Nonparametric Tests in Elementary Statistics Paper

Choose two of the following three questions and post your answer:

1. In your own words, what is a nonparametric test? What is a parametric test?
2. In your own words, identify an advantage of using rank correlation instead of linear correlation.
3. Which of the following terms is sometimes used instead of “nonparametric test”: normality test, abnormality test, distribution-free test, last testament, test of patience? Why is this term better than “nonparametric test”?

You may use the information in the textbook or cite a source.

Respond to two peers

Peer 1A parametric test is a statistical procedure based on population parameters to test hypotheses or estimate parameters. On the other hand, a non-parametric test is a statistical procedure to test hypotheses or estimate parameters, in which it is not necessary to make assumptions about the nature or shape of the population distributions (Triola, 2022). The first ones establish a good number of restrictions on the nature of the population from which the data is obtained, being the <<parameters>> the numerical values of the population. The second, also called << free distribution>>, do not require as many restrictions on the nature of the population, since they attend more to the ordering of the data than to its numerical value.

3.

Sometimes, instead of “non-parametric test” the name “distribution-free test” is used. Nonparametric tests are also called distribution-free tests because they do not require populations to have a particular distribution; for example, a normal distribution. It is better to use the term “distribution free test” because it is a more accurate description, because although the term nonparametric suggests that the test is not based on a parameter, there are some nonparametric tests that do depend on a parameter such as the median (Triola, 2022). However, nonparametric tests do not require a particular distribution, so the term “distribution free” better describes the characteristics of this procedure.

Reference:

Triola, M. F. (2022). Elementary Statistics (14th Ed.). Pearson.

Peer 2

n statistics, rank correlation has the advantage of being less sensitive to outliers and non-linear connections between variables than linear correlation. However, outliers and non-linear patterns are common in real-world data, which might skew the linear correlation value. Rank correlation can be used with paired data that are ranks or can be converted to ranks, unlike parametric methods. (Triola, 2018 pg. 678) Without making any assumptions about the nature of the relationship, rank correlation measures the degree of monotonic association between variables. It is more resistant to outliers and nonlinearities since it ranks the values of the variables rather than using their precise numerical values. The use of rank correlation can offer a more accurate indicator of association in circumstances when the relationship between variables might not be strictly linear or when the data contains outliers that may overpower the linear correlation. As a result, rank correlation is an effective tool for examining correlations in various datasets where linear assumptions might not be valid.

Reference:

Triola, M. F. (2018). Chapter 13: Nonparametric Tests. In Elementary statistics (pp. 678–678). essay, Pearson Education, Inc.