Computer Science Homework Help

• Discuss the difference between parametric statistics and nonparametric statistics.

Discuss the advantages and disadvantages of nonparametric statistics.

Describe the procedure for ranking which is used in both the Wilcoxon Signed-Rank Test and the Wilcoxon Rank-Sum Test

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  thanks, can you reply to these 2 posts back as per of the question

  Reply:

1)Parametric approaches require a number of assumptions, were the first developed, are considered, “traditional”. These include linear regression, logistic regression, linear discriminant analysis, etc. It also appliesar to non-parametric techniques used to provide models involving similar assumptions.Parametric data reduction models the data as a distribution, and summarizes it with parameters of that distribution.

Non-parametric data reduction does not use a model. It summarizes data with sample statistics or pictures.The same technique can be used by both. Describing a set of data by its mean and standard deviation can be considered estimates of the parameters of the underlying distribution, or just sample statistics.However, non-parametric data reduction is more likely to use order statistics, clusters and graphs than statistics like mean and standard deviation.Non-parametric approaches require no or few assumptions, have been developed more recently and are considered more modern. Decision trees, neural networks, and others fall within this camp.Which is more appropriate depends on the circumsta)nces. The problem with the latter is that the resulting models are opaque, i.e. difficult to understand. They will provide better results when problems are truly non-linear, but if not then their results may be worse (Hull, 1993.

Others have already pointed out how non-parametric works. I just wanna answer it from another point of view. So when we talk about parametric and non-parametric, in fact, we are talking about a functional f(x) in a hypothesis space, which is at beginning without any constraints. After a series of observations, say, X={x}ni=1 . In parametric way, you are gonna fit your assumed model f on the data, and find out the estimated value of your parameters, then you can forget about the observations. However, in non-parametric way, you don’t know what your functional is. So what you can do is to shrink your search space for the functional by fitting the observations, where each observation plays a role of constraining the functional. AND, you can not get rid of the data after training.In statistics, Wilcoxon signed-rank test. The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population means ranks differ (i.e. it is a paired difference test).Whereas, Wilcoxon rank-sum test is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.

References:

Hull, D. (1993, July). Using statistical testing in the evaluation of retrieval experiments. In Proceedings of the 16th annual international ACM SIGIR conference on Research and development in information retrieval (pp. 329-338).

2) Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Non-parametric tests are “distribution-free” and, as such, can be used for non-Normal variables.2)