📊 2cube factorial experim

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

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2cube factorial experiments in RBD – lay out – analysis

2cube Factorial Experiment in RBD

2cube factorial experiment mean three factors each at two levels. Suppose the three factors are A, B and C are tried with two levels the total number of combinations will be eight i.e. a0b0c0, a0b0c1, a0b1c0, a0b1c1, a1b0c0, a1b0c1, a1b1c0 and a1b1c1. The allotment of these eight treatment combinations will be as allotted in RBD. That is each block is divided into eight experimental units. By using the random numbers these eight combinations are allotted at random for each block separately. The analysis of variance table for three factors A with a levels, B with b levels and C with c 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 Factor C | c-1 | CSS | CMS | CMS / EMS AB | (a-1)(b-1) | ABSS | ABMS | ABMS / EMS AC | (a-1)(c-1) | ACSS | ACMS | ACMS / EMS BC | (b-1)(c-1) | BCSS | BCMS | BCMS / EMS ABC | (a-1)(b-1)(c-1) | ABCSS | ABCMS | ABCMS / EMS Error | (r-1)(abc-1) | ESS | EMS | Total | rabc-1 | TSS | |

Analysis

1. Arrange the results as per treatment combinations and replications.

Treatment combination | Replication

R1 R2 R3 … | Treatment Total

---|---|--- a0b0c0 | | | | | T1 a0b0c1 | | | | | T2 a0b1c0 | | | | | T3 a0b1c1 | | | | | T4 a1b0c0 | | | | | T5 a1b0c1 | | | | | T6 a1b1c0 | | | | | T7 a1b1c1 | | | | | T8

As in the previous designs calculate the replication totals to calculate the CF, RSS, TSS, overall TrSS in the usual way. To calculate ASS, BSS, CSS, ABSS, ACSS, BCSS and ABCSS, form three two way tables A X B, AXC and BXC. AXB two way table can be formed 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. 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

ASS= A X C two way table can be formed by taking the levels of A in rows and levels of C in the columns A X C Two way table

C A	c0	c1	Total
a0	a0 c0	a0 c1	A0
a1	a1 c0	a1 c1	A1
Total	C0	C1	Grand Total

B X C two way table can be formed by taking the levels of B in rows and levels of C in the columns B X C Two way table

C

B	c0	c1	Total
b0	b0 c0	b0 c1	B0
b1	b1 c0	b1 c1	B1
Total	C0	C1	Grand Total

-CF-ASS-BSS-CSS-ABSS-ACSS-BCSS

ESS = TSS-RSS- ASS-BSS-CSS-ABSS-ACSS-BCSS-ABCSS 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.