Elementary Statistics and Computer Application

Analysis

The results of repeated experiments are analysed using combined analysis of variance method.
The combined analysis is aimed at

1. To test whether there are significant differences between the treatments at various environments or loc or seasons etc.
2. Test the consistency of the treatment at different environments. i.e. to test the presence or absence of interaction of the treatment with environments.
The presence of interaction will indicate that the responses change with environment.

• In the first stage of the combined analysis the results of the individual locations are analysed based on the basic experimental design tried. In the second stage of the analysis various SS are computed by combining all the data.
If the basic design adopted is RBD with t treatments and r replications and p locations the ANOVA table will be

Sources of Variation	Degrees of Freedom	Sum of Squares	Mean Squares	F-ratio
Replication within locations	p(r-1)	RSS	RMS
Locations	p-1	LSS	LMS
Treatments	t-1	TrSS	TrMS	TrMS / LXTMS
Location x Treatments	(p-1)(t-1)	LXTSS	LXTMS	LXTMS / EMS
Combined error	p(r-1)(t-1)	ESS	EMS
Total	rtp-1	TSS

But before proceeding with the combined analysis it is necessary to test whether the EMS of the individual experiments are homogenous and the heterogeneity of EMS can be tested by either Bartlett’s test or Hartley’s test.

• When the EMS are homogenous the analysis is done as follows:
• Rep within location SS = Sum of replication SS of all locations
• Pooled error SS = sum of error SS of all locations
• The treatment X location two-way table is formed. From this two way table treatment SS, locations SS and treatment X location SS are computed.
The significance of treatment X location interaction is tested and if it is found to be significant then the interaction mean square is used for calculating the F value for treatments.

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