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The Hartigans' Dip Statistic measures unimodality in a sample: Specifically, it measures the greatest difference between the empirical cumulative distribution function and that unimodal cumulative distribution function which minimizes that greatest difference.

Freeman and Dale discuss three measures for detecting bimodality in an observed probability distribution:

  • The bimodality coefficient (BC),
  • Hartigan's dip statistic (HDS), and
  • Akaike's information criterion between one-component and two-component distribution models (AID).

Measures for detecting bimodality can be used to detect whether psychometric measurements include cases in which behavior was caused by different cognitive processes (like intuitive and rational processing).

According to Freeman and Dale, Hartigan's dip statistic is more robust against skew than either the bimodality coefficent and Akaike's information criterion.

The bimodality coefficient can be unstable with small sample sizes (n<10).

Bimodality measures for probability distributions are affected by

  • distance between modes,
  • proportion (relative gain) of modes, and
  • proportion of skew.

Bimodality measures for probability distributions are affected by

  • distance between modes,
  • proportion (relative gain) of modes, and
  • proportion of skew.

Of the three, Freeman and Dale found distance between modes to have the greatest impact on the measures they chose.

In Freeman and Dale's simulations, Hartigan's dip statistic was the most sensitive in detecting bimodality.

In Freeman and Dale's simulations, Hartigan's dip statistic was strongly influenced by proportion between modes.

In Freeman and Dale's simulations, the bimodality coefficient suffered from interactions between skew and proportion between modes.

According to Freeman and Dale, the bimodality coefficient uses the heuristic that bimodal distributions often are asymmetric which would lead to high skew and low kurtosis.

It therefore makes sense that it may detect false positives for uni-modal distributions with high skew and low kurtosis.

Freeman and Dale `are inclined to recommend' Hartigan's dip statistic to detect bimodality.

Intuitively, Akaike's information criterion between one-component and two-component distribution models (AID) tests whether a one model or another describes the data better, with a penalty for model complexity.

Freeman and Dale found Akaike's information criterion between one-component and two-component distribution models (AID) to be very sensitive to but highly biased towards bimodality.

Pfister et al. recommend using Hartigan's dip statistic and the bimodality coefficient plus visual inspection to detect bimodality.