Psychology

Prior to beginning work on this discussion forum, read the Instructor Guidance for Week 2; Chapter 10 in the textbook; pages 109 to 120 in Chapter 7 of the Jarman e-book; the Chi-Square Test, The Chi-Square Test: Often Used and More Often Misinterpreted, The Chi-Square Test of Independence, How to Chi-Square Test (Links to an external site.), and How to Interpret Chi-Squared (Links to an external site.) articles; watch the Two-Way Tables, Chi-Square Tests: Crash Course Statistics #29 (Links to an external site.), Chi-Square Test for Association (Independence) | AP Statistics | Khan Academy (Links to an external site.), and Chi-Square: Lecture 11 videos.

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Table 10.6 (Tanner, 2016)

The purpose of this discussion is to allow you to consider how nonparametric tests are used and how two types of chi-square tests compare. To do this, you will need to explain statistical concepts and assess assumptions, limitations, and implications associated with statistical tests.

For your initial post,

Describe the chi-square goodness-of-fit test. Explain what this test measures.
Explain how the chi-square goodness-of-fit test is similar to and different from a simple frequency distribution.
Describe the chi-square test of independence. Explain what this test measures and how it is similar to and different from the chi-square goodness-of-fit test.
How do you know when to use one analysis over the other?
Provide a real-world example in which either a goodness-of-fit test or a test of independence should be used.

ANSWER

Chi-square Test

A chi-square test can be used to measure the assumptions of data that is expected in a certain analysis (Thaseen & Kumar 2017). The main idea about this test is that it compares the observed data in a set of values with the data that is expected in a hypothesis. Chi-square tests are of various types ; independence type , homogeneity, and test of goodness of fit (Thaseen & Kumar 2017). This paper will discuss how nonparametric tests are used and how the various types of Chi-square tests compare.

Non-parametric test does not use any assumption in the distribution of data. One must know the data and its distribution for you to use the nonparametric test (Ramdas et.al 2017). The structure of nonparametric models is determined by the data rather than being described. This model has been a feature in much of spreadsheet application software like Microsoft Excel (Ramdas et.al 2017). This application software is very helpful in performing statistics especially in large businesses that have very huge financial transactions.

Within the same population, the independence type finds intersection between two variables that are in the same category (Thaseen & Kumar 2017). This independence type of test compares two variables that are in the same set with another independence variable. This is contrary to the goodness of fit test. (Thaseen & Kumar 2017). When comparing a sample that has been chosen randomly with another sample in a certain category in a large population, this type of test is recommended (Thaseen & Kumar 2017). The most common application of this test is to perform comparisons between random chosen samples with the population from which these samples have been obtained.

In conclusion, Chi-square tests are very helpful in estimating the output or the performance in a business or organization. They are also used in statistics in real-life situations.

References

Thaseen, I. S., & Kumar, C. A. (2017). Intrusion detection model using the fusion of chi-square feature selection and multi-class SVM. Journal of King Saud University-Computer and Information Sciences, 29(4), 462-472.

Ramdas, A., Trillos, N. G., & Cuturi, M. (2017). On Wasserstein two-sample testing and related families of nonparametric tests. Entropy, 19(2), 47.