6 Completely Randomized Design (CRD) PDF

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Design and Analysis of Single Factor Experiments 7/1/2019 Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 1 Design and Analysis of Single Factor Experiments: A single factor experiment is a simple experiment that consists of limited number of treatments belonging to a...

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Design and Analysis of Single Factor Experiments 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 1

Design

and

Analysis

of

Single

Factor

Experiments: A single factor experiment is a simple experiment that consists of limited number of treatments belonging to a certain factor.

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Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 2

Examples of single factors:  Different varieties of a crop:  Different levels of a pesticide.  Different genotypes of animals.

 Different strains of bacteria or fungi.  Different types of harvesters or tractors. 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 3

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Completely Randomized Design (CRD) 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 5

Completely randomized design is the simplest, most easily understood, and most easily analyzed designs.

In

CRD,

treatments

are

assigned

randomly to homogenous experimental units without any condition. 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 6

Total variation

Treatment variation 7/1/2019

Experimental error variation

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 7

Advantages of CRD:  Simple to use.  Flexible.  Easy statistical analysis.  Lost experimental unit don’t complicate

statistical analysis.  Degree of freedom of experimental error is

higher compared to other designs. 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 8

Disadvantages of CRD:  Needs homogenous experimental units.  The size of experimental error is relatively large to other designs.

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Uses of CRD:  Laboratory experiments.  Greenhouse experiment.

 Animal experiment.  It is very rarely used in field experiments.

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Mathematical model of CRD:

Where: Character measured Grand mean Treatment effect

Experimental error effect 7/1/2019

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An example: Research problem:  Papaya (Carica papaya) is generally propagated from seeds but seedlings are variable in both plant and fruit characteristic. Vegetative propagation of papaya is preferred sine it produces true-to type plant.  So, a researcher in the field of tissue culture wanted to study the effect the growth regulator, BAP, on micro-propagation of papaya in the tissue culture laboratory. 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 12

 Shoot tip explants of about one cm long were cultured on a medium supplement with different concentrations of BAP (0, 0.5, 1.0, 1.5 and 2.0 mg/l) in test tubes.  Each concentration repeated 4 times.

 All cultures were maintained at temperature of 25-270C and 16 hour photoperiod. Length of

roots was measured 4 weeks later. 7/1/2019

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Objective of the experiment: Effect BAP on Micro-propagation of Papaya (Carica papaya L.)

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Hypothesis: Null hypothesis: There are no significant differences in root length of papaya in response to different concentrations of BAP.

Alternative hypothesis: There are significant differences in root length of papaya in response to different concentrations of BAP.

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Randomization and layout of experiment: • Number of treatments (T): 5 concentrations of BAP • Number of replicates (R): 4 times • Total number of experimental units (N):

• N = T* R = 5*4 = 20 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 16

20 test tubes 7/1/2019

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Treatments were randomly distributed experimental units 7/1/2019

to

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 18

Data collection and organization Replication

Concentrations (root length in cm) Treatment Treatment of BAP (mg/l) total mean I II III IV T1: 0.0 mg/l T2: 0.5 mg/l T3: 1.0 mg/l T4: 1.5 mg/l T5: 2.0 mg/l Grand total Grand mean 7/1/2019

12 13 12 14

51

12.75

14 15 14 13

56

14.00

13 13 12 15 16 17 14 16 17 18 16 19

53 63 70

13.25 15.75 17.50

293 14.65

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 19

Testing hypothesis: Steps for analysis of variance: 1) Sum of squares 2) Degree of freedom 3) Mean squares 4) F values 5) Analysis of variance Table (ANOVA table) 6) Testing significance 7) General conclusion 8) Summary of results 7/1/2019

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1) Sum squares: Before calculation of sum of squares, the

correction factor is, firstly, calculated as follow:

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Sum of squares for total:

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Sum of squares for treatments:

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Sum of squares for error:

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2) Degree of freedom: Degree of freedom for total:

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Degree of freedom for treatments:

Degree of freedom for error:

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3) Mean squares: Mean squares for treatments:

Mean squares for error:

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4) F values

Calculated F value:

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Tabulated F value  Level of significance or probability: 1% or 5%  Degree of freedom for treatments: 4  Degree of freedom for error: 15

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Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 29

Table: distribution of F: alpha = 0.05 DFE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 7/1/2019

