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ANOVA and LSD TEST - contrasting results

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ANOVA and LSD TEST - contrasting results

Roberto
This post was updated on .
Dear all,
concerne to my issue, I obtained different results between ANOVA and LSD TEST (agricolae package), and I ask me why




>anova <- aov(SS ~ Treatment*Lot)
>summary(anova)

                     Df    Sum Sq   Mean Sq F value Pr(>F)
Treatment           7 0.0000534 7.622e-06   1.107  0.374
Lot            2 0.0000059 2.954e-06   0.429  0.654
Treatment:Lot 14 0.0001038 7.412e-06   1.077  0.401
Residuals            48 0.0003304 6.883e-06    

> LSD.test(anova, "Treatment")

Study:

LSD t Test for SS

Mean Square Error:  6.883013e-06

alpha: 0.05 ; Df Error: 48
Critical Value of t: 2.010635

Least Significant Difference 0.002486659
Means with the same letter are not significantly different.

Groups, Treatments and means
a        A1     0.03112188
ab       A2      0.03087886
ab       B1     0.02979624
ab       C1     0.02966558
ab       D1      0.02964944
ab       D2     0.02913658
ab       B2      0.02891764
 b       C2      0.0284452

how is it possible? my mistake to set anova?

Best regards,
Roberto
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Re: ANOVA and LSD TEST - contrasting results

John Sorkin
Roberto,
Please be more specific. What are the differences between ANOVA and LSD that give you concern?
John

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

>>> Roberto <[hidden email]> 11/19/2011 6:10 AM >>>
Dear all,
concerne to my issue, I obtained different results between ANOVA and LSD
TEST (agricolae package), and I ask me why




>anova <- aov(SS ~ Treatment*Lot)
>summary(anova)

                     Df    Sum Sq   Mean Sq F value Pr(>F)
Treatment           7 0.0000534 7.622e-06   1.107  0.374
Lot            2 0.0000059 2.954e-06   0.429  0.654
Treatment:Lot 14 0.0001038 7.412e-06   1.077  0.401
Residuals            48 0.0003304 6.883e-06    

> LSD.test(anova, "Treatment")

Study:

LSD t Test for SS

Mean Square Error:  6.883013e-06

Trattamento,  means and individual ( 95 %) CI

            SS      std.err replication        LCL        UCL
A30 0.02966558 0.0019037856           9 0.02583776 0.03349340
AM  0.02844520 0.0005186885           9 0.02740230 0.02948809
C30 0.02913658 0.0006792219           9 0.02777092 0.03050225
CM  0.02964944 0.0005398926           9 0.02856391 0.03073496
T30 0.02979624 0.0006920447           9 0.02840479 0.03118769
TS  0.02891764 0.0004981543           9 0.02791603 0.02991924
V30 0.03112188 0.0005157621           9 0.03008487 0.03215889
VM  0.03087886 0.0006874520           9 0.02949664 0.03226107

alpha: 0.05 ; Df Error: 48
Critical Value of t: 2.010635

Least Significant Difference 0.002486659
Means with the same letter are not significantly different.

Groups, Treatments and means
a        A1     0.03112188
ab       A2      0.03087886
ab       B1     0.02979624
ab       C1     0.02966558
ab       D1      0.02964944
ab       D2     0.02913658
ab       B2      0.02891764
 b       C2      0.0284452

how is it possible? my mistake to set anova?

Best regards,
Roberto


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Re: ANOVA and LSD TEST - contrasting results

Roberto
First of all, thank you for the reply to my topic.

Anova summary has shown no significative difference into Treatment (Pr 0.374), otherwise LSD Test has shown difference between 2 Treatment.
I suppose that's something strange.

Roberto

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Re: ANOVA and LSD TEST - contrasting results

Peter Dalgaard-2

On Nov 19, 2011, at 15:37 , Roberto wrote:

> First of all, thank you for the reply to my topic.
>
> Anova summary has shown no significative difference into Treatment (Pr
> 0.374), otherwise LSD Test has shown difference between 2 Treatment.
> I suppose that's something strange.
>

It isn't. You need to read up on "familywise error rate" and its connection to LSD and Tukey HSD tests (Google gets you there soon enough; I doubt people in here will rewrite textbook material just for you).

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: [hidden email]  Priv: [hidden email]

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Re: ANOVA and LSD TEST - contrasting results

Roberto
I didn't meant to rewrite textbook. I asked only for a clarification to my doubt, because I have started to study statistic recently.
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