Checking wether a data distribution is normal: Kolmogorov-Smirnov, Anderson-Darling and Shapiro-Wilk.
Anderson-Darling
Example: We want to know if the weight of some pieces has a normal distribution. So, a sample with 11 measurements of pieces weights (in pounds) was obtained: 148, 154, 158, 160, 161, 162, 166, 170, 182, 195, 236. We will test if this sample has a normal distribution.
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To use the tool Tests for Normality, the user must follow these steps:
1. Access the menu:
Action → Basic Statistics → Tests for Normality
2. The following window will appear;
3. With the cursor in the field Data Set select the column (table or row) that contains the data, which must be numeric;
4. In the board Type of Test, we have to select among the options Anderson-Darling, Kolmogorov-Smirnov or Shapiro-Wilk. In this example we will select the Anderson-Darling test;
5. In the board Show Results, we select between the options Current Cell or New Sheet. We suggest the option New Sheet, because Action does not have the undo command;
REMARK: When choosing the option Current Cell, the results will be printed from the cell where the cursor is. In this case, we have to put the cursor in an appropriate position previously (before step 1).
6. To finish, click Ok.
Kolmogorov-Smirnov or Shapiro Wilk tests are done in an analogous way: we just need to select the desired test in the board Type of Test. The interpretation of the results will also be analogous.
Results and Interpretation
Once the process is finished, the following results will be shown:
- As the P-value is 1.1929%, we reject the hypothesis of normality. Thus, with a 95% confidence level, we have evidences that data do not follow a normal distribution.
- Through the graphic Probability Paper we also can see that data do not follow a normal distribution: they are not on the line!
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