Also known as Cross Tab or Contingency table, Cross Tabulation is a statistical tool used for categorical data. Categorical data involves values that are mutually exclusive from each other. Data is always collected in numbers, but numbers have no value unless they mean something. For instance, 1, 2, and 3 are just numbers unless specified. See, 1 schoolbag, 2 umbrellas, and 3 notebooks.
Cross Tabulation is a mainframe statistical model that follows similar lines to help you make an informed decision relating to your research by identifying patterns, trends, and a correlation between parameters. When conducting a study, the raw data can usually be overwhelming and will always point to several confused possible outcomes. In such situations, Cross Tab helps you in arriving at a single theory beyond doubt by drawing trends, comparisons, and correlations between factors that are mutually inclusive within your study.
For examining the relationship or correlation within the data that is not obvious, Cross Tabulation can be used. This makes it quite useful in market research surveys and studies. A Cross Tab report shows the connection between two or more questions asked in the survey.
Understanding Cross Tabulation with Example
As mentioned, Cross Tab is the most preferred choice for statistical data analysis. Since it is a reporting / analyzing tool, you can use it with any level of data (ordinal or nominal).
Let’s say you can study the relation between two categorical variables like ‘Age and Purchase of Electronic Gadgets.’
There are two questions asked here:
- What is your age?
- What is the electronic gadget that you are likely to buy in the next 3 months?
From the above example, you can see the distinctive connection between age and the purchase of electronic gadgets. Certainly, it is interesting to see the correlation between the two variables through the data collected. Within Survey Research, Cross Tab allows for going deep and analyzing the probable data, making it simpler to identify trends and opportunities without getting inundated with all the data gathered from the responses.
Benefits of Cross Tabulation Survey Analysis
Having understood the purpose of Cross Tabulation, we will now analyze the three core benefits of this analytical approach:
Cut Down Confusions
At all times, a large volume of data collection can be confusing as well as devastating; thus, insights from them to bring up to date business decisions can be a terrifying task over and over again. By creating Cross Tab, data sets are further simplified by merely dividing the complete set into representative subgroups. This can subsequently be interpreted at a smaller, more manageable scale. Moreover, it trims down the possibility of making mistakes when evaluating the data, which means that the time is spent efficiently.
Innumerable Data Insights
Cross Tab helps to reduce the data sets into more manageable subgroups; Cross Tab allows researchers to give profound insights. It would be impossible to achieve insights into the relationships between categorical variables by only digging into the set as a whole. And this means that if tabs were not created, these insights would go unnoticed. Otherwise, at the very least, they would need much more groundwork to expose.
All Results Actionable
There is no uncertainty that the whole intention of performing statistical analysis on a data set is to uncover actionable understandings that will impact your end goal. These insights can impact the business by backing up thought processes and decision-making with hard data.
Because Cross Tabulation simplifies complex data sets, the particular impactful results are much easier to consider, expose, and record while developing overarching strategies. Additionally, the transparency presented by Cross Tab facilitates professionals to evaluate their current work and chart out future plans. No doubt, the advantages of using Cross Tabulations in Survey Analysis and all of these features make it possible as well as practical for even a new hand researcher:
- Able to put variables either in rows or columns
- Interpretations are accessible
- Little or no understanding of concepts necessary for analysis
- Readers can easily observe patterns of association and also distinguish if the pattern is weaker across some rows
In spite of covering all these plus points, a few disadvantages of using Cross Tabs are established as follows:
- Lead to a vast number of tables when there are multiple responses due to the different ways the variables can be cross-tabulated with each other
- Not all of the Cross Tabs may be significant, although it may not be apparent which ones are meaningful or not until one has done the cross-tabulations
- The number of items that can be cross-tabulated with each other can be limited if the sample size is small
Who can get the most out of the Cross Tabulation of Survey Data?
Although Cross Tabulation is used across various industries and job functions, definite personas profit the most from the insights provided by this analysis:
HR Managers / Executives
Administering surveys to employees to understand their feelings about a company is always a good idea for individuals responsible for the well-being of an organization’s culture. These surveys present valuable understandings, especially when Cross Tabs from the resulting response data are analyzed. Also, by using the same, HR Managers, Executives, and others responsible for corporate culture can learn how individuals and different departments feel about their managerial customs. Problem areas in specific divisions or job roles can be identified by conducting employee engagement, employee satisfaction, and exit interview surveys.
Market / Product Researchers
Cross Tabulation allows market researchers to portray precise, impactful insights from immense data sets. By creating Cross Tabs, market researchers can identify as well as evaluate the behaviors, feelings, and perspectives of specific subgroups of the population at large. Moreover, Market researchers can influence this analysis to answer questions like, “What is the variation between ‘boys’ and ‘girls’ planning to purchase a particular product?”
Employers in charge of Customer Satisfaction
The customer Satisfaction Survey is an essential instrument for receiving feedback about the goods and services provided by an organization. Managers responsible for customer satisfaction can evaluate things like the varying levels of happiness between new and long-term customers. And also, the likelihood that these customers would recommend the product or service to their friends or family by forming Cross Tabulations from the resulting response data.
School / College Administrators
Usually, when distributing course and instructor evaluation surveys to students, administrators will often cross-tabulate results with – class subjects, the time of the class, and other metadata. This helps to discover limitations in the curriculum to improve the education experience for students.
When to use Cross Tabulation for Analyzing Data?
