The bedrock of statistical power is "N" sample size. Suppose the group standard deviations are about the same, then a pooled estimate of the std dev's can be compted. Then if you have some assurance that each group has a minimum number of independent samples, that minimum number could be used for each group's sample size, and a worse case (lowest power) decision could be made. Similar to ANOM, Analysis of Means, assume minimum N =3:
Plot the group means, Y, versus the groups , X.
Add 3 reference lines to the Y axis: (1) the average of the group means; (2) that average + k*pooled std dev/sqrt(n); (3) that mean - k*pooled std dev/sqrt(n) where k =Tukey HSD Quantile( .95, #groups, #groups*(3-1) ), assuming minimum N =3,
This is a visual exploration of means that are different from the overall mean. I was reluctant to respond, because this is a "what if" analysis, and the summary data could be biased by extreme outliers, etc.
I have some formulas to compute the ANOVA using summary data, however, I found this JMP Usage Note circa JMP 8 http://www.jmp.com/support/notes/35/253.html that provides a surrogate method, attributed to David A. Larsen, to compute a Oneway Anova with summary data. It creates a visual display. This method doesrequire N. I decided to write a simple script (caveat emptor, not much testing) to implement the method via a function SummaryAnova(). The script is attached with a usage example. The attached script example:
uses the JMP sample data table Typying Data.jmp;
computes the raw data anova; creates a summary table;
then calls the SummaryAnova() function to perform the surrogate analyses.
While the statistical tests are the same, it is not as informative as raw data to look for outliers and perform subsequent analyses.
I suppose this could be used which an assumed minimal N to do a worse case "what if" analysis.
Without N, that is all I have. It always amazes me that so many summary reports that do not include N and N Missing. It is critical to any analyses.
Oops I had a scoping error in the previous version of the script. The updated versions is attached. Read on for a discussion of teh scoping error.
The script tasks were
SummaryOneway function scripting
Names Default to Here(1)
Regular oneway with raw data
Create summary table
The last task throws an error because the function was defined outside of the Here scope, so to run, I could have changed the last task to ::SumaryOneway. Instead I made Names Default to Here(1) to be tht first task.