Editing Multimodal distribution (section)

===van der Eijk's A===

This measure is a weighted average of the degree of agreement the frequency distribution.<ref name=Van_der_Eijk2001>{{cite journal | last1 = Van der Eijk | first1 = C | year = 2001 | title = Measuring agreement in ordered rating scales | journal = Quality & Quantity | volume = 35 | issue = 3| pages = 325–341 | doi=10.1023/a:1010374114305| s2cid = 189822180 }}</ref> ''A'' ranges from -1 (perfect [[bimodal]]ity) to +1 (perfect [[unimodal]]ity). It is defined as

<math display="block"> A = U \left( 1 - \frac{ S - 1 }{ K - 1 } \right) </math>

where ''U'' is the unimodality of the distribution, ''S'' the number of categories that have nonzero frequencies and ''K'' the total number of categories.

The value of U is 1 if the distribution has any of the three following characteristics:

* all responses are in a single category
* the responses are evenly distributed among all the categories
* the responses are evenly distributed among two or more contiguous categories, with the other categories with zero responses

With distributions other than these the data must be divided into 'layers'. Within a layer the responses are either equal or zero. The categories do not have to be contiguous. A value for ''A'' for each layer (''A''<sub>i</sub>) is calculated and a weighted average for the distribution is determined. The weights (''w''<sub>i</sub>) for each layer are the number of responses in that layer. In symbols

<math display="block"> A_\text{overall} = \sum_i w_i A_i </math>

A [[Uniform distribution (discrete)|uniform distribution]] has ''A'' = 0: when all the responses fall into one category ''A'' = +1.

One theoretical problem with this index is that it assumes that the intervals are equally spaced. This may limit its applicability.