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.

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