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Hi David;

Sorry for the delay in responding. This is really a complex subject and is really beyond the realm of technical support. You should consider talking to a consulting statistician about this.

If the residuals do not follow a normal distribution then transforming the data is an option. A transformation of the response may or may not exist which makes the residuals follow a normal distribution. If not, then you might be able to use one of the non-parametric methods to investigate the data. You could possibly use Stat > Non-parametrics > Kruskal-Wallis.

The assumptions of normality of the residuals and the randomness of the residuals are important. If one or the other is violated, there are not a lot of statistical options available. If you can find an appropriate transformation of the response, then this leads to the questions that you raised. We don't have the answer. There may not be a way of getting a precise multiple comparison.

Once you collect your data, I would be happy to take a look at the data. I might be able to give you some general suggestions or point you in the right direction.

Sincerely,
Cathy - Technical Support




--------------------------------------------------------------------------------
From:
Sent: Friday, February 20, 2004 8:33 PM
To:
Subject: RE: Minitab Technical Support


Hi Cathy,



Sorry for late reply! I've been on leave since last E-mail.



The test data is not available now. But I'm afraid if the data needs to be transformed. Then can I make multiple comparisons on transformed data to detect the difference of original data? Even the transformation is strictly monotone, the transformation would increase or decrease the distance between the groups. How can I make a precise multiple comparisons in that case?



Thanks!







-----Original Message-----
From:
Sent: Thursday, February 12, 2004 7:34 AM
To:
Subject: RE: Minitab Technical Support



Hi David;



We didn't say that were troublesome. You have an inquisitive soul!



The situation that you described is statistically possible. There are a couple of reasons why this could occur.



  1. There are 2 assumptions made for an ANOVA: 1. The residuals will have a normal distribution and 2. The variance of the data in group A is approximately equal to the variance in the other 2 groups. First, check these assumptions before comparing the means of the groups. If either of these assumptions is violated then you should not do these multiple comparisons.



  1. The results of the multiple comparisons indicate that there is PROBABLY no significant difference between A and B and that there PROBABLY is a significant difference between A and C. There is room for error.



If you send me your project, I can take a closer look and let you know what I think

Thanks,

Cathy

-----Original Message-----
From:
Sent: Sunday, February 08, 2004 10:54 PM
To:
Subject: RE: Minitab Technical Support

Hi Cathy,



Thanks for your help!



Another question: when I use Minitab to make a multiple comparison, there may be a contradict result for pairwise comparison. For example:



In the first run( treat A substract from treat B, treat C), there is no significant difference between treat A & treat B, but there is significant difference between treat A & treat C: treat A = treat B; treat A ¹ treat C



In the second run(treat B substract from treat C), there is no significant difference between treat B & treat C: treat B = treat C.



Can't we say treat A = treat C because treat A=treat B; treat B=treat C? Then how to explain treat A ¹ treat C in the first run?



Is there any other methods in Minitab to make a comparison on all combination of treat at one time(not pairwise) to avoid this kind of contradiction?



Thanks for your patience!



Regards,
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