I'm wondering if there is a way to do an ANOVA having only group means, group sd and group n. I have only seen this done in trivial cases, a 1-way ANOVA with a balanced design, usually in a teaching context. But I need it for a 4-way ANOVA with unequal variance, unequal cell sizes and with 2 nested effects. I've tried to "reverse engineer" the anovan code but without much success so wanted to ask if anyone has any experience in this area.

> I'm wondering if there is a way to do an ANOVA having only group means, 
> group sd and group n. I have only seen this done in trivial cases, a 1-way 
> ANOVA with a balanced design, usually in a teaching context. But I need it 
> for a 4-way ANOVA with unequal variance, unequal cell sizes and with 2 
> nested effects. I've tried to "reverse engineer" the anovan code but 
> without much success so wanted to ask if anyone has any experience in this 
> area.

What are your groups?  If they're defined by single predictors, I believe 
this could not be done.  If each distinct combination of your predictors 
defines a group, it should be possible though I have no software to offer 
that expects this type of input.

-- Tom 

 > What are your groups?  If they're defined by single predictors, I believe 
> this could not be done.  If each distinct combination of your predictors 
> defines a group, it should be possible though I have no software to offer 
> that expects this type of input.

The groups are not defined by a single predictor but by each distinct combination thereof. However, many of these groups are missing, i.e., unsampled in a random effect (and nested) sense. I think I am up a creek here so to speak and am looking at using Monte Carlo simulation for the whole mess. With the xbar, sd, and n I can generate random normal variables, bootstrap and then apply some notion of mean pval (probably the mean MC ANOVA) to get at effects wrt Ho. 

> The groups are not defined by a single predictor but by each distinct 
> combination thereof. However, many of these groups are missing, i.e., 
> unsampled in a random effect (and nested) sense. I think I am up a creek 
> here so to speak and am looking at using Monte Carlo simulation for the 
> whole mess. With the xbar, sd, and n I can generate random normal 
> variables, bootstrap and then apply some notion of mean pval (probably the 
> mean MC ANOVA) to get at effects wrt Ho.

This is a good idea.  In principle you have all the information you need to 
do the anova directly.  In practice, recreating data to reproduce that 
information may be the easiest way to proceed.

If you use random data for each group having exactly the desired mean and 
standard deviation, you should be able to get what you want and not have to 
do repeated Monte Carlo simulation.  Send me an e-mail directly if you want 
a pointer.

-- Tom 

This may be of interest:

http://www.psych.nyu.edu/cohen/Calc_ANOVA.pdf

To whit: "... an alternative formula for the calculation of [ANOVAs], which requires only the mean, standard deviation, and size for each cell"

Also includes formula for unbalanced designs, and a worked example.

Is all very accessible, though I'm not in a position to comment on its validity.

Best,
pete

"C Schwalm" <schw0516.nospam@umn.nospam.edu> wrote in message <gfnh2h$dov$1@fred.mathworks.com>...
> I'm wondering if there is a way to do an ANOVA having only group means, group sd and group n. I have only seen this done in trivial cases, a 1-way ANOVA with a balanced design, usually in a teaching context. But I need it for a 4-way ANOVA with unequal variance, unequal cell sizes and with 2 nested effects. I've tried to "reverse engineer" the anovan code but without much success so wanted to ask if anyone has any experience in this area.