Help with simple mean comparison

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Help with simple mean comparison

This is going to be a really simple question for you all, but one that I need help with.  Sorry in advance, I feel a bit stupid even asking, but I am trying to learn.

First of all, what is it called when you assign a letters to means like the ones below?

Based on the grouping below, how would I interpret which treatments are significantly different?  What conclusions can I draw from these results?  Is treatment CM3 significantly different from Ctrl?

Tukey Grouping                       Mean      N    Treatment

                                   A        192.58      9    CM3

                                   A

                             B    A        183.69      9    CM2

                             B    A

                             B    A        161.21      9    CM1

                             B    A

                             B    A        156.47      9    BM3

                             B    A

                             B    A        147.69      9    BM1

                             B    A

                             B    A        142.30      9    BM2

                             B

                             B              128.63      9    Ctrl

And also for this one, which are significantly different, and what conclusions can I draw from these results?

Tukey Grouping                       Mean       N   Treatment

                                   A        2.5178      9    BM3

                                   A

                             B    A        2.3400      9    BM2

                             B    A

                             B    A        2.2800      9    CM3

                             B

                             B    C        1.8111      9    BM1

                                   C

                                   C        1.6689      9    CM2

                                   D        0.9756      9    CM1

                                   D

                                   D        0.9111      9    Ctrl

Thank you very much for your help in advance.  I really appreciate it!

-Adam


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‎11-18-2013 09:10 AM
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Posts: 2,655

Re: Help with simple mean comparison

Adam,

From the first output, I would say that CM3(192.58) is significantly different from Ctrl(128.63)--they have exclusively different letters.  Any of the other means are not significantly different from one another, or different from the two extreme mean values.

The second is a little more complex.  CM2, BM1, CM3, BM2 and BM3 are significantly different from Ctrl and CM1.  CM1 is not different from Ctrl.  BM3 is significantly different from BM1 and CM2.  CM2 is significantly different from BM3, BM2 and CM3.

Hope this is helpful.

Steve Denham

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‎11-18-2013 09:10 AM
Respected Advisor
Posts: 2,655

Re: Help with simple mean comparison

Adam,

From the first output, I would say that CM3(192.58) is significantly different from Ctrl(128.63)--they have exclusively different letters.  Any of the other means are not significantly different from one another, or different from the two extreme mean values.

The second is a little more complex.  CM2, BM1, CM3, BM2 and BM3 are significantly different from Ctrl and CM1.  CM1 is not different from Ctrl.  BM3 is significantly different from BM1 and CM2.  CM2 is significantly different from BM3, BM2 and CM3.

Hope this is helpful.

Steve Denham

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Re: Help with simple mean comparison

Posted in reply to SteveDenham

Thank you for your help, Steve!

For the second one, are BM2 and BM3 significantly different from BM1?

Respected Advisor
Posts: 2,655

Re: Help with simple mean comparison

BM3 is significantly different from BM1 (A vs BC), while BM2 is not significantly different from BM1 (AB vs BC).  In the first comparison, there are no letters in common, while in the second, the letter 'B' is common to both.

This sort of labeling of means was developed in the agricultural sciences literature, which was the first real target for SAS.

Steve Denham

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