Goodness-of-fit test is a chi-square test technique used to study similarities between proportions or frequencies between groupings (or classification) of categorical data.

Tests of Independence is a chi-square technique used to determine whether two characteristics (such as food spoilage and refrigeration temperature) are related or independent.

Test of Homogeneity is a chi-square technique used to study whether different populations are similar (or homogeneous or equal) in reference to some characteristic or attribute (such as "do students national identity affects the time spend doing homework?").

The observed frequencies, O is the proportions relative to the total from experimental studies or observations of group or class within the category of interest (a distributions similar to Figure 11.1). The observed frequencies are also called the observed cell frequencies.

The degree of freedom, df, is a parameter used to look up chi-square values from the chi-square distribution table. It is related to the sample size or number of classification of data within a category.

The expected value, E, is the theoritical or known frequency

A table where categorical data are combined to show the relative frequencies and  their rows and column totals is called a contingency table.
 
The contingency coefficient, C is a statistics that measures the strength of the relationship between variables or categories in a contengency table of the chi-square statistics when the test suggest that variables or categories are related.

Summary of chi-square tests analysis