ANOVA analysis with only mean and standard deviation

This is probably a silly question, but how can I run ANOVA using only the mean, standard deviation, and the sample size?

i.e.

Group  mean    sd    n
1:    200      5    5
2:    100     22    5
3:    150     14    5


I am using Statsoft Statistica software.

I know how to run it using the spreadsheet with all the data, but I have never done this using only the information listed above.

Any information would be greatly appreciated.

• Hi Shinobi. As things stood, your original question "How do I make Package-A do calculation-X?" did not appear to be on topic for CrossValidated. I have edited it to be more clearly on topic (as well as fixed up some of the formatting). If you disagree with my edits, you can revert it to undo my changes, but then you should edit subsequently to present a statistical question rather than a "what buttons do I press in my package" question, or you can revert it without editing and flag it so the moderators can move it to StackOverflow. If you only disagree with some of my changes, you can edit it May 1, 2013 at 1:50
• You should also check that your original "+/-" values were definitely s.d.s and not standard errors of means or some other quantity (as @JeremyMiles pointed out). I reiterate it here because those "+/-" symbols disappeared in my edit - but the concern that these may not really be standard deviations remains. May 1, 2013 at 7:15

1 Answer

I don't know about Statistica, but this will work in any program.

Generate some random data of the correct sample size, once for each group.

Standardize it. Multiply it by the standard deviation. Add the mean.

Combine the groups.

Run your anova.

BUT: You say N=5, that makes me think you've got repeated measures. If that's the case, you don't have enough information, as you also need the correlations.

Are you sure +/- means SD? D don't like using +/- because it's not clear what it means - standard deviation, standard error, or confidence interval. If those are your real data, those are enormous differences.

• +1 I'd have been inclined to vote this question for closure as off-topic here (and indeed was just about to), but your general solution seems to make it highly useful for future users and more clearly relevant for CV. May 1, 2013 at 1:39
• Yes I am using St. Dev. not St. Err. (I should have made that more explicit). While this is not my actual data, the differences are huge and will be significant, I just need a p-value for completeness. May 1, 2013 at 13:39