A new statistical parameter was defined in order to determine the range of applicability of the mixing length concept in two bubble columns. Gas holdup time series (60,000 points) were measured in two bubble columns (0.15 and 0.4 m in i.d.) by a conductivity wire-mesh sensors. The new statistical parameter phi was defined as the ratio of the mean value of the signal to three times the average absolute deviation (3AAD) and it was correlated to the mixing length. It was found that this new correlation was not valid in all hydrodynamic regimes. It is applicable only in the transition flow regime. Such a clarification has not been provided in the literature so far. In the narrow bubble column, the results were also confirmed on the basis of the Kolmogorov entropy and another statistical parameter. The new parameter phi was also used for flow regime identification. In the narrow bubble column, the first transition velocity U-trans was identified at 0.034 m/s; whereas, the second U-trans occurred at 0.112 m/s. In the large bubble column, the two U-trans values were identified at 0.045 and 0.101 m/s, respectively.