Report of the Committee of the Statisticians, constituted by Kerala Public Service Commission for Standardisation of mark.
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The Kerala Public Service Commission entrusted the committeewith the task of standardisation of marks obtained by candidates in three examinations on three different dates with different question papers based on the same syllabus for the post of Reserve Conductor in KSRTC. The committee has the opinion that the standardization is required only if there is significant variation in difficulty levels in
between the different question papers.
One cannot determine which question is more difficult simply by reading the questions. It is not fair to decide a question is more difficult based on intuition or subjectivity of a person. The decision can be taken only based on empirical evidence.
So, the committee decided to compute the index of difficulty (difficulty level) of each question in each question paper. The index of difficulty (p) of a question is defined as the proportion of correct answers of that question (that is the number of correct answers of the question divided by the total number of candidates who wrote the examination with the respective question paper)( Nitko (1996), Crocker & Algina, 1986). The larger the proportion getting a question right, the easier the question. The higher the difficulty index indicates the easier the question and the lower the index of difficulty indicates the question is difficult. The index of difficulty will be always in between 0 and 1. The index of difficulty‘0’ means the maximum is the difficulty and‘1’ means the difficulty is minimum. There are two practices in the literature for the computation of difficulty indices. 1) based on the upper 27% and the lower 27% groups and 2) based on the total candidates. Several studies shown that, there will be no significant difference in difficulty indices based on two procedures when the size of the data is large. Here also the indices based on two procedures computed and confirmed that there is no significant variation between them. Here, we suggest the computation of difficulty indices based on total candidates
The questions in each question papers are to be divided into five strata as follows:
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