I'm in the process of updating a meta-analysis and in one of the new studies, effect sizes are reported as Tau-U. Two of the effect sizes are reported as Tau-U = 1.00.
I am using Andy Field's meta-analysis syntax for SPSS.
For the meta-analysis, I have been converting effect sizes to Pearson's r. When I convert a Tau-U of 1.00 to r, using the syntax created by David Walker, it stays as 1.00.
When I put a perfect r value (i.e., r = 1.00) into Field's SPSS syntax, however, I get a divide by zero error because the syntax is converting the r-values to z-values.
How should perfect effect sizes like this be handled? Should I remove them from the analysis? I can't seem to find any guidance on this and would very much appreciate someone at least pointing me in the right direction.
Hello Matt,
The simple answer would be, avoid using that syntax!
You don't indicate the type of study or effects you're researching, but since tau-u often is applied to single subject research, it is important to recognize that there may well be complete absence of overlap across phases, such that an absolute value of 1.0 is indeed possible (whereas, in real life, it is highly unlikely that one would observe a correlation of +/- 1.0 in scores on two continuous variables). It might make sense to consider a different metric, such as non-overlap, for your ES if you're trying to aggregate results of SS design studies.
If you must continue with the syntax, substitute a value of .99 for the observed Tau of 1.00. That will bias your results slightly, but it is unlikely to make much difference, especially if values of 1.00 are rare and you have a moderate to large number of effect estimates/studies in your data set.
Good luck with your work.
During a meta-analysis with correlations, a correlation is first transformed to the Fisher's z scale. During this process, as you can see in the attached file showing the conversion to the Fisher's z scale, the z will go to infinity if the correlation equals one. In this case, I just set the correlation to 0.999999..... (i.e., a number very close to one).
Be suspicious. I would check the methods for a clue and pay close attention to the sample sizes. I would check any transformations. If everything else checks out, then Gordon's answer seems reasonable.
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