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provide a reasonable basis for estimating inventory shrinkage.
Dr. Bates’ principal criticism of Dr. Roberts’ conclusion is that
Dr. Roberts’ correlations are not relevant to analyzing the
accuracy of the KFS division shrinkage accruals because Dr.
Roberts’ correlations measure the tendency of shrinkage to vary
in proportion to sales from inventory to inventory and store to
store within each department and KMA rather than the tendency of
annual shrinkage for the business to vary in proportion to annual
sales for the business. Dr. Bates is of the opinion that it is
correlation of year-to-year changes in business level shrinkage
and sales that is relevant to determining the accuracy of
shrinkage accruals. Dr. Bates states: “[Dr. Roberts’] more
restricted conclusion is technically correct, but irrelevant for
assessing the propriety of accruing shrinkage as a percentage of
sales for tax purposes.”
In his oral testimony, Dr. Roberts made clear to us the
limitations of any conclusions to be drawn from a consideration
of statistical correlation. A strong correlation between two
variables (e.g., shrinkage and sales) does not necessarily mean
that one can predict the value of one variable (e.g., shrinkage)
based on the value of the other (e.g., sales). To say that there
is a strong correlation between two variables means only that
there is a strong linear relationship between the two.
Neither Dr. Bates nor Dr. Roberts finds the other's
computation of correlation inconsistent with his own. That is
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