MHB Parametric and non-parametric data

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Parametric data assumes a normal distribution and is analyzed using statistical methods that rely on this assumption, such as t-tests and ANOVA. Non-parametric data does not assume a specific distribution and is analyzed using methods like the Mann-Whitney U test and Kruskal-Wallis test. The choice between parametric and non-parametric analysis depends on the data characteristics, including sample size and distribution. Parametric tests are generally more powerful when the assumptions are met, while non-parametric tests are more flexible for non-normal data. Understanding these differences is crucial for accurate data analysis in research.
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I need the answer of the following question in 500 words. It was set in a university exam. But no where I found the straight forward answer. Please help

Question: Differentiate between Parametric and non-parametric data. How these data are analysed? (Word limit 500)
 
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I would suggest that you type out your attempt so our helpers can perhaps give you some guidance.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
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