Question 6′ a). what is Nonpar

a)

Nonparametric tests are sometimes calleddistribution-free tests because they are based onfewer assumptions (e.g., they do not assume that the outcome isapproximately normally distributed). Parametric tests involvespecific probability distributions (e.g., the normal distribution)and the tests involve estimation of the key parameters of thatdistribution (e.g., the mean or difference in means) from thesample data. The cost of fewer assumptions is that nonparametrictests are generally less powerful than their parametriccounterparts

b)

There are some situations when it is clear that the outcome doesnot follow a normal distribution. These include situations:

• when the outcome is an ordinal variable or a rank,
• when there are definite outliers or
• when the outcome has clear limits of detection.

here non-parametric test can be used

c)

Consider a clinical trial where study participants are asked torate their symptom severity following 6 weeks on the assignedtreatment. Symptom severity might be measured on a 5 point ordinalscale with response options: Symptoms got much worse, slightlyworse, no change, slightly improved, or much improved. Supposethere are a total of n=20 participants in the trial, randomized toan experimental treatment or placebo, and the outcome data aredistributed as shown in the figure below.

Distribution of Symptom Severity inTotal Sample

The distribution of the outcome (symptom severity) does notappear to be normal as more participants report improvement insymptoms as opposed to worsening of symptoms.