What skewness and kurtosis measure
Skewness measures asymmetry. Positive values mean a long right tail, as with incomes and reaction times; negative values mean a long left tail. Excess kurtosis measures how heavy the tails are compared with a normal distribution, which has a value of 0. See skewness and kurtosis explained.
Worked example
The example reaction times have mean 460.75 ms and median 433.5 ms, and the mean is pulled up by two slow responses. Skewness is 1.75, which is strong right skew, and excess kurtosis is 3.05, meaning heavy tails. Dividing each by its standard error gives z = 3.42 and z = 3.07, both beyond ±1.96.
Rules of thumb
| |Skewness| | Usual description |
|---|---|
| Below 0.5 | Roughly symmetric |
| 0.5 to 1 | Moderately skewed |
| Above 1 | Strongly skewed |
These are conventions, not rules. In large samples the z-values flag very small departures, so look at the size of the skewness as well.
Which formula is this?
The calculator reports the adjusted sample statistics G₁ and G₂. These are the values given by Excel’s SKEW and KURT functions and SPSS, and they match SciPy with bias=False. Some software reports unadjusted values, which differ noticeably in small samples.
Frequently asked questions
What is a good skewness value?
Between -0.5 and 0.5 is usually called roughly symmetric. Values beyond 1 in either direction indicate strong skew.
What does excess kurtosis mean?
It is kurtosis minus 3, so a normal distribution scores 0. Positive values indicate heavier tails and more extreme values than a normal distribution.
Does this match Excel?
Yes. The calculator uses the adjusted formulas behind Excel's SKEW and KURT functions.
What should I do with skewed data?
For positive right-skewed data, a log transformation often helps. Otherwise, use a rank-based test. With large samples, t-tests and ANOVA are robust to moderate skew.