1 161.469 18.5128 10.1278 7.7087 6.6080 5.9874 5.5914 5.3177 5.1174 4.9647 4.8443 4.7472 4.6672 4.6001 4.5430

Number of Means 2 3 199.493 215.737 18.9995 19.1642 9.5522 9.2767 6.9444 6.5915 5.7861 5.4095 5.1433 4.7570 4.7374 4.3469 4.4590 4.0662 4.2565 3.8626 4.1028 3.7083 3.9823 3.5875 3.8853 3.4903 3.8055 3.4106 3.7389 3.3439 3.6824 3.2874

4 224.500 19.2467 9.1173 6.3882 5.1922 4.5337 4.1204 3.8378 3.6331 3.4781 3.3567 3.2592 3.1791 3.1122 3.0555

5 230.066 19.2969 9.0133 6.2561 5.0503 4.3874 3.9715 3.6875 3.4817 3.3258 3.2039 3.1059 3.0255 2.9582 2.9013

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Table: distribution of F: alpha = 0.01 DFE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 7/1/2019

1 4063.25 98.5043 34.1141 21.1977 16.2582 13.7450 12.2466 11.2586 10.5612 10.0444 9.6461 9.3302 9.0737 8.8615 8.6830

2 4992.22 98.9977 30.8155 17.9994 13.2737 10.9246 9.5467 8.6492 8.0216 7.5594 7.2057 6.9266 6.7009 6.5148 6.3589

Number of Means 3 5404.03 99.1505 29.4553 16.6939 12.0599 9.7796 8.4512 7.5911 6.9918 6.5523 6.2167 5.9526 5.7394 5.5639 5.4170

4 5636.51 99.2654 28.7098 15.9766 11.3919 9.1482 7.8465 7.0060 6.4221 5.9943 5.6684 5.4120 5.2054 5.0354 4.8932

5 5760.41 99.3038 28.2359 15.5219 10.9670 8.7460 7.4605 6.6319 6.0570 5.6363 5.3160 5.0643 4.8616 4.6950 4.5556

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 31

5) ANOVA table: SOV Treatment Experimental error Total

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SS

DF

61.33

4

19.25 15

MS

F-cal

15.325 11.942

F-tab 0.05 0.01 3.08 4.89

1.283

80.55 19

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 32

6) Testing significance

 Since the calculated f value (11.942) is greater than tabulated f value at 0.05 (3.08) and

0.01(4.89)

levels

of

significance,

null

hypothesis is rejected.

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7) General conclusion:

There are significant differences in root length of papaya in response to different concentrations of BAP.

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8) Summary of results: Standard error (SE±) =

Coefficient of variation (CV%) =

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CV % is used to measure accuracy in which experiment is carried out  CV % in laboratory experiment should be less than 20%.

 CV % in Field experiment should be less than 40 %.  CV % in surveys experiment should be less than 60 %. 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 36

Table. 1 Effect BAP on Micro-propagation of Papaya (Carica papaya L.) Concentrations of BAP (mg/l) Mean of root length (cm)

0.0 mg/l

12.75

0.05 mg/l 1.0 mg/l 1.5 mg/l 2.0 mg/l

13.25

14.00

SE±

0.566

CV %

7.73

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15.75

17.50

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 37

Mean of root length (cm)

20

17.5

15.75 15

12.75

13.25

14

10

5 0 0.0 mg/l 0.05 mg/l 1.0 mg/l 1.5 mg/l Concentrations of BAP )mg/l)

2.0 mg/l

Fig. 1. Effect BAP on Micro-propagation of Papaya (Carica papaya L.) 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 38

Reference: Dafaallah, A. B. (2017).Fundamentals of Design and Analysis of Agricultural. Experiments (Observation – Experimentation –Discussion), Part One. First Edition. University of Gezira House for Printing and Publishing, Wad Medani, Sudan. Pp 246. Dafaallah, A. B. (2017). Fundamentals of Design and Analysis of Agricultural Experiments (Observation – Experimentation –Discussion), Part Two. First Edition. University of Gezira House for Printing and Publishing , Wad Medani, Sudan. Pp 204. 7/1/2019

Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 39

Thanks Dr. Awadallah Belal Dafaallah E-mail: [email protected]; [email protected] Tel: +249902295166

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