Obraz (127)

In- class item analysis ci correlation

Corrclation is a mcasurc of thc extent to which two scts ot measurcmcnts, madę on the same population, agree in the way they rank or classify that population. If they agree totally, we have a perfecl positive correlation of + 1.0. Most positivecorrelations will o! course be lower than this. Not all cigarette smokers develop lung cancer, for example. but a significant proportion do. The le\cl of significance can be stated. and we can say: such a correlation would only occur by chance 5 times in 100, or once in 100 times. etc. We can also have a ncgativc corrclation. For example if, of 100 sailors, the 5 talłest do not work in submarines, whereas a good number of thc rest do, we have a perlect negative correlation, in this group, between the two categories ‘height and ‘working in submarines*.    ____

d) correlation for ąuessing

lt is sometimes thought that successful guessing, in the absencc of Ą knowledge, can havc a substantial ełTect on multiple-choicc test rcsults. This is not the case, in a test of reasonable length, provided a correction is madę to allow for ^uch guessing. The students must of course, in fairness, be told beforehand that wrong answers will be penaliscd, not simply ignored, in arriving at a studenfs scorc, and that they should therefore leave a blank where they are not reasonably surę. On a 4-choice test of 100 items. pureguesswork would give an averagc raw score of a bo ut 25 - an individual figurę might be rather higher or lower. but would be most unlikcly to be very much higher or lower. The correction to be applied must therefore bc such that a raw score of 25 or less would come out as a score of zero. The formula to be applied is:

. . ,    Total wrong answers

T otal righl answers —    —— ------—-—_:-

Number of choices — 1

In the case we are looking at. Number of ehoices is 4, so Number of choices minus 1 is 3. Thus if Total right answers is 25, which coutd be achieved by pure guesswork, then

The teaching of Engłish as a/i iniemaiionał language

_ Total wrong answers (75)

Total right answers (25)---------

works out at 25 minus 25, that is 0%.

We will look at two other possihiłities, one where the total of right answers is 55, and one where it is 97.

...    Total wrong answers (45)

Total right answers (55) ~ —    -----—----——

3

works out at 55 minus 15, that is, 40%.

w

o

f-

'S')

works out at 97 minus l, that is 96%.

On a True/Faise test, of course, Number of choices minus 1 is I, so the fuli total of wrong answers is subtracted from Total right answers.