Normal Distribution of Data

When data has been screened to minimize or ensure no error, the data then need to be checked for the normality of its distribution.
Several ways can be utilized to check whether the data is normally distributed or not, and they can be divided into graphical and numerical means.

GRAPHICAL

1) Histogram

Step 1

• On the Menu Bar, choose "Graphs" --> "Legacy Dialogs" --> Histogram.
• A pop-up window will appear.

Step 2

• Insert relevant variable in the "Variable" box.
• Check the "Display normal curve" option to view the data distribution more clearly by overlaying the curve on the bars.

 

 

Referring to the graphs above, the data distributions look quite normal.

2) P-P Plot and Q-Q Plot

Step 1

• On the Menu Bar, select "Analyze" --> "Descriptive Statistics" --> "P-P Plots" or "Q-Q Plots".
• A pop-up window will appear.

 

 Both data on the plots can be said as normally distributed as the dots are closely aligned to the straight line.

NUMERICAL 

1) Normality Statistics: Skewness and Kurtosis

Step 1

• On the Menu Bar, select "Analyze" --> "Descriptive Statistics" --> "Descriptives".
• A pop-up window will appear.

Step 2

• Insert relevant variable(s) in the "Variable(s)" box.
• Click "Options".
• Check on "Kurtosis" and "Skewness" under "Distribution".
• Click "Continue" then "OK". 

Step 3

• Calculate the normality of distribution by dividing Statistic with its Standard Error. 
• The acceptable value to be considered as normal distribution is when the index value of Skewness or Kurtosis is within ±1.96.
• e.g. Skewness index for Total scores of Scale A: 0.182/0.512=0.36. The Kurtosis index: 0.75/0.992=0.76. Thus, the data is said to be normally distributed.

 

Report Writing (example)

Total scores of Scale A is normally distributed, with skewness of 0.36 (SE=0.512) and kurtosis of 0.76 (SE=0.992).  

2) Normality Statistics: One-Sample Kolmogorov-Smirnov Test

Step 1

• On the Menu Bar, select "Analyze" --> "Nonparametric Tests" --> "Legacy Dialogs" --> 1-Sample K-S".
• A pop-up window will appear.

Step 2

• Insert relevant variable in the "Test Variable List" box.
• Click "OK". 

 

Step 3

• Determine the distribution normality by focusing at the "Asymp. Sig. (2-tailed)" (asymptotic significance value) in the table.
• If the value is greater than 0.05 (p>0.05), it is said that the distribution is normal while if the value is smaller than 0.05 (p<0.05), it is said that the distribution is not normal.
• e.g. Asymp. Sig. value in the table below is 0.315 which is greater than 0.05. Thus, the distribution of the data is considered normal.

 

Report Writing (example)

One-sample Kolmogorov-Smirnov test of normality indicates that the total scores of Scale A is normally distributed with (M=8.05, SD=1.36). D=0.96, p=0.315.