Is Data Tangible or Intangible?

Did you know that electronic information is tangible? From the apps you use, the games on your phone, right down to every message you send – all of it appears to invisibly float away and live somewhere far off in the ethers, but actually, most of it will land with a thump in our earthly domain.

Because of our impression that information is invisible, we can end up taking the resources it requires for granted. Data centers or server farms dot the globe, and actually come with considerably large carbon footprints, because of not only the power the require to run them, but also to keep them cool. In the United States Continue reading

Mind Your Measurement Scales in Market Research

Welcome to the Making Molehills out of Mountains University (MMoM U) Market Research Data Analysis 101 or MARDA 1 as we like to call it in the halls of academia.  Today we discuss the four different types of scales used in measuring behavior.  Open your books and let’s get started…

The four scales, in order of ascending power are:

  • Nominal
  • Ordinal
  • Interval and
  • Ratio

Nominal Scale

Nominal is derived from the Latin nominalis meaning “pertaining to names”.  But, seriously, who cares? That tells us nothing except how much academics love showing off.  The Nominal Scale is the lowest measurement and is used to categorize data without order.  For your market research data analysis exercise a typical nominal scale is derived from simple Yes/No questions.

How the nominal scale (and all these scales) is used statistically is for the next lecture.  For now, just know the behavior measured has no order and no distance between data points. It is simply “You like? Yes or no?”

Ordinal Scale

From the Latin ordinalis, meaning “showing order”… Enough of that.  An Ordinal Scale is simply a ranking.  Rate your preference from 1 to 5.  Careful!  There’s no distance measurement between each point.  A person may like sample A a lot, sample B a little, and C not at all and you would never know.  Here we have gross order only, learning that the subject likes A best, then B, then C.  Determining relative positional preference is a matter for the next scale.


Ah, the Interval Scale.  It’s the standard scale in market research data analysis.  Here is the 7 point scale from Dissatisfied to Satisfied, from Would Never Shop Again to Would Always Shop,  etc.  The key element in an Interval Scale is the assumption that data points are equidistant.  I realize savvy market analysts might say, “Hold on Professor. What about logarithmic metrics where the points are not equidistant?” To which I say, “Correct! but the distances are strictly defined depending on the metric used, so don’t get ahead of yourself. This is MARDA 101.”

For now, understand that with the Interval Scale, we can interpret the difference between orders of preference.  Now we can glean that Subject 1 Loves A, Somewhat Likes B and Sorta Kinda Doesn’t Like C.

Subject 2 Somewhat Likes A , Sorta Kinda Doesn’t Like B and Hates C.  Both subjects ranked the samples A, B, & C on an Ordinal Scale but for very different reasons as discovered by using the Interval Scale. Got it?  Good.

Moving on.


Similar to the Interval Scale it’s not often used in social research.  Like Interval, it has equal units but it’s defining characteristic is the true zero point.  Ratio, at its simplest, is a measurement of length. Even though you cannot measure 0 length; a negative length is impossible, hence, the true zero point.

To sum up, I leave you with the the chart below, indicating various measures for each scale.

Direction of Difference
 Amount of Difference
Absolute Zero
 Nominal  X
 Ordinal  X  X
 Interval  X  X X
 Ratio  X  X X X

Dangers of Converting an Ordinal Scale to its Numerical Equivalent

When surveys are executed, respondents are often asked to respond according to an ordinal scale.  They are asked to what extent they agree or disagree with a given statement on a scale reflecting the numbers 1 to 5 as: 1 strongly agree, 2 agree, 3 neutral, 4 disagree, 5 strongly disagree.   This type of data, called ordinal data, is not as straightforward, when conducting your survey results analysis, to analyze as it may first appear.

It is common practice to convert the answers into their numerical values and analyze the data based on the assumption that the resultant numerical equivalents are simple numerical data. This simple conversion violates the rules for analyzing ordinal data but in certain circumstances it is still appropriate.  In others, the result of the analysis may be misleading. The difference depends on the distribution of the response data.

For example in a survey based on an ordinal scale of 1 to 5 with 100 respondents, we begin our survey results analysis by converting the scale points to their numerical equivalents. But,  before we decide to do this we should examine whether the response is a Normal, single-peaked, symmetric distribution or not Normal, meaning if the response is bi-modal (with no central tendency).  Further, in the case of an equal number of responses in each category, typical of uniform distribution, there is again no central tendency.

It is possible and possibly useful to determine the mean in the case of single-peaked symmetric distribution, but when there is no central tendency, as is the case of bi-modal or symmetric distributions, the mean is virtually meaningless.  When the data is Normal, the risks of misanalysis are low but if you want to avoid scale violations such as these there are three possibilities to consider.

  1. Use the properties of multi-nomial distribution to estimate proportion of responses in each category and determine the standard deviation error, or
  2. Convert the ordinal scale to a dichotomous variable and use logistic regression to assess the impact of other variables on an ordinal scale variable, or
  3. Use rank correlation (Spearman or Kendall) to evaluate the association between ordinal scale values.

However, if you want to add together ordinal scale measures of related variables to give overall scores for a concept, then scale violations may be unavoidable.  Be aware, though, that if the response is anything other than approximately Normal, your survey results analysis may be misleading.