Chi-square and Associated Tests

What is a Chi-Square Test?

A Chi-Square is a statistical method used to test relationships between categorical variables. If you are using this type of test, your null hypothesis will be that there is no relationship in the categorical variables. For example, in this past election in the US, we could use the Chi-Square to test if there is a significant relationship between the intent of the vote and political party membership. A Chi-Square test is mostly used to check tests of independence when using a bivariate table (cross-tabulation). A bivariate table showcases the distributions of two categorical variables simultaneously. The intersections of the categories of the variables always appear on the cells of the table. When testing for independence, we are verifying whether a relationship exists between two variables. We can do this by comparing the pattern of responses observed in the cells to the patterns we expect to see if the variables are truly independent of each other.

Types of Chi-Square Tests

The two types of chi-square tests use the chi-square statistic and distribution for different purposes. These two tests are:

The chi-square goodness of fit test

This is a nonparametric test that strives to find out how the observed value of a given event differs significantly from the expected value. The term goodness of fit is used in this context to mean a comparison of the observed sample distribution and the expected probability distribution. The chi-square goodness of fit test help statisticians understands how well theoretical distribution fits the empirical distribution. To perform this test, divide the sample data into intervals then compare the number of points that fall into the interval with the number of points in each interval that you are expecting.

Chi-square test of independence

This type of test checks for a relationship between two variables that are in a contingency table. In simple terms, it tests whether distributions of categorical variables differ from one another. In a contingency table (two-way table) data is classified according to two categorical variables. One category appears in rows while the other in columns. You should note that the chi-square test of independence only works for categorical variables. You cannot use it to compare continuous variables or continuous and categorical variables. Also, this type of test cannot provide inferences about causation.

The Chi-square statistic

We use the formula below when performing a chi-square test.

Chi squared test

In the formula:

The subscript c denotes the degrees of freedom
O is the value that has been observed
E is the value that is expected
The summation symbol tells you to perform a calculation for every single data item in your set of data

Rarely, you will manually use this formula to compute a vital chi-square value by hand. This is because the calculations can be lengthy and tedious. Instead, competent researchers now opt for technology like the chi-square test in SPSS and chi-square p-value n Excel.

Chi-square P -Values

A p-value from a chi-square test tells the researcher if the results from the test are significant or not. Before you perform a chi-square test and get the p-value, you will need two vital pieces of information:

The degrees of freedom. This refers to the number of categories minus one
The alpha level. This level is chosen by the person carrying out the test. In most cases, the alpha level is 5%. However, there are also levels like 0.01 or 0.10.

These two pieces of information will be given to you in a question when you are studying AP statistics or elementary statistics. Do you need assistance with your Chi-square test task? Get in touch with us now.