In statistics, we use skewness and kurtosis to measure the shape of a distribution.
Skewness measures the asymmetry of a distribution. This value can be positive or negative.
- A negative skew indicates that the tail is on the left side of the distribution, which extends towards more negative values.
- A positive skew indicates that the tail is on the right side of the distribution, which extends towards more positive values.
- A value of zero indicates that there is no skewness in the distribution at all, meaning the distribution is perfectly symmetrical.
Kurtosis is a measure of whether or not a distribution is heavy-tailed or light-tailed relative to a normal distribution.
- The kurtosis of a normal distribution is 0.
- If a given distribution has a kurtosis less than 0, then it tends to produce fewer and less extreme outliers than the normal distribution.
- If a given distribution has a kurtosis greater than 0, then it tends to produce more outliers than the normal distribution.
The following example shows how to calculate skewness and kurtosis for a given dataset in SPSS.
Example: How to Calculate Skewness & Kurtosis in SPSS
Suppose we have the following dataset in SPSS that shows the exam scores received by various students in some class:
To calculate the skewness and kurtosis for the distribution of exam scores, click the Analyze tab, then click Descriptive Statistics, then click Descriptives:
In the new window that appears, drag Exam_Score to the Variables panel:
Then click the Options button. In the new window that appears, check the boxes next to Kurtosis and Skewness:
Then click Continue. Then click OK.
The following output will appear:
From the output we can see the values for the skewness and kurtosis of the distribution:
- The skewness is -1.551. Since this value is negative, it indicates that the distribution is left-skewed.
- The kurtosis is 2.230. Since this value is greater than zero, it indicates that the distribution has heavier “tails” than a normal distribution.
In addition to calculating these metrics, it can be helpful to create a histogram to visualize the distribution.
To do so, click the Graphs tab, then click Histogram:
In the new window that appears, drag Exam_Score into the Variable panel:
Once you click OK, a histogram will be generated that shows the distribution of exam scores:
We can see that the distribution is indeed left-skewed (the “tail” extends to the left side of the distribution), which matches the fact that we calculated the skewness to be negative.
By calculating the skewness and kurtosis along with creating a histogram, we now have a pretty good understanding of the distribution of exam scores in this dataset.
The following tutorials explain how to perform other common tasks in SPSS: