Chl-Square
The purpose of this discussion is to allow you to consider how various non-parametric tests are used and how they compare to other tests with similar variables. To do this, you will need to identify the appropriate application of course-specified statistical tests, examine assumptions and limitations of course-specified statistical tests, and communicate in writing critiques of statistical tests.
Describe the chi-square goodness-of-fit test.
Provide a detailed explanation of what this test measures, and how it is similar to and different from the independent t-test and the chi-square test of independence.
How do you know when to use one analysis over the other? Provide a real-world example.
Guided Response: Review your classmates' posts and respond to at least three of them. Compare the real-world examples identified by two of your classmates with the one you selected and respond substantively. Do you agree or disagree with their analyses of when to use one test over the other?
Describe the chi-square goodness-of-fit test.
The chi-square goodness-of-fit test is defined by the textbook as, "a test for significant differences in the frequency with which nominal data occur in distinct categories" (Tanner, D., n.p.). It is like the independent variable measured in a one-way ANOVA. This test does test one variable but unlike a lot of other tests, it can measure more than one category.
Provide a detailed explanation of what this test measures, and how it is similar to and different from the independent t-test and the chi-square test of independence
The textbook uses the example of a psychologist wanting to test drug addictions that manifest in different clerical work. The independent variable is the vocation, but this can manifest into many different clerical categories such as, laborers, the unemployed, teachers, etc. This allows for the person studying the case to be able to measure different categories while still having only one independent variable.
It is similar to both the independent t-test and chi-square test of independence because all three have testing the independent variable in common. The chi-square test of independence adopts back measuring the dependent variable, giving the test two different variables to measure similar to what can be found in independent t-tests. While the chi-square goodness-of-fit sticks to just one variable while having numerous categories that can be considered and measured.
How do you know when to use one analysis over the other? Provide a real-world example.
I believe that a good rule of thumb to use when deciding when to use an analysis over the other is to consider all the information provided. In this course, many of the real-world studies that I read utilized the t-test. I believe the t-test is used way more frequently than the other tests because it is easier to measure and get information that is not skewed and allows for more statistically significant findings.
Take the example from last week's assignment of chocolate consuming versus test scores, consuming chocolate being the independent variable and test scores being the dependent variable. In this example and any others similar to it, I believe using the t-test would be perfect. A real-world example of when to use the chi-square goodness-of-fit test could be when a new business wants to come into a town and wants to know how likely it is that the multiple different neighborhood sectors would shop at their store.
This would take into consideration multiple different sectors from that neighborhood, i.e. the people from the business district who work blue collar jobs, the people from the elderly people's home, the young adults who live near the college, etc. and they can use the multiple different categories to test the independent variable of shopping at the store. In other words, the study conducted would include grouping people into say five different categories of neighborhood sectors and measuring how often each person in that category shops at the store.
This could help an incoming business to know that if the people in the town are going to want to shop at their store or continue to keep going to the other neighborhood store out of loyalty, convenience, budget, etc. If most people in this town did not shop at this store, then it would give the business a pretty good idea to not put their store in that town. The example used for the Chi-Square Test of Independence used the categories of race and two different variables to measure how often people voted in comparison to their race.
References
Tanner, D. (2016). Statistics for the behavioral & social sciences, second edition.