Data Levels and Measurement

Overview.  On this page you'll learn about the four data levels of measurement (nominal, ordinal, interval, and ratio) and why they are important.  Let's deal with the importance part first.

Knowing the level of measurement is important for two reasons.  Each of the levels of measurement provides varying level of detail.  Nominal provides the least amount of detail, ordinal the next higher amount of detail, and interval and ratio the most amount of detail.

Nominal level variables just groups data into categories.  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.  Typically, the description of the variable is presented as frequencies and percentages.

Ordinal level variables are nominal level variables with an order.  For example, horse race winners can be assigned labels of first, second, third, fourth, and these labels has an ordered relationship among them.  As with nominal level variables, ordinal level variables are described with frequencies and percentages.

Interval and ratio level variables--continuous level variables--also called  have the most detail associated with them.  These variables have number associated with them and have the arithmetic properties.  For example, a variable can be the amount of milk used in cookies, ranging from 1 cup through 5 cups of milk, with increments of 1/4 cup each.   This variable has the properties of arithmetic such that 2 cups of milk has two as much milk as 1 cup of milk.  Continuous level variables are typically described by its mean and standard deviation.

The second reason levels of measurement are important to know is because different statistical tests only allow variables with particular levels of measurement.  There are different statistical tests to examine different research questions.  And those statistical tests have variables that only permit particular levels of measurement.  For example, chi-square tests only use nominal level data.  Mann-whitney U test uses ordinal level of data, while ANOVA tests use continuous level for the dependent variable and nominal for the independent variable.  To learn which tests use what types of variable, please download the free whitepaper.

Learn which Variables' Levels of Measurement Map onto Statistical Tests

level of meas

Nominal data levels of measurement

A nominal variable is one in which numbers only labels are used, even if we assign numbers to those labels.  For example, if we want to categorize male and female respondents, we could use a number of 1 for male, and 2 for female, but 1 and 2 in this case do not represent any order or distance.  They are simply used as labels.  We can use a nominal scale to show the categories of a variable as a numeric value.  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 scale variables.

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

Ordinal data levels of measurement

Ordinal scale variables have a meaningful order to them.  We can assign an order to the observation or respondent.  For example, we can assign rank 1, which is higher than rank 2, and 2 is higher than 3, etc.  Instead of rank 1, 2, 3, we can use any other number system that preserves the same order.  This is because we do not know for sure what the distance between 1 and 2 is, or what the distance between 2 and 3 is.

We can use the statistic's median, various percentiles (such as the quartile), and the rank correlation on ordinal data.  In addition to this statistic, we can use frequency tables and cross tabulations on ordinal data.  Arithmetic mean should not be calculated on the ordinal scale variables.

Interval scale data levels of measurement

An interval scale variable can be used to compute the commonly used statistical measures such as the average standard deviation and the Pearson correlation coefficient.  Many other advanced statistical tests and techniques also require interval scaled or ratio scaled data.

Most of the behavioral measurement scales are used to measure attitudes of respondents on a scale of 1 to 5, or 1 to 7, or 1 to 10.  Some researchers use these 1 to 5 scale as Likert scales.  A 5-point Likert scales are often labeled as 1 (=strongly disagree), 2 (=disagree), 3 (= neutral), 4 (=agree), and 5 (=strongly agree).   The difference between an interval scale and an ordinal scale variable is that the distance between ordinal data is the same, but in ordinal data the distance is not fixed.  That is to say, using the 5-point Likert scale as an interval scale assumes that the difference between strongly agree and agree is the same relative difference as between neutral and agree.

Ratio scale data levels of measurement

All arithmetic operations are possible on a ratio scaled variable.  These include computation of mean, standard deviations, and Pearson correlation.  Additionally, the statistical tests such as the t-test, F-test, correlation and regression can be used with ratio-level variables.  An example of ratio scale data would be the gross sales of a company, the expenditure of a company, the income of a company, etc.