Nonparametric, Statistics Problem Example

Respond to the following questions.

• What do you determine when you perform nonparametric statistics?

The use of non-parametric statistics is generally used for the analysis of problems without a fixed probabilistic distribution, usually a normal distribution. That is, most problems one may encounter in statistics is related to the assumption of a distribution (usually the normal) that dictates assumptions about the underlying such as mean and standard deviations, etc.

• When are nonparametric statistics used? Give an example.

Non parametric statistics are typically used in several circumstances:

1. If the sample size is particularly small and does not typically exceed the normal distribution threshold of 30 data points.
2. If after examining the descriptive statistics, it does not appear that the underlying distribution is one known.

• When is the one-wayX² test used?

A one-wayX² test is typically used when one is examining the difference between two categorical variables in trying to understand if there is a difference between the expected and actual amount. That is, if there is a statistically significant between the two categories.

• When is the two-wayX² test used?

A two-wayX² test is typically used when is examining two variables with more than two categories each. Although the general analytical purpose is similar to the one-way test, that is, one is typically interested in understanding the difference in the groups. The categories, however, are usually more.

• Assume that each of the following studies cannot be analyzed using a parametric procedure. For each of the following studies, indicate the appropriate nonparametric procedure, and explain why you chose it.

1. One group of mothers has played classical music for their babies every day for 6 months while another group of mothers has not. The babies are tested to determine if there is a significant difference in the motor coordination skills of these two groups.

One-way chi-squared- there are two groups of children measuring whether there is a difference in the motor coordination between the two groups.

2. College freshmen with high test anxiety are assigned to three groups. One group receives free individualized counseling, one group participates in a class to teach them how to reduce their anxiety, and the third group receives no treatment. They are tested to determine if there is a significant difference in the test anxiety level of the three groups in a test situation.

Two-way chi squared- there are more than two groups with a total of three groups looking at different interventions to test anxiety.

3. Two record companies have rated how likely a new artist’s songs are is to be the next “big hits.” The ratings are analyzed to determine the amount of agreement between the two companies’ opinions.

Likely a two-way chi-squared since there are two record companies but probably are rating more than two songs of the artist.