Shapiro-Francia Test
Shapiro-Francia Test of Normality
Greater than 50 Measurements
Other Normality Tests:
Description:
The Shapiro-Francia method tests for normal distribution of the data. The 1992 guidance document recommends this as the preferred test for normality in data sets with greater than 50 measurements.
In ChemStatimplementation, the Shapiro-Francia test can test the normality of data for any parameter for a selected monitoring location, for all background monitoring locations, for all compliance monitoring locations, and for all monitoring locations. Select the monitoring location group from the right-click menu. The selected group should contain at least 50 measurements. Use the right-mouse-click context menu to select the monitoring location group.
The Shapiro-Francia test can also be used to test for normality of the residuals. From the normality sub-menu on the right-click menu, select Residuals to test the residuals. Select Data to test the actual parameter concentrations for normality.
Use:
To test for normality in data sets with greater than 50 measurements. The test can be performed on the selected monitoring location, all compliance monitoring locations, all background monitoring locations, or all monitoring locations.
Remarks:
The computer implementation supports a maximum of 2000 measurements. Table A-3 in the 1992 guidance provides values only up to n = 99. The original Shapiro-Francia publication also provided tables for n up to 99. For n larger than 99, the value for n = 99 is used.