jay warner had earlier elaborated on the use of the term ... "item
independence" ... to mean that the position of an item in the test would
not impact on the likelihood of examinees answering the item correctly or
not ... yes ... this is usually the meaning given to that term
but, i would like to mention some (two) caveats to this
first, we are assuming of course a power kind of test ... that is, time is
sufficient to work on all the items ... and it is your knowledge about the
item that will determine if you answer it correctly or not (available test
time is not a factor)
second, but more subtle, is the idea that in a general purpose test (say
first test in stat 101), there generally will be only ONE item per idea ...
concept ... objective ... thus, information from one item is highly
unlikely to aid an examinee when encountering other (later coming) items
... BUT, this arrangement does not have to be ...
think about a test that is ONLY on the standard deviation ... and it has 10
items. now, we might have 10 totally different kinds of items, though still
all related to the standard deviation OR, we might have 10 items ... 4 of
which present you with some numbers, and then ask you to calculate the
standard deviation ... let's say that you have items 1,3,5, and 7 ... like
this ... it seems that the probability of answering say 5 and 7 gets better
having had 1 and 3 first ... DUE TO PRACTICE, REMEMBERING SOMETHING BASED
ON HAVING HAD TO WORK 1 AND 3 FIRST ... than if you only put (say) #7 on
the test ...
so, when we say items are independent of one another in the sense used by
jay ... this necessarily means some ancillary assumptions too ...
the difficulty of course in interpreting an aggregate TOTAL score is one of
saying that (on the 10 item test above) ... a score of 6 versus 5 ... or 9
versus 8 ... in each case ... the higher score is interpreted as meaning
you have one more unit of information or knowledge than the next lower
score ... but, if there are position effects (non independence), then it
makes it much more difficult (and probably inaccurate) to interpret
differences in scores that way ...
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