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.
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.
Post 1
The chi-square goodness-of-fit test can be best explained as a way to test if a hypothesis is actually reasonable, as long as only 1 variable is involved. This weeks learning activity gave me first hand experience using these tables and figure out how they work. Let’s say you have a pack of 500 gummy bears and you want to find out how many our yellow,blue,green,orange, or red. You hypothesize since there are 500 gummies and 5 colors, there should be 100 of each kind. Actually however there are 80 yellow, 145 blue, 155 green, 120 orange, and 100 red. Through this test you can determine how close to accurate your hypothesis actually is. The formula used is (1*K).
With the chi-square goodness-of-fit test along with simple frequency distribution, we study how likely or frequently, direct variables will be showing up in our research. The difference between the two is that while the simple frequency will show us the frequent likelihood of something or an item occurring, with the chi-square we are using those direct numbers to determine the exact percentage of times they will occur. Also, with simple frequency this histograms are used more frequently.
This test can be explain as utilizing multiple variables that are associated with the end hypothesis you are trying to depict. Let’s say you want to see if there is a relationship. For example we could be looking at results that are looking at peoples level of happiness and productivity they feel in their lives to the amount of rest they get on a normal day. The formula for this chi-test is (R*K).
To determine which form of analysis to use, it always depends on what you researching, how many variables are being counted, and what your goal end result is.
Post 2
Hey Everyone!
The chi-square test overall is a way to measure whether multiple separate categorical results have any correlation or we are able to compare with one another. When looking at the chi-square goodness-of-fit test it measures one variable which will have multiple categorical options. A few examples of a such categorical variable could be age group or religion. Than comparing simple frequency distribution to this approach, it seems very similar as it also compares various points of categorical data, although it is often displayed as a histogram.
A chi-square test of independence measures multiple variables against each other which each will include various categorical options. The difference between the independence measure and the goodness-of-fit measure is that in the independence they measure more than one variable. One would know which analysis to use when accessing the study group. If there are various categorical groups which one is seeking to measure, than you would use the independence measure. If it is one single categorical group than it is the goodness-of-fit test.
A real life example of a sort of study is if a coffee shop is interested in accessing how much they should staff on certain days. So the store manager decides to count the amount of transactions which are processed on each day of the week. This opportunity would call for the chi-square goodness-of-fit test since it is measuring the amount of transactions per each day of the week. Being that the only variable that is being measured is the day of the week, I feel like this would call for the goodness-of-fit test.
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