When you need to analyze the differences between variables in statistics in the same population, you need to use the Chi Square test. Let’s say that you wanted to discover if the marital status and the education level were related in a specific country. You would need to gather a sample of the population and you would need to perform some kind of survey.
After you have the results of the surveys, you would then need to check the frequency distribution of the level of education and the marital status of the population sample.
So, When To Use Chi Square test?
After gathering all the data and checking for the frequency distribution of both variables, you could finally use a Chi Square test to validate the frequencies that you observed or to add any additional necessary contest to what you observed.
One of the things that you need to understand in what concerns to the chi square test is not only related to when to use chi square test but the kind of test that you need to perform.
The reality is that there are two different kinds of chi-square tests and you can use both when you are trying to check for the distribution:
#1: Chi Square Test For Independence:
With this chi square test, you will need to compare the two variables you are analyzing in a table – the contingency table, to see if they are related or not. Simply put, with this test, you will be able to discover if the distribution of the variables differ from each other or not.
When you end up with a small chi square result, you can conclude that the data you observed fits the expected data very well. So, you can also say that there is a relationship. On the other hand, when you end up with a very large chi square result, you can conclude that the data that you observed doesn’t fit what you were expecting. So, you can also say that there isn’t a relationship between the two variables.
#2: Chi Square Goodness Of Fit Test:
With this chi square test, you will be able to determine if a specific sample of data matches the population or not.
Now that you already know when to use chi square variable, you need to know that the formula used to calculate the chi square is:
where:
– the subscript c – are the degrees of freedom
– O – is the observed value
– E – is your expected value
While this is the formula that it is used to calculate the chi square test, the truth is that you will hardly apply it manually. After all, if you check the formula, you are using summations which means that these calculations would not only be very long as they would be very tedious as well.
Take a look at our Chi Square calculator.
When you finally get to a result of the chi square test of the variables that you are analyzing, you can compare it to a critical value from this chi square table. In the case the chi square value is higher than the critical value, then you can assume that there is a significant difference.
There are two specific occasions when to use chi square test:
#1: During Market Research:
When researchers need to determine if the data they observed is a representation of what they expected or if the two variables are independent. This is done by using the goodness of fit test mentioned above.
#2: During Surveys:
This is one of the best uses that you have for the chi square test. After all, it allows you to analyze cross tabulations of the data you got from the survey you conducted.
When you use cross tabulations, you will get access to both percentage and frequency of a specific answer. So, you will be able to determine the statistical importance of how different categories or segments have answered the same question.
