I suppose you could compute the correlation on the data you have, and use that. Or if there are published studies done in your field on similar data with similar study design, you could use the correlation from those studies. Or lastly, you could use your subject matter knowledge to come up with an estimate of the correlation.
Your problem statement seems to indicate you are going to use the Satterthwaite t-value as the correlation (am I understanding that properly)? That does not seem appropriate to me.
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Paige Miller