1). Can the formal hypothesis testing approach be used for nonparametric tests? How are parametric and nonparametric statistics different? How are parametric and nonparametric statistics similar?
Both kinds of tests can be used for formal hypothesis testing including the 5 step approach. The primary difference between them is that the parametric tests assume a particular distribution such as the normal or t distribution. Nonparametric tests do not assume this. Both are similar in that they use information about a sample to draw inferences about a population.
2). Under what circumstances must a nonparametric test be used? Explain. What are the strengths and weaknesses of nonparametric tests? Can the outcomes of nonparametric tests be generalized to populations?
Nonparametric tests must be used when the data don’t satisfy the normal assumption of the parametric test. They can also be used for medians or for contingency tables that don’t fall into any distribution. Nonparametric tests are useful because they don’t assume any particular distribution. I can use them when my data is non-normal, such as in a test for means.
Nonparametric tests can also be used when the distribution is to be drawn from the data. For example, in the chi-square test for independence, I can’t use a test that relies on a particular distribution because the distribution is always different. Another advantage of a non-parametric test is that it can be used for measures such as median that don’t have any equivalent parametric test. Unlike the mean, sample medians do not fall into a normal distribution, because medians do not use all of the available information in the sample. The main weakness of a nonparametric test is that it may have less power than the equivalent parametric test.
3). Why do you use the chi-square statistic? What type of data is used with chi-square analysis?
The chi-square statistic can be used in two different but related contexts. The first is to find out...