Contingency Tables

Contingency tables are used for detailed description of quantitative data and comparison of differences between various respondent groups. They help analyze the relationship between two categorical variables.

About

Contingency Tables, also known as cross-tabulation, are statistical tools used to analyze the relationship between two or more categorical variables. By organizing data into a matrix format, they allow for the visualization and analysis of patterns and dependencies. Contingency Tables are widely used in research, marketing, and data analysis to test hypotheses, identify correlations, and guide decision-making. They offer a concise way to represent complex data and are valuable in deriving actionable insights.

Suitable for

  • more detailed description of quantitative data,
  • comparison of differences between various groups of respondents,
  • researchers who are not afraid of Excel and simple calculations.

Deliverables

Contingency Table Matrix

A table displaying the frequency distribution of variables, showcasing the relationship between two categorical variables in rows and columns.


Interpretation Report

A comprehensive report outlining key findings, the significance of the relationship between the variables, and insights that can inform design decisions.


Data Visualization

Graphical representations of the contingency table, such as bar charts or mosaic plots, to enhance understanding and communication of results.


Data Collection Summary

Documentation of data sources, methods of collection, and any demographic or contextual details that could influence the interpretation of the data.


Statistical Analysis Report

A report on the statistical tests used to determine the dependency between the variables, such as Chi-Square test or Fisher's Exact test, including test statistics and p-values.


Recommendations List

A prioritized list of actionable recommendations based on insights gained from the contingency table analysis, which can be used by the design and development team to improve the user experience.


Feedback Loop Plan

A description of how the findings will be shared with stakeholders and integrated into the overall UX design and development process, as well as the methodology for measuring any changes made as a result of the findings.

Procedure

1

Identify Variables

Determine the two categorical variables you want to examine for a possible relationship. These variables should have two or more categories, ideally having a logical connection that can impact each other.

2

Create a Hypothesis

Formulate a null hypothesis stating that there is no relationship between the two variables, and an alternative hypothesis stating that there is a relationship between the two variables.

3

Collect Data

Gather data regarding the two selected variables from the relevant participants, ensuring to have a representative sample of the population.

4

Prepare Contingency Table

Create a table with rows representing one categorical variable and columns representing the other categorical variable. Assign cell values based on the number of instances where the categories from each variable intersect.

5

Calculate Row and Column Totals

Add up the cell values for each row and column and place these sums at the end of each row and column within the table.

6

Calculate Expected Frequencies

For each cell in the contingency table, calculate the expected frequency by multiplying the row total and column total corresponding to that cell, and then divide it by the overall total. Place the calculated values in the contingency table, adjacent to the corresponding observed values.

7

Compute the Test Statistic

Calculate the chi-square (X²) test statistic using the formula: X² = Σ((observed frequency - expected frequency)² / expected frequency), where 'Σ' denotes the sum of all the calculated values for each cell in the table.

8

Determine the Degrees of Freedom

Calculate the degrees of freedom using the formula: df = (number of rows - 1) x (number of columns - 1).

9

Find the Critical Value

Consult a chi-square distribution table to locate the critical value that corresponds to your chosen level of significance (e.g., 0.05) and the calculated degrees of freedom.

10

Interpret the Results

Compare the calculated chi-square statistic to the critical value. If the statistic is greater than or equal to the critical value, you can reject the null hypothesis, meaning there is a significant relationship between the two variables. If the statistic is less than the critical value, you cannot reject the null hypothesis, meaning there is no significant relationship between the two variables.

Prerequisites

Time

60 minutes or more


Materials

collected data, Excel or another tool for working with data


People

1 researcher

Resources

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