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## Have means, standard deviation, min, and max data for various groups. How to do statistical tests?

Hello,

I have multiple groups which each have a mean, min, standard deivation and max value. I don't know how many samples there were. How would I do statistical tests such as ANOVA with this data set?

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Super User

## Re: Have means, standard deviation, min, and max data for various groups. How to do statistical test

TUStudent,

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  does require 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.

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Super User

## Re: Have means, standard deviation, min, and max data for various groups. How to do statistical test

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.

//--------------------------

• SummaryOneway function scripting
• Names Default to Here(1)
• Regular oneway with raw data
• Create summary table
• SummaryOneway()

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.

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