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We will explain “skewness” and “kurtosis,” which are concepts related to the normal distribution.
Skewness indicates “how much the distribution is skewed from the normal distribution,” and kurtosis indicates “how skewed the distribution is from the normal distribution.”
The distribution of the population may be symmetrical, the peak may be on the right, there may be two peaks, etc. Therefore, when using the normal distribution as the standard distribution, the dispersion metrics used to examine how skewed the distribution of a population is are “skewness” and “kurtosis” (Figure 1).
[Figure 1] Understanding skewness(G) and kurtosis(H) through shapes
The closer “skewness” or “kurtosis” are to 0, the closer the distribution of the population is to a normal distribution. However, there is no statistical standard that a distribution is normal if these values are within a specific interval.
From experience, if both the skewness and kurtosis of the frequency distribution are between -0.5 and 0.5, the shape of the frequency distribution is determined to be normal.
Among the three distributions shown in Figure 2, it can be stated that B is a normal distribution because its “skewness” and “kurtosis” are both between -0.5 and 0.5.
[Figure 2] Which one is a normal distribution?
Figure 3 shows data on the number of times 29 women in their 20s visited their family doctor in one month. Let’s find the skewness and kurtosis of this distribution, and determine whether these data follow a normal distribution.
[Figure 3]
Skewness and kurtosis are calculated using Excel functions.
Skewness = SKEW (number 1, number 2 …)
Kurtosis = KURT(number 1, number 2 …)
In this example, skewness = 1.1719 and kurtosis = 1.6798. Given that both skewness and kurtosis are 0.5 or higher, we found that the frequency distribution of the number of visits to the family doctor is not a normal distribution.
Next time, we will explain the “normal probability plot.”
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