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You're able to blank the chart by using the following formula: WINDOW_SUM(SUM([Number of Records])) >= 10 and excluding False in the filters (or selecting only True). I think this is what you were trying to do using SIZE().
You should then be able to bring up another worksheet in place of the now blank worksheet containing your message. Check this great post by Joe Oppelt and Matt Lutton for details: We made a video of Sheet Swapping and Legend/Filter Popping on a dashboard.
Andrew, your formula worked, thank you!!
FYI for anyone else attempting to do this -- to make the filter work properly across multiple worksheets, I had to go into the Filter shelf in each worksheet and set "Compute Using" to the dimension the worksheet is based on (in the CEO example, the dimension was "CEO Compensation Type"). This hides any column without a sample size meeting the threshold (here, 10). The default is "Table (across)", which can have unintended effects.
I haven't yet attempted the sheet swapping, but thanks for pointing me to the video.