Introduction. In a test, I would like to use both the Fisher's moment coefficient of skewness (Joanes, 1998) $g_{\text{Fisher}} = \frac{m_3}{{m_2}^{3/2}} = \frac{\frac{1}{n}\sum_i (x_i - \overline{x})^{3}}{\left(\frac{1}{n}\sum_i (x_i - \overline{x})^{2} \right)^{3/2}}$ and the Bowley’s coefficient of skewness (Ekström & Jammalamadaka, 2012), $g_{\text{Bowley}}=\frac{Q_{0.75} + Q_{0.25} - 2 \times Q_{0.5}}{Q_{0.75} - Q_{0.25}}$ (which is bounded $[-1,1]$).
Question. I found that the rule of thumb to understand the outcome of the Fisher's moment coefficient of skewness is the following (Normality Testing - Skewness and Kurtosis, likely coming from Bulmer, 1979, Principles of Statistics, Chapter 4 Descriptive properties of distributions, on Page 63):
- If skewness is less than -1 or greater than 1, the distribution is highly skewed.
- If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed.
- If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.
However, I did not find any reference reporting such a rule of thumb for the Bowley’s coefficient of skewness (e.g. research on Web of Science, by using "Bowley" and "skewness" as key words). Do you know a reference about a rule of thumb for understanding the Bowley’s coefficient of skewness (similar to that one above mentioned for the Fisher's one)?
