📊 2Square factorial experi

This lesson builds core statistical understanding for BSc Agriculture exam preparation through clear concepts, worked structures, and application-focused interpretation.

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2Square Factorial Experiments in RBD – lay out – analysis

2Sqaure Factorial Experiments in RBD

22 factorial experiment means two factors each at two levels. Suppose the two factors are A and B and both are tried with two levels the total number of treatment combinations will be four i.e. a0b0, a0b1, a1b0 and a1b1. The allotment of these four treatment combinations will be as allotted in RBD. That is each block is divided into four experimental units. By using the random numbers these four combinations are allotted at random for each block separately. The analysis of variance table for two factors A with a levels and B with b levels with r replications tried in RBD will be as follows:

Sources of Variation	d.f.	SS	MS	F
Replications	r-1	RSS	RMS
Factor A	a-1	ASS	AMS	AMS / EMS
Factor B	b-1	BSS	BMS	BMS / EMS
AB (interaction)	(a-1)(b-1)	ABSS	ABMS	ABMS / EMS
Error	(r-1)(ab-1)	ESS	EMS
Total	rab-1	TSS

As in the previous designs calculate the replication totals to calculate the RSS, TSS in the usual way. To calculate ASS, BSS and ABSS, form a two way table A X B by taking the levels of A in rows and levels of B in the columns. To get the values in this table the missing factor is replication. That is by adding over replication we can form this table. RSS = A X B Two way table

B A	b0	b1	Total
a0	a0 b0	a0 b1	A0
a1	a1 b0	a1 b1	A1
Total	B0	B1	Grand Total

ESS= TSS-RSS-ASS-BSS-ABSS By substituting the above values in the ANOVA table corresponding to the columns sum of squares, the mean squares and F value can be calculated.

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Summary Cheat Sheet

• Focus: core definitions, classification logic, and design/analysis workflow from this lesson.
• Exam Use: revise key terms, assumptions, and interpretation steps for objective and descriptive questions.
• Practice: solve one representative numerical or conceptual question from this topic.

References

1 source • [1]

[1]

Standard BSc Agriculture Statistics notes used for lesson preparation.