The modern world is characterized by the availability of big amounts of data from various sources and the need to process them. It means that structuring data, categorizing, and processing acquire the top priority. That is why statistics, methods of statistical analysis, and tools helping to perform it are critical. Thus, using contingency tables, it is possible to work with different variables, compare and analyze them, and acquire necessary results. They also simplify the understanding of relations between particular phenomena and outline regularities necessary for their understanding.
At the moment, there are numerous definitions of a contingency table. One of the most generalized and understandable ones views it as a table representing the distribution of one variable in rows and another in columns, which helps to understand the association and correlation between two of these aspects (Everitt, 2019). In other words, it is a mechanism employed in statistics to introduce categorical data regarding frequency counts (Everitt, 2019). It simplifies future operations with numbers and promotes a better understanding of how they might interact.
In such a way, from the definition, one can understand how continency tables can be used. This sort of matrix shows frequencies for specific combinations of values. Thus, each cell shows the combination of the variable from a row and a column. It is also used to understand whether the distribution of one variable depends on another. For this reason, this tool can be used in surveys as part of sociological research, in business, engineering, and other spheres where statistical analysis is required.
Furthermore, a contingency table represents a specific type of information. It offers a tabular representation of categorical data or information that can be divided into specific groups (Lydersen et al.,2020). These might include age, gender, sex, educational level, income, or social status. Thus, a contingency table shows the combinations of the variables and how various aspects of categorical data interact (Lydersen et al.,2020). It is essential for statistical analysis and better information processing.
Another important aspect of contingency tables is that they help test for relations’ significance. For instance, they classify outcomes of variables presented in rows and others that can be found in columns. Thus, the discovered intersections indicate frequencies for every unique combination presented in the table (Spiegelhalter, 2021). Analyzing these numbers, it is possible to test the significance of relations between categorical data. It is essential for better investigation and accurate outcomes.
Contingency tables can also use chi-sure and FET statistics. The first one is a test measuring how the model compares to data observed in real conditions, assuming the sample is large (Lydersen et al.,2020). Thus, the second one is the test used to determine whether there is an association between two categorical variables, assuming the sample is small (Lydersen et al.,2020). Usually, they are seen as alternatives and can be used in various situations. For instance, a chi-square can be employed when two categorical variables are compared and analyzed to determine whether they are interrelated (Spiegelhalter, 2021). FET can be used in a similar situation when two nominal variables exist, and it is necessary to determine whether the proportions of one alter regarding the value of another (Spiegelhalter, 2021). Thus, speaking about chi-square results, the null hypothesis can be rejected if the value is bigger compared to the critical value (Lydersen et al., 2020). As for FET’s results, they can also be used to prove or refute the null hypothesis by interpreting acquired data and whether it meets expectations (Everitt, 2019). In such a way, contingency tables are a potent tool to work with categorical data and analyze it.
References
Everitt, B. (2019). The analysis of contingency tables (2nd ed.). Chapman and Hall.
Lydersen, S., Laake, P., & Fagerland, M. (2020). Statistical analysis of contingency tables. Routledge.
Spiegelhalter, D. (2021). The art of statistics: How to learn from data. Basic Books.