are the means of the two normal distributions and σ is their standard deviation. The following test for the case p = 1/2 was described by Schilling et al. Let The separation factor (S) is If the variances are equal then S = 1. The mixture density is unimodal if and only if A sufficient condition for unimodality is If the two normal distributions have equal standard deviations a sufficient condition for unimodality is Summary statistics Bimodal distributions are a commonly used example of how summary statistics such as the mean, median, and standard deviation can be deceptive when used on an arbitrary distribution. For example, in the distribution in Figure 1, the mean and median would be about zero, even though zero is not a typical value. The standard deviation is also larger than deviation of each normal distribution. Although several have been suggested, there is no presently generally agreed summary statistic (or set of statistics) to quantify the parameters of a general bimodal distribution. For a mixture of two normal distributions the means and standard deviations along with the mixing parameter (the weight for the combination) are usually used – a total of five parameters. Ashman's D A statistic that may be useful is Ashman's D: where μ1, μ2 are the means and σ1 σ2 are the standard deviations. For a mixture of two normal distributions D > 2 is required for a clean separation of the distributions. van der Eijk's A This measure is a weighted average of the degree of agreement the frequency distribution. A ranges from -1 (perfect bimodality) to +1 (perfect unimodality). It is defined as 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 (Ai) is calculated and a weighted average for the distribution is determined. The weights (wi) for each