Unfortunately the only way to conduct a repeated-measure ANOVA is to have the actual pairs of data values.  Nothing prevents you from treating the within-subject variable as between-subject.  Afterall, the within-subject design was saving you a degree of freedom so without it your making support for your hypothesis harder.  That is, any statistically significant result you get with a between-subejcts analysis would also be significant if it were within-subject.  You could calculate it by hand from means and SD (and N), or use an online stats calculator like the link below.  Hope this helps Renato! ~ Kevin

http://graphpad.com/quickcalcs/ttest1/?Format=SD

Unfortunately the only way to conduct a repeated-measure ANOVA is to have the actual pairs of data values.  Nothing prevents you from treating the within-subject variable as between-subject.  Afterall, the within-subject design was saving you a degree of freedom so without it your making support for your hypothesis harder.  That is, any statistically significant result you get with a between-subejcts analysis would also be significant if it were within-subject.  You could calculate it by hand from means and SD (and N), or use an online stats calculator like the link below.  Hope this helps Renato! ~ Kevin

http://graphpad.com/quickcalcs/ttest1/?Format=SD

I was about to offer a similar suggestion. But Kevin's is better. Thanks for the link too!

Great advise from Kevin! But why don't you have the raw data to your experiment, Renato?

Hey Rainer, 

So it is a long story, so here we go:

I am studying cardiovascular function in reptiles. These animals typically have two aortas - left and right - so in order to measure total blood flow I measured only the flow in the left aorta and estimated total flow based on this recorded value. To do so, in a previous experiment I calculated a correction factor that had, of course, a standard deviation. So what i had to do is to calculate the standard deviation of the product of two variables - correction factor and left aorta blood flow. So now I have the values of mean, standard deviation and sample size (n) of total flow, but I don't have the individual values for total flow. If you have any suggestions, I would be more than happy to hear it!  :-)

Do you actually *need* total flow? Why can't you just use the left-aorta flow only?

Logically, the flow from one aorta will be directly proportional to the flow from both aortas. You get a number that can be related to your other cardiovascular functions - the same as if you were measuring millilitres per second, or cubic inches per minute - it's just a number. This should hold unless the ratio for Left/Right aortas is different for different species of reptile.

(I'm not a zoologist/anatomist/biologist so I won't feel threatened if I'm totally wrong.)

Hi Hume, I have recently been considering this possibility of using left aorta blood flow alone as you mentioned. The problem is that from total blood flow I have to calculate several indexes that I can not calculate with left aorta blood flow alone, hence, so far calculating total blood flow is the only way I can get to respond my hypothesis indeed, but I will put a hard thought on this idea as well :-)

Hi, I'm coming to this with a similar problem. I have only means, standard deviations and sample sizes. I have calculated all the f and p values by hand using  between-subjects ANOVA logic, and I'm happy with my results, but I'm not convinced that it is valid to do a between-subjects ANOVA on within-subjects data. I tested a repeated-measures data set on my own in SPSS, and 5/7 of the p values were lower for the repeated-measures ANOVA than for the univariate ANOVA, but the fact that 2 were not makes me doubt that the univariate is always more conservative. So the question is, how can I be sure that the values from my univariate ANOVA are valid? And secondly, is there a paper I should cite in support of my claim that it is valid?

 In fact, the more I think about it, the more I doubt that it is valid. Doesn't having repeated measures data violate the assumption of independence crucial to a univariate anova?

A within-subject ANOVA does not violate the assumption of independence because we mean *logical* independence of the numbers.  For example, if we wondered if some kind of test questions are harder than others, we could calculate the percent correct for each student for his or her multiple-choice, fill-in-the-blank, and essay items (i.e., within-subject).  Those percents are independent because there's no logical reason that somebody couldn't get 100% on one kind and 0% on another, or vice-versa, or any combination of percents in between.  So, even though empirically students' percents are probably highly correlated (due to students knowledge, conscientiousness about studying, etc.), the math doesn't necessitate that.  It *would* violate the assumption of independence to compare (for example) multiple-choice percent to the overall percent because *logically* (mathematically) the overall percent incorporates the multiple-choice percent.

I'm concerned about your other point Christopher!  I'm afraid, I'm wrong, because it is genuinely possible to have a significant between-subjects test and have that significance go away when it's analyzed within-subject.  I just used Excel to create 500 random data sets (20 pairs of "A" and "B" numbers, with a fixed difference of 9 and error variance for each number by randomizing up to +/-20).  For each I calculated the paired-sample t-test and the independent sample t-test (w/ Excel formulas).  I get about half with higher independent p-values (as expected) and half lower (contrary to expectation).  Studying it further, I realize there's a very specific pattern.  If the correlation between A and B is positive, p-value always favors the within-subject analysis, and the range of differences favoring the within-subject design gets bigger the larger the positive correlation.  But the pattern is exactly reverse if the correlation between A and B is *negative*!  So it looks like we can only safely use the between-subjects test as an alternative to a within-subjects test if it's reasonable to assume that the values are positively correlated.  

Hi Kevin, thanks for you response and for looking deeper into the issue.

http://statpages.info/anova1sm.html  Simple as it gets.