Hypothesis Tests

Hypothesis Tests
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Question One
A non-parametric test is a statistical test of hypothesis conducted whenever the probability distribution of a population is unknown, and assumptions of normality or any other specific distribution cannot be made. They are non-parametric in the sense that they do not depend on the precise values of population parameters since the probability function of the population is undefined and no assumptions are intended to be made. On the other hand, a parametric test is a statistical test of hypothesis based on parameters of known population distribution, and if not known, assumptions of the population parameters and distribution function (usually of normality) are made (Triola, 2006).
Question Two
The Pearson’s linear correlation evaluates the extent of a linear association between two continuous random variables and that the association can be represented using a fitted straight line is plotted. The approach, therefore, requires a normal distribution and is parametric. However, the Spearman’s rank correlation is non-parametric and does not require normality. As a result, it is more diverse and can even be applied to identify some relationships that are not necessarily linear. For example, rank correlation can be used to show the magnitude and direction of a monotonic relationship; a relationship that cannot be shown using Pearson’s approach if it is not strictly linear (Triola, 2006).
Question Three
A non-parametric test simply implies that assumptions of normality are not made on a hypothesis test of a distribution.

A non-parametric test, therefore, doesn’t “impose” a population to a certain distribution, even though the population in itself may have a specific distribution, say, Poisson. On the other hand, a distribution-free test implies that the population would have a null distribution and if it does have a specific one, it is overlooked (Triola, 2006).

References
Triola, M. F. (2006). Elementary statistics. Reading, MA: Pearson/Addison-Wesley.