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Recent questions in Contingency Table
High school probabilityAnswered question
Hallie Stanton Hallie Stanton 2022-11-04

I have two binary matrixes, of the same size (e.j. 5000x5000). Those matrixes represent the same area, divided in cells of the same size. Each cell of one matrix can be true or false, meaning some property is present or not in this cell. One matrix represents the presence of a property A, and the other one the property B.
Therefore, I can easily build a 2x2 contingency table using as variables the presence/absence of A and B:
A=1 A=0
B=1 a b
B=0 c d
a= number of cells where both A and B are present
b= number of cells where only B is present
I can apply a chi-square test on this table, building an "expected" contingency table, to assess the independency of both properties.
But I also need to assess if the number of cells that "overlap" (cells that are are true in both matrixes, i.e. where both A and B are present) is higher or lower than expected if both properties were independent. Of course I can compare real and expected value of a in the real and the expected contingency tables, but what I need is some thing like a probability or a measure of how much overlap is higher or lower than expected. In some way, it can also be seen as a measure of the "correlation" between both properties? I know if I had a smaller number of cells I could use Fisher's exact test, where obtained p-value will indicate the "direction" of the relationship between A and B. But as Fisher's exact test implies factorials, it is not possible.

High school probabilityAnswered question
Nigro6f Nigro6f 2022-10-18

Is responses in statistics the equivalent to random variables in probability?
The focus of this class is multivariate analysis of discrete data. The modern statistical inference has many approaches/models for discrete data. We will learn the basic principles of statistical methods and discuss issues relevant for the analysis of Poisson counts of some discrete distribution, cross-classified table of counts, (i.e., contingency tables), binary responses such as success/failure records, questionnaire items, judge's ratings, etc. Our goal is to build a sound foundation that will then allow you to more easily explore and learn many other relevant methods that are being used to analyze real life data. This will be done roughly at the introductory level of the first part of the required textbook by A. Agresti (2013), which covers a superset of A. Agresti (2007)
in which, is responses here (statistics) the equivalent to random variables in probability
another page in that site says
Discretely measured responses can be:
Nominal (unordered) variables, e.g., gender, ethnic background, religious or political affiliation
Ordinal (ordered) variables, e.g., grade levels, income levels, school grades
Discrete interval variables with only a few values, e.g., number of times married
Continuous variables grouped into small number of categories, e.g., income grouped into subsets, blood pressure levels (normal, high-normal etc)
We we learn and evaluate mostly parametric models for these responses.
are variables and responses interchangeable here?

Contingency tables are used to analyze data and help answer questions about the relationship between two or more variables. They are used to measure the association between variables, calculate probabilities, and draw conclusions. Contingency tables can be useful in solving problems involving equations and answering questions about probability. Plainmath provides tutorials and examples to help you learn how to use contingency tables and apply them to your own problems. With clear explanations, detailed equations, and helpful answers, you can become an expert in contingency tables.