layer are the number of responses in that layer. In symbols A 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. Bimodal separation This index assumes that the distribution is a mixture of two normal distributions with means (μ1 and μ2) and standard deviations (σ1 and σ2): Bimodality coefficient Sarle's bimodality coefficient b is where γ is the skewness and κ is the kurtosis. The kurtosis is here defined to be the standardised fourth moment around the mean. The value of b lies between 0 and 1. The logic behind this coefficient is that a bimodal distribution with light tails will have very low kurtosis, an asymmetric character, or both – all of which increase this coefficient. The formula for a finite sample is where n is the number of items in the sample, g is the sample skewness and k is the sample excess kurtosis. The value of b for the uniform distribution is 5/9. This is also its value for the exponential distribution. Values greater than 5/9 may indicate a bimodal or multimodal distribution, though corresponding values can also result for heavily skewed unimodal distributions. The maximum value (1.0) is reached only by a Bernoulli distribution with only two distinct values or the sum of two different Dirac delta functions (a bi-delta distribution). The distribution of this statistic is unknown. It is related to a statistic proposed earlier by Pearson – the difference between the kurtosis and the square of the skewness (vide infra). Bimodality amplitude This is defined as where A1 is the amplitude of the smaller peak and Aan is the amplitude of the antimode. AB is always < 1. Larger values indicate more distinct peaks. Bimodal ratio This is the ratio of the left and right peaks. Mathematically where Al and Ar are the amplitudes of the left and right peaks respectively. Bimodality parameter This parameter (B) is due to Wilcock. where Al and Ar are the amplitudes of the left and right peaks respectively and Pi is the logarithm taken to the base 2 of the proportion of the distribution in the ith interval. The maximal value of the ΣP is 1 but the value of B may be greater than this. To use this