Consensus
Explanation
One measure of dispersion that could be used with ordinal data is called consensus (Tastle & Wierman, 2007; Tastle, Wierman, & Rex Dumdum, 2005). This measure ranges from 0 to 1. A zero would indicate a complete lack of consensus, the number of people that tend towards one end of the ordinal variable (i.e. fully disagree) is then the same as the number of people who tend to the other end (i.e. fully agree), while consensus of one would indicate all respondents gave the same answer.
Although the interpretation of the measure of consensus is relatively straight forward, the calculation is bit tricky.
Obtaining the Measure
with SPSS
Formula
The formula for the measure of consensus is:
\(Cns(X) = 1 + \sum_{i=1}^n p_i \text{log}_2(1 - \frac{|i-\mu_x|}{d_x})\)
With:
\(\mu_X = \frac{\sum_{i=1}^k i\times F_i}{n}\)
\( d_X = k - 1 \)
\( p_i = \frac{F_i}{n}\)
\(n\) is the sample size, \(F_i\) the frequency of the i-th category, and \(k\) the number of categories
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