Question

Statisticians and other professionals are interested to account for the ways variables are related. This is also true when someone moves from nominal to interval data. Document possibilities/techniques/methodologies to account for viable relationships between/among nominal and interval data.

Answer 1

Chi-square tests of independence are most appropriate for nominal level data  

The Mann-Whitney U test is most appropriate for an ordinal level dependent variable and a nominal level independent variable.

An ANOVA is most appropriate for a continuous level dependent variable and a nominal level independent variable.

An interval variable can be used to compute commonly used statistical measures such as the average (mean), standard deviation, and the Pearson correlation coefficient.

Many other advanced statistical tests and techniques also require interval or ratio data.

In a nominal level variable, values are grouped into categories that have no meaningful order.

Nominal data cannot be used to perform many statistical computations, such as mean and standard deviation, because such statistics do not have any meaning when used with nominal variables.

However, nominal variables can be used to do cross tabulations. The chi-square test can be performed on a cross-tabulation of nominal data.

For example, gender and political affiliation are nominal level variables.

Members in the group are assigned a label in that group and there is no hierarchy.

Typical descriptive statistics associated with nominal data are frequencies and percentages.

Interval and ratio level variables (also called continuous level variables) have the most detail associated with them

Mathematical operations such as addition, subtraction, multiplication, and division can be accurately applied to the values of these variables.

An example variable would be the amount of milk used in cookie recipe (measured in cups).

This variable has arithmetic properties such that 2 cups of milk is exactly twice as much as 1 cup of milk. Additionally, the difference between 1 and 2 cups of milk is exactly the same as the difference between 2 and 3 cups of milk.

Interval and ratio level variables are typically described using means and standard deviations.