Measurement Scales

Nominal Scales:  Like the name implies, these are really just names.  Hair color, gender, and marital status are examples of nominal variables.  There is no ordering among the categories (blonde hair is not more or less than brown, various industry classifications are not "more" or "less") and averaging is not appropriate for this type of data.   The measures used to describe this type of data are the percentages that fall into each category or the mode (the most commonly selected category). 

Nominal scales are for classification - they are not "measures" in the true sense of the term as they do not represent "quantities",  "magnitudes",  "frequencies", or the like.  They are simply classifications.  You use nominal scales when the categories are exhaustive (include all alternatives, even though one may be "other") and mutually exclusive (none fall into more than one category). 

You can summarize these data as the percentage of respondents who fall into each category or as the mode, which is the term used to describe the most common category selected.  The mode (most common category) can be used to express the "middle" of the distribution, however, the frequency distribution (percentages in each category) will generally suffice.  There is no measure of variability for this type of data.

Ordinal Scales:  These reflect ordered categories (e.g., small, medium, or large).  We can say one category reflects more of the attribute we are measuring than does another, or that the top category reflects more than those below it, but we cannot say how much more.  "Satisfaction", for example, can be rated from less to more highly satisfied, but we are not sure if the difference between being "Very Satisfied" and being "Satisfied" is really equivalent to the difference between being "Dissatisfied" and being "Very Dissatisfied."  This limits the math, and therefore, the statistics we can use with this type of data.   Averages, for example, are not really appropriate here.  As a result, the statistical tests for these type of data tend to use other approaches, such as looking at rankings across the categories in each group.

Most items on surveys have ordinal scale alternatives as selections that the respondents can choose from.  We generally use 5-point scales, that include negative (e.g., "Very Dissatisfied", "Dissatisfied"), neutral ("Neutral"), and positive alternatives ("Satisfied", "Very Satisfied").  Five-point scales are sufficient for showing change in most instances and we find these easier to express in writing in reports than we do some 7-point scales.

These data can also be summarized as the percentage of respondents who fall into each category.  The median can be used to indicate the center or mid-point of the distribution and the interquartile range can be used as an indication of variability in the data. 

Some users of statistics feel comfortable applying statistics for interval scales to these data if items are summed to produce a total score (e.g., a satisfaction or a loyalty index) or there are a wide range of ordered categories, but purists are uncomfortable with this approach.  There are, however, a variety of statistical procedures (referred to as non-parametric statistics) that can be used to test for the significance of differences between groups or subgroups or to assess the significance of changes that occur over time.

Interval Scales:   With interval scales we have ordered categories that are equidistant from each other.  If the categories are labeled A, B, and C, we can say A < B < C and (C-B) = (B-A).  If this is starting to look like algebra, then you can appreciate that we can use more complex mathematics in analyzing this type of data and indeed we are now able as a result to apply more powerful analytical procedures.  Unfortunately, questionnaires rarely generate true interval-level data.  Analyses of variance and t-tests are examples of the types of tests for group differences that are commonly used with interval scale data. 

For this type of data, we can compute mean (average) scores or medians and percentiles.  Typically, the median is preferred if the data are skewed (biased towards lower or higher scores) or the range can go to very high values (as in housing costs or income levels) as the median is less affected by skew and outliers than is the mean.  Measures of the variance, the standard deviation, or the median absolute deviation can be used to express variability in the responses.  Confidence intervals can be computed for sample means to express the range within which the population mean is likely to lie.

The statistics for testing for group differences or changes over time that are available for this type of data (e.g., the t-test, the Analysis of Variance or ANOVA, etc.) tend to be more powerful.  In large samples, there is the risk that even trivial differences will be statistically significant.  For this reason, some researchers advocate the use of confidence intervals.  When the confidence interval for the difference between two means does not span 0, then the findings will always be statistically significant. 

Ratio Scales:  These are interval scales with true zero points.  Sometimes it seems this only matters to physicists, who invented the Kelvin scale (which has an absolute 0) so that they could use forms of mathematics that are not possible with measures taken in Fahrenheit and Celsius, which are interval level measures.  For practical purposes in the behavioral sciences, we are would generally be happy if we could get true interval level measurement and it is unlikely we will ever measure attitudes, opinions, or intentions with anywhere near this level of precision.

Tip:  Always use the highest level of measurement that is available to you.  It is better to express age in years than it is to express it in categories (children, adolescents, young adults, etc.) as you have more power in analyzing the data.  Also, you can always break continuous data down into categories for reporting purposes, but you cannot turn categorical data into continuous data later if you change your mind.