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### ANOVA without raw data

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```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.
```
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Reply schw0516.nospam (27) 11/15/2008 10:05:05 PM

```> 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

```
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Reply tlane (589) 11/16/2008 4:03:26 AM

``` > 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.
```
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Reply schw0516.nospam (27) 11/16/2008 5:59:03 PM

```> 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

```
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Reply tlane (589) 11/17/2008 6:22:44 PM

```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.
```
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Reply peter4330 (4) 7/31/2012 10:24:14 AM

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