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Continuing from vol.59, we will explain how to investigate the frequency distribution is the normal distribution.
Similar to skewness and kurtosis, the method to check whether the frequency distribution is normal from the trend of cumulative relative frequency of observed data (sample) is called “normal probability plot.”
Normal probability plots calculate a statistic called the z value from the cumulative relative frequencies. Let’s check whether Figure 1 is normally distributed using a normal probability plot.
[Figure 1] Cumulative relative frequency of frequency distribution
The z value is the value on the horizontal axis where the lower probability in the z distribution (standard normal distribution) is the cumulative relative frequency. Additionally, the z value can be calculated using an Excel function:
z = NORM.S.INV (cumulative relative frequency)
The calculated z values are listed in the table below.
[Table] List of z values added
Draw a scatter plot (Figure 2) with the z value on the vertical axis and the class value on the horizontal axis. This graph is called “normal probability plot.”
[Figure 2]
If the scatter points exhibit a linear tendency, it can be concluded that the shape of the frequency distribution is a normal distribution.
[Points of focus for judgment]
・The degree to which a straight line fits the scatter points can be determined by the coefficient of determination.
・If the coefficient of determination is 0.99 or higher, the frequency distribution is determined to be a normal distribution.
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