DURBIN TEST - Balanced Incomplete Block Design


This test reduces to the Friedman test if the number of treatments equals the number of experimental units per block.

Use this test rather than parametric tests if "normality" assumptions are not met.

The test is called "balanced" because:

The test is "incomplete" because not all treatments are applied to each block.

This tool operates in much the same way as most of the others with no specific departures from the usual methods needed.

Note that labels are not used in the output, however the column titles can be included in the input range with no harm. Row labels should not be included in the range.

Click here for information about general script usage.

In the following example, seven people test three of seven samples of a product and rank the three samples 1,2,3.

This is the input data:

	Product						
Person	A	B	C	D	E	F	G
1	2	3		1			
2		3	1		2		
3			2	1		3	
4				1	2		3
5	3				1	2	
6		3				1	2
7	3		1				2
							

This is the script output:

							
Durbin Test - Balanced Incomplete Block Design							
(There were no ties)							
Durbin T:	8						
df(1):	6						
df(2):	8						
P(F<=f) One-tail:	0.005						
F-Critical(95%):	3.5806						
F-Critical(99%):	6.3707						

Interpretation

The null hypothesis is that no variety of product tends to be preferred over the other.

The output provides the Durbin "T" statistic which is tested using the F distribution.

In this case, the null hypothesis is rejected as the P value for a one-tail test is less than .01.

Note: Multiple comparisons between treatments is not (yet!) part of the output.



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