Technical Report - International Military Testing Association

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A comparison of the two Set8 or’ statbtics will reveal differences
due to rounding error. The amount of this rounding error 18 basically
controlled by the number of decimal placea compb:atfonr are curried out
to before the rounding process is introduced. The raw acore mean and
standard deviation will contain rounding errors 8~ Viii each itcm’p-.
value and point-biserial correlation. The production and surming of
reliability Fndictr vi11 result in varying mounts of rounding error
in the derived mean and ottndard deviation. Consequently, the difference
batvttn tha derived mean and standard deviation and the mean and standard
* deviation based on the raw 8COitl vi11 vary froai ttlt to tert.
One method that may be used to interpret the tlgniflconce of these
difference8 conaisto of developing an empirical probability table of
differences bared on data of known reliability. In its simplest form,
thlr table would be produced by deriving means and standard deviations
from a rample of one to two hundred eets of item analysis data, then
comparing them vith mt@nS and standard deviations developed fran their
respective raw score di&tributiona. The mean and standard deviation
of the distribution of abroluta differences would form a rough probabi1it.y
table which may be used In evaluating re8ult8 from future u&e of the
interprogram method.
If canputations art carried cut to the fifth decimal places before
rounding, the difference between there #et6 of mtdns and etandard &viationo
due to rounding error vi11 be minimal. Consequently, any difficulty
that may occur in any of the three programs vi11 yicid rtsulte eubstantially
outride those indicated in the rxnplrcal probability table.
Under these conditions, the Jnttrprogram mtt’md can ba a prtcirt
method of checking machine produced item analysis.
The actual vorking time required, which includtr the running of
thb* item-test covariance progrm to arrive at the final rtoultr, 18
approximately one hour par thirty-two ratem, or thirty-tvo 150 quertion
teats.
The primary value of this method is to provide a precise and
relatively quick check of sttm of itan analycllr data that will � tparatt
out the nicety-five percent that is completely accurate.
In thoaa instancea where the differences between the derived and
raw #core � tsns and rtandard deviations art too great to be accounted
for by rounding error, the difficulty may be in the raw score. the
item analyria or derived rteult8, or finally an error In checking the
derived results againrt the raw score results.
Reference
Cullikrtn, Ii., Theory of mental ttatu.
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105
New York: Wiley, 1958.
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