12DMRT bisa menjadi salah satu dari mereka yang tidak

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12 Duncan's multiple range test (DMRT)

Presentation · September 2019

DOI: 10.13140/RG.2.2.16262.93764

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Awadallah Belal Dafaallah

Faculty of Agricultural Sciences, University of Gezira, Sudan 85PUBLICATIONS 119CITATIONS

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Comparisons of

Means Procedures

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7/1/2019 Design and Analysis of Agricultural Experiments - Dr. Awadallah Belal Dafaallah 2

Introduction:

 Comparisons of means procedures are also

noun as means separation or multiple comparisons.

 They are not statistical designs.

 They are methods or means of comparing different statistical means or averages within the designs.

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 In any design in AVOVA table, F-cal for treatments can be either significant or not significant.

 If F-cal for treatments is not significant (there are no real differences between the treatment means), therefore, there is no need to compare the treatment means.

 If F-cal for treatments is significant (there are real differences between the treatment means), therefore, there is a need to compare the treatment means.

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 Then, F-test just shows without the details of

whether there are real differences between the treatment means or not.

 To get the real differences between the

treatment means we use means separation methods which could be classified into two types of tests.

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Comparisons of means procedures Tests planed before

carrying out the experiment

Orthogonal contrasts

Orthogonal polynomial contrast

Tests planed after carrying out the experiment

LSD.

DMRT Tuky’s test

Norman – Keules test Scheffes test

Dunnett test

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Duncan's multiple range test (DMRT)

 DMRT is one of the most common methods used in comparing treatment means.

 This test is summarized the way in finding

several significant differences with increasing values which, depending on the extent of the distance between the treatment means after arranged or organized.

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The use of DMRT :

 It is used whether F-cal for treatment is significant or not.

 It is used to make all possible comparisons between treatment means.

 It is used to compare the mean of control treatment with the rest of the treatment means.

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An example:

 With reference to the example No (1), where

the aim is to study the effect BAP on micro- propagation of Papaya (Carica papaya L.).

 After experiment carried out insuring that F-cal for treatments is significant, the researcher decided to use DMRT.

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Table. 1 Effect BAP on Micro-propagation of Papaya (Carica papaya L.)

Concentrations of BAP (mg/l)

0.0 mg/l

0.05 mg/l

1.0 mg/l

1.5 mg/l

2.0 mg/l Mean of root

length (cm) 12.75 13.25 14.00 15.75 17.50

SE± 0.566

CV % 7.73

• Number of treatments = 5

• Number of replicates = 4

• Degree of freedom = 15

• Mean squares = 1.283

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Least significant range

Standard error

Studentized significant range

Steps for DMRT:

Least significant range is calculated from the following equation:

Where:

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1) Calculate standard error of mean.

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2) Get the SSR values from Duncan's table with:

 Level of significance or probability: 5%

 Degree of freedom for treatments: 4

 Degree of freedom for error: 15

Number of

means 2 3 4 5

S.S.R 3.0143 3.1634 3.2342 3.3125

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dfe Number of Means

2 3 4 5 6 7 8 9 10

2 6.0849 8.3308 9.7980 10.8810 11.7340 12.4345 13.0266 13.5381 13.9875 3 4.5007 5.9096 6.8245 7.5016 8.0370 8.4780 8.8521 9.1766 9.4620 4 3.9265 5.0403 5.7571 6.2870 6.7065 7.0528 7.3465 7.6015 7.8264 5 3.6354 4.6017 5.2185 5.6731 6.0329 6.3299 6.5823 6.8014 6.9947 6 3.4605 4.3390 4.8956 5.3049 5.6285 5.8953 6.1222 6.3192 6.4931 7 3.3439 4.1648 4.6812 5.0601 5.3591 5.6058 5.8154 5.9975 6.1581 8 3.2612 4.0410 4.5288 4.8858 5.1672 5.3991 5.5962 5.7673 5.9183 9 3.1991 3.9485 4.4149 4.7554 5.0235 5.2444 5.4319 5.5947 5.7384 10 3.1511 3.8768 4.3266 4.6543 4.9120 5.1242 5.3042 5.4605 5.5984 11 3.1127 3.8195 4.2561 4.5736 4.8229 5.0281 5.2021 5.3531 5.4863 12 3.0813 3.7728 4.1985 4.5076 4.7477 4.9469 5.1159 5.2625 5.3946 13 3.0553 3.7341 4.1509 4.4529 4.6897 4.8841 5.0490 5.1920 5.3181 14 3.0332 3.7014 4.1105 4.4066 4.6385 4.8290 4.9903 5.1300 5.2533 15 3.0143 3.1634 3.2342 3.3125 4.5947 4.7816 4.9399 5.0770 5.1979

Significant Studentized Range: alph value=0.05

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Number of

means S.S.R L.S.R.

2 3.01 0.566 1.71

3 3.16 0.566 1.79

4 3.23 0.566 1.83

5 3.31 0.566 1.87

3) Calculate lest significant range as follow:

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4) Organize or arrange treatment means ascending or descending.

5) Table of mean differences.

6) Compare differences with lest significant range values.

7) Results and discussion.

Same as mentioned before

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Treatment number

Concentration of BAP

Means arranged descending

Mean differences

T_i-T₅ T_i-T₄ T_i-T₃ T_i-T₂ 5 2.0 mg/l 17.50 4.75^

(1.87)

4.25^ (1.83)

3.50^ (1.79)

1.75^ (1.71) 4 1.5 mg/l 15.75 3.00^

(1.83)

2.50^ (1.79)

1.75^ (1.71) 3 1.0 mg/l 14.00 1.25^Ns

(1.79)

0.75^Ns (1.71) 2 0.5 mg/l 13.25 0.50^Ns

(1.71) 1 0.0 mg/l 12.75

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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.

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Thanks

Dr. Awadallah Belal Dafaallah E-mail: [email protected];

[email protected] Tel: +249902295166

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