Contingency Table

Contingency Table


Institution Affiliation


Simple Understanding of Contingency Table

These types of tables are used in statistic to analyze and summarize categorical variables. Contingency Tables have a unique characteristic of displaying two types of variables at the same time through frequency distribution tables. Contingency tables generate an intensive summary of expected frequency, especially in the Excel analysis. For example, the statistical data summary may be made through 2*2 or pivot tables (Cox, 2018). The table format for the statistical brief can equally be generated in the form of matric system, especially for multivariate data sequences.

Use of Contingency Tables

Contingency Table is used as statistical tools to sense data where there is one than more variable. These types of tables are also known as cross tab or cross-tabulations to generate form, grid, and matrix. For example, a research study of the correlation between male and female who own pets such as a cat or dog (Hosner, 2016). Contingency Tables will provide a good summary for data collected with the total in respective column and row.

  Cat Dog Total
Male 41 11 52
Female 10 38 48
Total 51 49 100

These tables are used in the different statistical test such as Barnard’s test, Fisher’s exact test, T-test, and Pearson’s chi-square test.

Different Types of Data Displayed in the Contingency Tables

Categorical data are displayed in these types of the table as groups or tables variables. One or two table variables are sued in the broad procedure of defining column and row variables. The cross tabs section can either use data types for non-summarized and summarized information. The column database usually uses categorical or numerical data types based on the proportion of statistics (Hosner, 2016). The database system for Contingency Tables has frequency and grouping variables.

How Contingency Tables Tests Relationship Significant among Data

The Contingency data usually use Chi-square tests to present effects of data types. Categorical data types are represented in column and row relationships. The chi-squared analysis provides a significant level of variable distributed differently. The hypothesis test for the data create some cell for frequencies warrant, which is interpreted between cells. Two variables are represented at the same time in the frequency distribution table (Cox, 2018). These frequencies are the sum for different rows to fit in margin frequencies. The number of frequencies cells must be equal to N or number of variables. Chi-square hypothesis generates a good summary and interpretation for categorical data.

Difference between FET and Chi-square test in Contingency Tables

The FET is used in Contingency Tables in the marginal frequencies conditions of comparing two proportions. The type 1 error is guaranteed in this test which can be less than p-values. The Chi-square test is more actual to generate expected cell frequencies. Another difference is that FET has an association for two variables while the Chi-squared test is applied when there are large expectations for cell sizes (Hosner, 2016). Equally, the use of FET in Contingency Tables is pretty fast compared to Chi-square tables, notably for approximation calculations. The expected cell count dictates the differences between FET and Chi-square based on the display of Contingency Tables.

Cases Where we use Chi-square Test instead of FET

Chi-square is used in the case where data to be tested one-sided. This test assumes a particular margin for bigger tables. The data test for Chi-square is used primarily where variables of interests have categorical relationships. Chi-square is selected in the statistical analysis when categorical variables are independent (Richardson, 2011). For example, when Contingency Tables have to answer a question on normality, chi-square test will be used since it provides many tests for asymptotic distributions. FET is not preferred in the statistical analyses when there is a significant relationship between two variables.

Interpretation of Chi-square Test and FET

Chi-square test is interpreted by determining values of degree of freedoms, then comparing results using multiple categories single sample. In the Chi-square distribution, the degree of freedom is taken as the total number of groups and then subtracts one. The data will be evaluated by p-value, especially when evaluating critical value (Cox, 2018). The probability is another way of observation deviation for random variables Chi-square.

The FET data can be interpreted through a descriptive statistic for different categorical variables. In the Contingency Tables, more than one variable is dragged into columns and rows based on sample size (Richardson, 2011). After selecting the FET statistical analysis, exact options for the data is set with a limit. Results for this test will be generated with a consideration of significant level and p-values. At this point, Contingency Tables will display outcomes which will create a reasonable ground for interpreting hypotheses.


Cox, D. R. (2018). Analysis of binary data. Routledge.

Hosner, B., (2016). /books /9781305465510/ pageid/233

Richardson, J. T. (2011). The analysis of 2× 2 contingency tables—Yet again. Statistics in medicine30(8), 890-890.