The formula you are trying to use is inappropriate for Likert scale data. The
formula you cited is good for binary data (i.e. proportions). You need to use a
variant of that formula:
n =(z-sq)(greatest variance)/me-sq
Where z is the z-score, say 1.96 for 95% confidence.
greatest variance is the variance on the question with the
greatest variance among the questions asked.
me-sq is the margin of error squared.
To use this you should do a pilot study of your questions to obtain a
variance figure from your Likert scale data. I know of no technique for
determining sample size w/o having some idea of your variability up front.
Hope this helps.
Al Ovedovitz
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