Question

Explain the relationship between types or levels of data and types of statistical analyses available to such levels of data. Feel free to illustrate with examples

Answer 1

Knowing the level of measurement of your variables is important for two reasons. Each of the levels of measurement provides a different level of detail.

The second reason levels of measurement are important to know is because different statistical tests are appropriate for variables with different levels of measurement.  

1) Nominal data levels of measurement

A nominal variable is one in which values serve only as labels, even if those values are numbers.

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.

2) Ordinal data levels of measurement

Values of ordinal variables have a meaningful order to them. For example, education level (with possible values of the high school, undergraduate degree, and graduate degree) would be an ordinal variable.

We can use frequencies, percentages, and certain non-parametric statistics with ordinal data. However, means, standard deviations, and parametric statistical tests are generally not appropriate to use with ordinal data.

3) Interval scale data levels of measurement

For interval variables, we can make arithmetic assumptions about the degree of difference between values. An example of an interval variable would be temperature.

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.

4) Ratio scale data levels of measurement

All arithmetic operations are possible on a ratio variable. An example of a ratio variable would be weight (e.g., in pounds).  A ratio variable can be used as a dependent variable for most parametric statistical tests such as t-tests, F-tests, correlation, and regression.