New Indices for Refining Multiple Choice Questions

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td align="left"> </td><td align="center">True alternative</td><td align="center">Distractor 1</td><td align="center">Distractor 2</td><td align="center">Distractor 3</td><td align="center">Distractor 4</td><td align="center">Sum</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td align="left">Group answers</td><td align="center">25</td><td align="center">3</td><td align="center">12</td><td align="center">8</td><td align="center">2</td><td align="center">50</td></tr><tr><td align="left" rowspan="2">Proportional penalty</td><td align="center" rowspan="2">0</td><td align="center"><span style="width: 22.4971ptpx;"><svg height="11.9171pt" id="M98" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 22.4971 11.9171" width="22.4971pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td><td align="center"><span style="width: 42.0797ptpx;"><svg height="11.9171pt" id="M102" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 42.0797 11.9171" width="42.0797pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data 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id="g113-53"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td></tr><tr><td align="center">(8/25)</td><td align="center">(2/25)</td><td align="center">(3/25)</td><td align="center">(12/25)</td><td align="center">(1)</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Possible correction for guessing, proportional to the group answers.

Journal of Probability and Statistics

tab6

Table 6

Table 6: New Indices for Refining Multiple Choice Questions 