Question

How do we check whether the data collected in a research project comes from a Normal distribution?

Answer 1

For checking given data comes from normal distribution there are certain tests.

1) From Histogram :

Plot the histogram of a given data check whether this histogram is bell shaped or not . If the histogram is bell shaped then the given distribution is normally distributed . In this data mean = median = mode . So from histogram we can check the normality .

2) From Descriptive Statistics :

Suppose from histogram it is not clear to identify the given data is normal or not . We can use another method firstly we calculate mean and standard deviation of the data after that we use empirical rule of statistics rule ( 68 - 95 - 99.7 ). So calculating one sigma limit that is ( mean - standard deviation, mean - standard deviation ) and check whether 68 % of the data falls within that limit or not .Then checking two sigma limit ( mean - 2 * standard deviation , mean + 2 * standard deviation ) about 95 % falls in this interval or not . Then calculating 3 sigma limit ( mean - 3 * standard deviation , mean + 3 *standard deviation ) nearly 99.7 % data falls within the limit . If all three condition are satisfied then we say the Given data comes from the normal distribution .

3) Using Normal Probability Plot :

There is another method to check the normality by using Normal Probability Plot , here we plot the normal probability plot and check the nature of the plot . The straight diagonal line in normal probability plot indicating normal distributed data.

4) Shapiro wilk test :

This is also famous test to check the normality . In this test we define a hypothesis , Ho: The given data is normally distributed .Vs H1 : The given data is not normally distributed . If P value is less than level of significance then we reject the null hypothesis it means our data is not normal . Otherwise P value is greater than level of significance then we fail to reject the null hypothesis which means given data is normally distributed .

there are more methods like Anderson Darling test , kolmogorov Smirnov test for checking normality.