Skewness vs Kurtosis in Data A

skewness and kurtosis are 2 important statistical measures used to assess the distribution of data and determine whether it deviates from a normal distribution... skewness measures the degree of asymmetry in a dataset... a distribution is considered positively skewed (right-skewed) when the tail extends further to the right, indicating that a small number of high values are pulling the mean upward... conversely, a negatively skewed (left-skewed) distribution has a longer tail on the left, indicating the presence of unusually low values... a skewness value close to zero suggests that the distribution is approximately symmetrical, which is a characteristic of a normal distribution... understanding skewness helps researchers identify potential biases in the data and determine the suitability of statistical techniques that assume normality...

kurtosis measures the degree of peakedness or tail heaviness of a distribution compared to a normal distribution... a distribution with high kurtosis (leptokurtic) has a sharper peak and heavier tails, indicating a greater likelihood of extreme values or outliers... in contrast, a distribution with low kurtosis (platykurtic) has a flatter peak and lighter tails, suggesting fewer extreme observations... a mesokurtic distribution has a kurtosis similar to that of a normal distribution... while skewness focuses on the symmetry of the data, kurtosis focuses on the concentration of values around the mean and the presence of outliers...

in research, both measures are commonly used during preliminary data screening, particularly before conducting advanced statistical analyses such as regression, factor analysis, or Structural Equation Modelling (SEM)... as a general guideline, skewness values between -2 and +2 and kurtosis values between -7 and +7 are often considered acceptable for many multivariate analyses, although stricter thresholds may be applied depending on the methodology and discipline... when distributions exhibit substantial skewness or kurtosis, researchers may need to transform the data, remove outliers, or employ robust statistical techniques... therefore, examining skewness and kurtosis is an essential step in ensuring data quality and validating the assumptions underlying statistical analyses...

key difference:

• skewness = shape and symmetry of the distribution
• kurtosis = peakedness and likelihood of extreme values (outliers)

for PhD viva purposes, a simple explanation would be: "skewness tells us whether the data are distributed evenly around the mean, while kurtosis indicates whether the distribution contains unusually extreme observations compared to a normal distribution."