Which of the following is not an assumption of parametric tests?

The reasoning behind the selected answer relates to the fundamental assumptions that govern parametric statistical tests. Parametric tests typically require certain conditions to be met to ensure valid results.

Normality of the data distribution is indeed a core assumption; many parametric tests assume that the data follows a normal distribution, especially with smaller sample sizes. Homogeneity of variance, or homoscedasticity, means that different groups being compared should have approximately equal variances, which is crucial for tests like ANOVA. Independence of observations is also vital; it means the data points must not influence one another, ensuring that each observation provides unique information.

In contrast, the notion of a normal distribution for all sample sizes is not a valid assumption for parametric tests. According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the mean will tend toward a normal distribution regardless of the shape of the population distribution, which allows for the application of parametric tests even if the data are not perfectly normal, especially with large sample sizes. Therefore, the incorrect understanding in the question is based on the belief that all sample sizes must adhere to a normal distribution when using parametric methods, which is not the case. Thus, this distinguishes it as not an assumption