On scales and decision-making based on arithmetic mean

Abstract

ordinal scales, grading scales, equivalent scales, arithmetic mean or average, grade or mark conversion, decision-making,

Fuzziness and Bias in Decision-Making Processes Using an Arithmetic Mean Criterion

“…Given the ordinality characteristic of the educational grading scales, it is well known that arithmetic mean is not an appropriate statistic (Stevens, 1951(Stevens, , 1955Ieta, 2004). However, in our recent work (Ieta et al, 2004) we have demonstrated a theorem for the selection of equivalent ordinal scales. Comparison of arithmetic mean (ranks) originating on different ordinal scales is appropriate for such scales.…”

“…Some brief remarks will be made regarding a possible application of arithmetic mean ranks, as defined and studied so far (Ieta et al, 2004), to a candidate selection process. A two-stage candidate selection process will be considered.…”

“…It has been demonstrated (see B.2 in Ieta, 2004) that the rank of average of a concatenated set lies between the rank of averages of individual sets. This ordinal property does no longer hold if the (rank of) average is calculated on a scale S X non-equivalent to S i (and to S G ).…”

“…The school also uses S 12 for calculating averages that include sets of grades originating on S 100 . Analysis and observations related to scales S 4 , S 12 , and S 100 can be found in Ieta et al, (2004). The conversion of grades from S 12 (or S 4 ) to S 100 fails to make all the fine distinctions between subranks possible on S 100 .…”

“…Those having grades on both S 100 and S 4 , whose average is evaluated on S 12 (equivalent to S 4 ) where the average, as a letter grade, will usually be diminished relative to its l.g. equivalent on S 100 (Ieta et al, 2004). A student studying at School2 and having a mixture of grades from S 4 and S 100 will likely be at a disadvantage relative to his/her peers if the overall average of the grades is needed in certain types of selection processes.…”