There are two types of categorical data, which are nominal and ordinal. Nominal data do not have any innate priority over the other. These categories do not have any hierarchical importance. Example, castes like Hindu, Sikh, Jain, Muslim, etc. Any one of these categories does not have any priority over another category. Skin color is another example of nominal data. Other examples of categorical data are gender, marital status, eye color, hair color, color of t-shirt worn, birth city, etc. The other type of categorical data is ordinal data. These types of data have a hierarchical importance. One class is superior or inferior to the other. Examples of ordinal data are marks of students, economic status, temperature (low, medium, high) etc.
Relationship between two categorical variables
The two variables are analyzed usually using probabilities or frequencies. If there is any association or relation between the two variables, then they both will be dependent of each other. Also, their probability will be dependent on each other. A popular test known as chi-square is used to test the hypothesis that there is an association between the two categorical variables. A contingency table is used for a binary or dichotomous variable.
Example: For a data where analysis is to be done and data about two categories say gender (male and female) and credit card are given. Suppose this is to check how many males and females have credit cards. Data is given as:
Where Y indicates yes and N indicates No, the person does not have a credit card.
For such a data, a contingency table is made. This table helps in better understanding of the data in a systematic manner. Contingency table for the same is given below:
From this table it can be inferred that there are 150 males and 80 females who have credit cards. There are 120 males and 100 females who do not have credit cards. Using this contingency table, chi-square test is used, and statistical hypothesis is tested.
This is a graphical representation of the data.
Relationship between categorical variable and a continuous variable
A continuous variable is the one that can take any value in the number line. This type of variable contains any value that can be measured on a scale. Examples of continuous variables are measurement of height, age, weight, etc.
One of the ways to evaluate such problems is using logistic regression or the Kruskal-Wallis H test. Few parametric tests can also be used like ANOVA or t-test. Correlation between the two variables is needed to form.
Which test to use when?
If the independent variable is categorical and the dependent variable is continuous, then ANOVA is used. If the independent variable is continuous and the depend
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