Topic 2: How to check normality of data?

Normality checking (How to check the normality?)

The three important methods of checking the normality of data are,

Histogram method: Plot a histogram for the data and check whether the curve is symmetrical. If the curve is symmetrical, data/variable follows normality.

Shapiro-Wilk test: The null-hypothesis of this test is that the population is normally distributed. So if p value is greater than 0.05, data follows normality. Usually applied when sample size is small.

Kolmogorov Smirnov test (K S test): The null-hypothesis of K S test is that the population is normally distributed. So if p value is greater than 0.05, data follows normality. Usually applied when the sample size is large.

Theoretical Properties of a normal distribution/normal curve are

• Normal curve is bell-shaped
• Normal curve is symmetric about the mean
• The mean is at the middle and divides the area into halves
• The mean, median, and mode are equal
• The total area under the curve is equal to one
• The normal curve approaches, but never touches, the x-axis and extends up to positive and negative infinity
• Unimodel in nature (only one mode)
• Skewness=0
• Kurtosis=3 (mesokurtic)
• For a normal curve [Fig ],
  • 68.27% of the observations lie between mean ± 1SD
  • 95.45% of the observations lie between mean ± 2SD
  • 99.73% of the observations lie between mean ± 3SD
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    Reference:  "Handbook on Biostatistics for Health Professionals, Karun M K and Amitha P, (2019), BCC publications"
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