If there are no "pathologies" in the data, the following would be a likely explanation.
The over test is not significant because the differences among all the various treatments and the control are not large enough to be convincing. The overall test is kind of generic. It is looking for whatever differences there might be. The Dunnett test is more specific. It is looking for differences between each treatment and the control; it does not care whether the treatments are similar. Because the Dunnett test is more specific, it has more power than the overall test to detect differences between treatment and control.
Note, however, that you may have a fairly "borderline" situation. Any test you do will sometimes produce false positives or false negatives. Running multiple tests increasing your chances of falsely declaring a difference and decreases your chances of falsely missing a difference. Any decision you make may be wrong. It is important to ask, "What are the consequences of incorrectly saying that the difference is or is not significant?" The alpha and beta error rates can help quantify this, but describing how is beyond the scope of a quick Email answer.
One way to simplify things would be to calculate confidence intervals for all the differences of interest. You'll probably want to use "experimentwise" confidence intervals rather than "comparisonwise" confidence intervals.
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Emil M Friedman, PhD
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----- Original Message -----
From: "Alan Sharpe" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Wednesday, July 09, 2003 4:40 AM
Subject: ANOVA with Dunnetts
> Allstatters,
>
> Could anyone tell me what the most likely explanation or justification is
> for when a 1-way ANOVA indicates that no difference exists between
> treatment means, but a Dunnetts test indicates a difference between the
> control and one of the treatments.
>
> Thanks in advance
> Alan Sharpe
>
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