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Cross tabulation also known as cross-tab or contingency table is a statistical tool that is used for categorical data. Categorical data involves values that are mutually exclusive to each other. Data is always collected in numbers, but numbers have no value unless they mean something. 4,7,9 are simply numerical unless until specified. For example, 4 apples, 7 bananas, and 9 kiwis.
Cross tabulation is usually used to examine the relationship within the data that is not evident. It is quite useful in market research studies and in surveys. A cross table report shows the connection between two or more question asked in the survey.
While deploying a survey if the survey creator decides to send the survey to two different groups of people, cross tabulation helps to compare side by side, the responses of the two groups.
Cross-tab is a popular choice for statistical data analysis. Since it is a reporting/ analyzing tool it can used with any level of data: ordinal or nominal, because it treats all data as nominal data (nominal data is not measured it is categorised).
Let’s say you can analyze the relation between two categorical variable like age and purchase of electronic gadgets.
There are two questions asked here:
In this example you can see the distinctive connection between the age and the purchase of the electronic gadget. It is not surprising but certainly interesting to see the correlation between the two variables through the data collected.
In survey research crosstab allows to deep dive and analyze the prospective data, making it simpler to spot trends and opportunities without getting overwhelmed with all the data gathered from the responses.
Chi square or Pearson's chi- square test, is any statistical hypothesis, which is used to determine whether there is a significant difference between expected frequencies and the observed frequencies in one or more category.
Another significant term that we will introduce here is “Null hypothesis”. The null hypothesis, basically assumes, any kind of difference or importance one can see in a set of data is by chance. The opposite of the null hypothesis is called the “alternative hypothesis”.
Applying chi square to surveys is usually done with these question types:
For example, we need to find out if there is any association between the buyer behavior of purchasing electronic devices and the region where it is sold then the data will be entered like the one in the table below:
As mentioned earlier the Chi square test helps you determine if two discrete variables are associated. If there's an association, the distribution of one variable will differ depending on the value of the second variable. But if the two variables are independent, the distribution of the first variable will be similar for all values of the second variable.
Using cross tabulation and chi square we derive the following inference:
Applying the Chi square calculation to the above values:
Pearson's chi square= 0.803, P- Value= 0.05
So what does this mean?
We need to pay attention to the p- value. Compare the p-value to your alpha-level which is commonly 0.05
In this example Pearson chi-square statistics is 0.803 (with a p-value 0.05). So with an alpha-value of 0.05, we therefore, conclude that there is no correlation and is insignificant.