This document discusses 2^3 factorial experiments and provides an example. It explains that a 2^3 factorial design involves three factors, each with two levels, yielding eight combinations. The example tests the effects of three fertilizer factors (N, P, K) on rice yield, with two levels for each factor. Statistical analysis is conducted in SPSS to test for differences between treatment mean combinations and determine if factors have individual or interactive effects. The results find no significant differences, so the null hypothesis that the treatment means are equal is not rejected.

1. 2^3 Factorial Experiment in SPSS
Almaszabeen Badekhan
BAM-15-43
Department of
Agricultural Economics
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2. Introduction
• Factorial experiment is an experiment whose design
consists of two or more factors, each with discrete
possible values or levels and whose experimental units
are on all possible combinations of these levels across all
such factors.
• If we have three factors each taking two levels , then
there will be eight combinations , this is 2x2x2 factorial
design.
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3. History
• Factorial designs or Complex designs were used by John
Bennet Lawes and Joseph Henry Gilbert in the 19th
century (Rothamsted experimental station).
• The term factorial was used for the first time by Fisher
in his book “The Design of Experiments”.
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4. Applications
• Traditional research methods generally study the effect
of single factor at a time.
• Social researchers often use factorial designs to assess
the effects of educational methods, whilst taking into
account the influence of socio-
economic factors and background .
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5. • In agricultural sciences, with a need for field testing ,
often uses factorial designs to test the effect of variables
on crops.
• In large scale studies, it is difficult and impractical to
isolate and test each variable individually.
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7. Example for 2^3 Factorial Design
• An experiment was laid out with four replications to test
the effect of two levels of N (N0= 0 kg/ ha, N1= 40 kg/ha)
and two levels of P (P0= 0 kg/ha, P1= 30 kg/ha) and two
levels of K (K0= 0 kg/ha, K1= 20 kg/ha) on the field of
paddy. The data pertaining to yield of paddy for various
treatment combinations are given below. Analyze the data
and give conclusions.
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8. Rep 1 Rep 2 Rep 3 Rep 4
N0P0K0 1
20 31 15 7
N1P0K0 N
14 24 12 6
N0P1K0 P
17 27 15 16
N0P0K1 K
24 19 20 18
N1P1K0 N*P
35 29 36 33
N1P0K1 N*K
40 64 44 52
N0P1K1 P*K
30 22 28 36
N1P1K1 N*P*K
64 53 58 51
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9. Procedure for Factorial Design in SPSS
• Analyse- General Linear Model- Univariate- Yield[under
dependent variable]- rep, n, p, k- [under Fixed Factor]-
Model- Custom- rep, n, p, k- button[ rep, n, p, k- n*p, p*k,
n*k, n*p*k under Model]- Continue- OK
• H0 – There is no significant difference between the
treatment mean combinations.
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16. • Results-There is no significant difference between the
treatment mean combinations. we do not reject H0.
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