Cross Tabulation for analyzing data is very significant, but only if done in the correct manner and at the right time. Fundamentally, it measures how different variables are related to each other. Each variable has data recorded in a specific table or matrix, and this is then compared. Usually, Cross Tabs for analyzing data involve counting how often certain variables occur, which is known as the frequency.
Another factor to be considered here is that Cross Tabulation for evaluating information only works with quantitative data. It makes it far easier to manage the data since it becomes structured. The tables in which the data is stored are known as Contingency Tables. This measures how likely it is for a specific relationship to exist. Generally, a single variable is first studied. And this will prove whether there is any Univariation in existence, grouping different pieces of data into ranks of values.
Once this has been completed, it becomes possible to perform Cross Tabs for analyzing data across multiple variables, known as Bivariation or a Joint Contingency Table.
Here, data is used to prove that a particular relationship is a two-way street – ‘only if,’ ‘only and,’ ‘if and,’ ‘when and,’ so on. Before you start with Cross Tabulation for analyzing data, you must understand what quantitative variables actually are. There are discrete variables, which have a value of a set number. Also, there are continuous variables, which can choose only a set amount of benefits. Mostly, these two are not used together, and continuous variables are the most common types.
No doubt, Cross Tabs is an enormously complex area of work. Although it is possible to do these statistics manually using tools in Excel, the majority would use specially designed software. More often than not, this software is provided by a survey designer. Furthermore, this allows customers to understand the data that they have collected through their questionnaires, better.
The Statistics Associated
- Chi-squared – Analyze the statistical significance of the Cross Tabulations. Chi-squared should not be calculated for percentages. The Cross Tabs must be transformed back to absolute counts (numbers) before calculating chi-squared. Further, it is problematic when any cell has a joint frequency of less than five.
- Contingency Coefficient – A variant of the Phi Coefficient that adjusts for statistical significance. Values range from 0 (no association) to 1 (the theoretical maximum possible association).
- Cramer’s V – Another variant of the Phi Coefficient that regulates the number of rows and columns. This also estimates range from 0 (no association) to 1 (the theoretical maximum possible association).
- Lambda Coefficient – Evaluates the strength of association of the Cross Tabulations when the variables are measured at the nominal level. Here, values range from 0 (no association) to 1 (the theoretical maximum possible association).
Asymmetric Lambda measures the percentage of improvement in predicting the dependent variable.
Symmetric Lambda measures the percentage improvement when the prediction is made in both directions.
- Tau b – Investigates the potency of the relationship of the Cross Tabulations when both variables are measured at the ordinal level. Formulate adjustments for ties and is most suitable for square tables. In this, values range from -1 (no association) to +1 (the theoretical maximum possible association).
- Tau c – When both variables are measured at the ordinal level, the connection of the Cross Tabulations is examined. Points range from -1 (no association) to +1 (the theoretical maximum possible association). It makes adjustments for ties and is most suitable for rectangular tables.
- Gamma – Tests the strength of association of the cross-tabulations when both variables are measured at the ordinal level. Utilities range from -1 (no association) to +1 (the theoretical maximum possible association). Also, this mode does not make any adjustments to either table size or ties.
Cross Tabulation and Chi-Square
Chi-Square or Pearson’s Chi-Square test is a statistical hypothesis that is used to determine whether there is any significant difference between the expected frequencies and the observed frequencies in one or more categories. An important consideration when cross-tabulating the findings of your study is the verification carried out to find out whether what is represented in the Cross Tab is true or false.
To resolve this dilemma, Cross Tabulation is computed along with the Chi-Square analysis, which helps identify if the factors involved in the study are independent or related to each other. If the two factors are independent, then the tabulation is termed insignificant, and the study would be termed a Null Hypothesis which means that since the elements are not related to each other, the outcome of the study is unreliable. On the contrary, if there exists a relation between the two factors that would confirm that the tabulation results are significant and can be relied on to make strategic decisions.
Applying Chi-Square to surveys is usually done with these question types:-
– Dates and number (when associated together)
– Product name
Cross Tabulating and Filtering Results
A good example is illustrated below:
You wish to see how Managers, Executives, and Interns compare to one another in answering the question about attending next year’s seminar. To find this out, you have to look into response rates utilizing Cross Tabulation. Here the result of the survey is shown by subgroup.
From the above table, you can make out that a large majority of the Managers (80%) and Executives (86%) plan to attend the tutorial next year. However, the Interns who plan to attend the seminar look different, with only under half (46%) of them intending to come.
With anticipation, some of the other questions will assist you to figure out why this is the case. Also, actions can be taken on what you can do to improve the seminar for Interns so more of them will arrive year after year.
Using a filter is an added useful tool for modeling data. The meaning of Filtering is actually the narrowing of your focus to one particular subgroup, and sorting out the others. Hence instead of comparing subgroups to one another, here we just look at how one subgroup answers the question.
To give an example, you could limit your focus to merely women, or only men, then re-run the Cross Tab by type of attendee to compare male managers, male executives, and male interns. There is one thing you have to be cautious of as you slice and dice your results. Each occasion you apply a filter or Cross Tab, your sample size decreases. For ensuring your results are statistically significant, it may be helpful to use a sample size calculator.
Many studies put forward that Cross Tabulation is one of the most preferred methods of analyzing market research or survey data. In fact, Qualtrics estimates that Cross-Tabulation Analysis and Single Variable Frequency Analysis together account for more than 90% of all research analyses. Therefore you can undoubtedly go ahead and use Cross Tabulation in your Survey Analysis. Unquestionably it is very useful for uncovering hidden relationships in your raw data.