality and scale requirements, especially with smaller samples; parametric tests are not restricted to large samples—their use depends on meeting assumptions rather than sample size alone; and parametric tests do rely on data assumptions rather than being assumption-free.