# Chi-Square tests are nonparametric tests. Discuss the following: What are the differences between parametric tests and nonparametric tests? What are the requirements for Chi-Square tests? What are the limitations of Chi-Square tests?

Question
Chi-square tests
Chi-Square tests are nonparametric tests. Discuss the following:
What are the differences between parametric tests and nonparametric tests?
What are the requirements for Chi-Square tests?
What are the limitations of Chi-Square tests?

2021-01-20
Chi-square tests are non parametric tests
Difference between parametric and nonparametric tests:
Parametric tests 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. Nonparametric tests don’t require that your data follow the normal distribution. They’re known as distribution-free tests and, as such, can be used for non-Normal variables.
Requirements for Chi-Square tests:
The sampling method should be simple random sampling. The variable under study should be categorical. The expected value of the number of sample observations in each level of the variable should be at least 5.
Limitations of Chi-Square tests:
All participants measured must be independent, means that an individual cannot fit in more than one category. The data must be frequency data The expected value of the number of sample observations in each level of the variable should be at least 5. Chi-square not be used if the sample size is less than 50

### Relevant Questions

Explain what changes would be required so that you could analyze the hypothesis using a chi-square test. For instance, rather than looking at test scores as a range from 0 to 100, you could change the variable to low, medium, or high. What advantages and disadvantages do you see in using this approach? Which is the better option for this hypothesis, the parametric approach or nonparametric approach?
Chi-square tests are nonparametric tests that examine nominal categories as opposed to numerical values. Consider a situation in which you may want to transform numerical scores into categories. Provide a specific example of a situation in which categories are more informative than the actual values.
Find the type and the number of variables for which the Chi-square goodness-of-fir tests are used.
Distinguish the difference (purpose) between the two different types of chi-square
1.Chi-square test for independence (CTI)
2.Chi-square test for goodness of fit (CGF)
3.What type of variables are we using for a chi-square?
Chi-square tests are best used for which type of dependent variable?
nominal, ordinal
ordinal interval
nominal, interval
nominal, ratio
For each of the following situations, state whether you’d use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test:
a) Is the quality of a car affected by what day it was built? A car manufacturer examines a random sample of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week.
b) A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients, testing whether the cholesterol level (in milligrams) is related to whether or not a person has heart disease.
c) A student wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly chosen students and performs a test.
You want to know whether people in different regions of the country are equally likely to vote Sarah Duterte, Peter Cayetano, Mar Roxas, or any candidate other than the three in the next election. You would use
A. chi-square test of independence.
B. either chi-square test (goodness-of-fit or test of independence), depending on how you set up the problem.
C. chi-square goodness-of-fit test.
D. both chi-square tests, in order to check the results of one with the other.
A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the $$\displaystyle{x}^{{2}}$$-statistic?